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Veda Skills Quantitative Aptitude Unit 6: Profit, Loss and Discount

Profit, Loss and Discount is Unit 6 of Veda Skills Quantitative Aptitude. This page has the complete chapter notes across 3 topics, 172 practice MCQs with answers and explanations, 13 important short and long questions and 40 flashcards, written for SSC, Bank, Railway and placement exams and free to read.
  • 3 topics
  • 172 MCQs
  • 10 short answers
  • 3 long answers
  • 40 flashcards
  • 3 games
  • ~150 min read
  • English

Checked before publishing: 23 automated checks, including a plagiarism check against the textbook's own words. How we check our content

Cost Price, Selling Price and Profit

Work out profit and loss and their percentages on the cost price, find the selling price or cost price from a percentage, and solve the exam favourites: same selling price with gain and loss, cost of x equals selling price of y, rates per dozen and overheads.

What you will be able to do

  • I can find profit, loss and their percentages from the cost price and selling price.
  • I can find the selling price from the cost price and a profit or loss percent, using a multiplier.
  • I can find the cost price when the selling price and the percent are given.
  • I can solve "same SP", "CP of x = SP of y" and overhead questions.

Key points

  • Cost price (CP) is what the seller pays; selling price (SP) is what the buyer pays.

  • Profit = SP − CP when SP > CP; loss = CP − SP when SP < CP.

  • Profit % and loss % are always calculated on the cost price.

  • SP = CP × (100 + profit %) ÷ 100 and SP = CP × (100 − loss %) ÷ 100.

  • CP = SP × 100 ÷ (100 + profit %): divide by the multiplier, do not subtract the percent from SP.

  • Two items sold at the same SP, one at x% gain and one at x% loss, always give an overall loss of x² ÷ 100 %.

  • If the CP of x articles = the SP of y articles, profit % = (x − y) ÷ y × 100.

  • Repair, transport and other overheads are added to the cost price.

Full explanation

Raju's phone-cover stall

A small Indian shopkeeper weighing vegetables on a balance, coins and notes on the counter.

Raju sells phone covers outside a metro station. He buys each cover from a wholesaler for ₹80 and sells it for ₹100. His friend asks, "Are you making 20% profit, or 25%?" Both numbers sound right. Only one is.

This topic gives you the rules that settle it, and the shortcuts exams expect.

CP, SP, profit and loss

A farmer selling a basket of mangoes to a trader.

  • Cost price (CP): what the seller paid, ₹80.
  • Selling price (SP): what the buyer pays, ₹100.
  • Profit $= SP - CP = ₹20$ when SP is bigger.
  • Loss $= CP - SP$ when SP is smaller.

Two boxes joined by an arrow: cost price ₹80 to selling price ₹100, with the arrow labelled profit ₹20, which is 25% of CP.

Profit percent is on CP

$$\text{Profit}% = \frac{\text{Profit}}{\text{CP}} \times 100 = \frac{20}{80} \times 100 = 25%$$

The 20% his friend had in mind is $20 \div 100$, profit on SP. Exams never mean that unless they say "profit on selling price".

Multipliers make it fast

Write every percent change as one multiplier. A 25% profit means $SP = CP \times \frac{5}{4}$; a 20% loss means $SP = CP \times \frac{4}{5}$.

Example: CP ₹840 at 15% profit: $840 \times 1.15 = ₹966$.

Table of multipliers: 10% profit 1.10 or 11/10; 20% profit 1.20 or 6/5; 25% profit 1.25 or 5/4; 12.5% loss 0.875 or 7/8; 20% loss 0.80 or 4/5.

Going back: finding the CP

To go from SP back to CP, divide by the multiplier.

Example: a fan is sold for ₹1,080 at 20% profit. $CP = 1080 \div \frac{6}{5} = 1080 \times \frac{5}{6} = ₹900$.

Trap: $1080 - 20%$ of $1080 = ₹864$ is wrong, because the 20% was on CP, not on SP.

A whole week at Raju's stall

The same rule works for every item: find the profit or loss, then divide by that item's CP.

Table of Raju's sales: phone cover CP 80 SP 100 gives +25%; charger 250 to 300 gives +20%; earphones 400 to 360 gives −10%; screen guard 40 to 60 gives +50%.

The same-SP trap

Two cycles are sold for ₹3,000 each, one at 20% gain and one at 20% loss. It feels like break-even. It is not: the loss is on a bigger CP.

Three cards: cycle 1 sold for ₹3,000 at 20% gain cost ₹2,500; cycle 2 sold for ₹3,000 at 20% loss cost ₹3,750; together CP ₹6,250 and SP ₹6,000, a loss of ₹250 or 4%.

CP of x equals SP of y

If the cost of 20 pens equals the selling price of 16 pens, the seller gains 4 pens on every 16 sold.

$$\text{Profit}% = \frac{x - y}{y} \times 100 = \frac{4}{16} \times 100 = 25%$$

If $y > x$, the same formula gives a loss.

Rates and overheads

Rates: bought 6 for ₹10, sold 4 for ₹10. Make the counts equal (LCM 12): CP of 12 $= ₹20$, SP of 12 $= ₹30$, profit 50%.

Overheads: a scooter bought for ₹18,000 with ₹2,000 repairs has CP ₹20,000. Sold at ₹23,000, profit $= 3000 \div 20000 = 15%$.

Back to Raju

Raju now tells his friend: 25% profit, because profit is measured on what he paid. He also knows that to make 40% on a ₹80 cover he must sell it for $80 \times 1.4 = ₹112$.

Exam summary: percent on CP, multiply to go forward, divide to go back, and add every expense to CP.

Mind map of profit and loss: profit percent on CP, finding SP and CP with multipliers, the same-SP trap, CP of x equals SP of y, and overheads.

Concepts and terms

Profit percent

Profit as a part of the cost price, times 100. Bought at ₹80, sold at ₹100: 20 ÷ 80 × 100 = 25%.

Multiplier

A percent change written as one number: 25% profit is × 1.25 = × 5/4, 20% loss is × 0.8 = × 4/5.

Effective cost price

Purchase price plus every expense before the sale, such as repair or transport.

Same SP rule

Gaining and losing the same percent on equal selling prices is never break-even; it is a loss of x²/100 %.

Did you know

Kirana shops often work on a profit of only 8 to 12% per item; they earn by selling many items every day.

Accountants call the point where total sales equal total costs the break-even point: no profit, no loss.

Memory tricks

Base of the percent — Profit sits on Cost — Profit and loss percents are on CP. (Discount, in the next topic, sits on MP.)

Going forward or back — CP to SP multiply, SP to CP divide — With a 25% profit, SP = CP × 5/4 and CP = SP × 4/5.

Practice MCQs with answers (64)

Q1 Ramesh buys a ceiling fan for ₹400 and sells it for ₹520. What is the profit percent? beginner
  • A 130%
  • B 35%
  • C 25%
  • D 30%
Show answer
Answer: 30%
Why:

Profit = ₹120; on CP: 120 ÷ 400 × 100 = 30%.

Q2 Sunita buys a bicycle for ₹2,400 and sells it for ₹2,760. What is the profit percent? beginner
  • A 15%
  • B 10%
  • C 115%
  • D 20%
Show answer
Answer: 15%
Why:

Profit = ₹360; on CP: 360 ÷ 2,400 × 100 = 15%.

Q3 A shopkeeper buys a watch for ₹1,600 and sells it for ₹2,000. What is the profit percent? beginner
  • A 30%
  • B 25%
  • C 20%
  • D 125%
Show answer
Answer: 25%
Why:

Profit = ₹400; on CP: 400 ÷ 1,600 × 100 = 25%.

Q4 Imran buys a school bag for ₹750 and sells it for ₹840. What is the profit percent? intermediate
  • A 112%
  • B 17%
  • C 12%
  • D 10 5/7%
Show answer
Answer: 12%
Why:

Profit = ₹90; on CP: 90 ÷ 750 × 100 = 12%.

Q5 A dealer buys a television for ₹12,500 and sells it for ₹15,000. What is the profit percent? intermediate
  • A 25%
  • B 16 2/3%
  • C 120%
  • D 20%
Show answer
Answer: 20%
Why:

Profit = ₹2,500; on CP: 2,500 ÷ 12,500 × 100 = 20%.

Q6 Lakshmi buys an air cooler for ₹4,500 and sells it for ₹5,040. What is the profit percent? intermediate
  • A 12%
  • B 112%
  • C 17%
  • D 10 5/7%
Show answer
Answer: 12%
Why:

Profit = ₹540; on CP: 540 ÷ 4,500 × 100 = 12%.

Q7 Harish buys a table for ₹900 and sells it for ₹765. What is the loss percent? beginner
  • A 20%
  • B 15%
  • C 10%
  • D 85%
Show answer
Answer: 15%
Why:

Loss = ₹135; on CP: 135 ÷ 900 × 100 = 15%.

Q8 A trader buys a mixer-grinder for ₹2,500 and sells it for ₹2,200. What is the loss percent? intermediate
  • A 17%
  • B 13 7/11%
  • C 12%
  • D 88%
Show answer
Answer: 12%
Why:

Loss = ₹300; on CP: 300 ÷ 2,500 × 100 = 12%.

Q9 Ramesh buys a desk lamp for ₹640 and sells it for ₹560. What is the loss percent? intermediate
  • A 17.5%
  • B 14 2/7%
  • C 87.5%
  • D 12.5%
Show answer
Answer: 12.5%
Why:

Loss = ₹80; on CP: 80 ÷ 640 × 100 = 12.5%.

Q10 Sunita buys a chair for ₹1,500 and sells it for ₹1,200. What is the loss percent? beginner
  • A 20%
  • B 25%
  • C 80%
  • D 15%
Show answer
Answer: 20%
Why:

Loss = ₹300; on CP: 300 ÷ 1,500 × 100 = 20%.

Q11 A shopkeeper buys a mobile phone for ₹4,800 and sells it for ₹4,200. What is the loss percent? intermediate
  • A 17.5%
  • B 12.5%
  • C 14 2/7%
  • D 87.5%
Show answer
Answer: 12.5%
Why:

Loss = ₹600; on CP: 600 ÷ 4,800 × 100 = 12.5%.

Q12 A saree costs a shop ₹840. At what price must it be sold to make a profit of 15%? beginner
  • A ₹126
  • B ₹714
  • C ₹966
  • D ₹855
Show answer
Answer: ₹966
Why:

SP = 840 × 1.15 = ₹966.

Q13 An electric iron costs a shop ₹1,250. At what price must it be sold to make a profit of 12%? beginner
  • A ₹1,100
  • B ₹1,262
  • C ₹150
  • D ₹1,400
Show answer
Answer: ₹1,400
Why:

SP = 1,250 × 1.12 = ₹1,400.

Q14 An air cooler costs a shop ₹3,600. At what price must it be sold to make a profit of 8%? intermediate
  • A ₹3,888
  • B ₹288
  • C ₹3,312
  • D ₹3,608
Show answer
Answer: ₹3,888
Why:

SP = 3,600 × 1.08 = ₹3,888.

Q15 A pair of shoes costs a shop ₹460. At what price must it be sold to make a profit of 25%? beginner
  • A ₹115
  • B ₹575
  • C ₹345
  • D ₹485
Show answer
Answer: ₹575
Why:

SP = 460 × 1.25 = ₹575.

Q16 A bicycle costs a shop ₹2,000. At what price must it be sold to make a profit of 17.5%? intermediate
  • A ₹350
  • B ₹1,650
  • C ₹2,350
  • D ₹2,017.5
Show answer
Answer: ₹2,350
Why:

SP = 2,000 × 1.175 = ₹2,350.

Q17 A table bought for ₹1,800 is damaged and has to be sold at a loss of 15%. What is its selling price? beginner
  • A ₹2,070
  • B ₹1,815
  • C ₹270
  • D ₹1,530
Show answer
Answer: ₹1,530
Why:

SP = 1,800 × 0.85 = ₹1,530.

Q18 A desk lamp bought for ₹750 is damaged and has to be sold at a loss of 8%. What is its selling price? intermediate
  • A ₹690
  • B ₹810
  • C ₹758
  • D ₹60
Show answer
Answer: ₹690
Why:

SP = 750 × 0.92 = ₹690.

Q19 A television bought for ₹2,400 is damaged and has to be sold at a loss of 12.5%. What is its selling price? intermediate
  • A ₹2,700
  • B ₹2,100
  • C ₹2,412.5
  • D ₹300
Show answer
Answer: ₹2,100
Why:

SP = 2,400 × 0.875 = ₹2,100.

Q20 By selling a ceiling fan for ₹690, a shopkeeper gains 15%. What was the cost price? intermediate
  • A ₹793.5
  • B ₹675
  • C ₹600
  • D ₹586.5
Show answer
Answer: ₹600
Why:

CP = SP ÷ 1.15 = 690 ÷ 1.15 = ₹600. Taking 15% of the SP is the trap.

Q21 By selling a watch for ₹1,080, Imran gains 20%. What was the cost price? beginner
  • A ₹1,296
  • B ₹1,060
  • C ₹864
  • D ₹900
Show answer
Answer: ₹900
Why:

CP = SP ÷ 1.2 = 1,080 ÷ 1.2 = ₹900. Taking 20% of the SP is the trap.

Q22 By selling a mobile phone for ₹2,760, a dealer gains 15%. What was the cost price? intermediate
  • A ₹2,400
  • B ₹3,174
  • C ₹2,745
  • D ₹2,346
Show answer
Answer: ₹2,400
Why:

CP = SP ÷ 1.15 = 2,760 ÷ 1.15 = ₹2,400. Taking 15% of the SP is the trap.

Q23 By selling a school bag for ₹1,365, Lakshmi gains 5%. What was the cost price? intermediate
  • A ₹1,296.75
  • B ₹1,300
  • C ₹1,433.25
  • D ₹1,360
Show answer
Answer: ₹1,300
Why:

CP = SP ÷ 1.05 = 1,365 ÷ 1.05 = ₹1,300. Taking 5% of the SP is the trap.

Q24 By selling a used scooter for ₹4,725, Harish gains 35%. What was the cost price? advanced
  • A ₹3,071.25
  • B ₹6,378.75
  • C ₹3,500
  • D ₹4,690
Show answer
Answer: ₹3,500
Why:

CP = SP ÷ 1.35 = 4,725 ÷ 1.35 = ₹3,500. Taking 35% of the SP is the trap.

Q25 By selling a chair for ₹612, a trader loses 15%. What was the cost price? intermediate
  • A ₹520.2
  • B ₹597
  • C ₹703.8
  • D ₹720
Show answer
Answer: ₹720
Why:

CP = SP ÷ 0.85 = 612 ÷ 0.85 = ₹720. Taking 15% of the SP is the trap.

Q26 By selling a mixer-grinder for ₹2,034, Ramesh loses 10%. What was the cost price? intermediate
  • A ₹2,260
  • B ₹2,237.4
  • C ₹1,830.6
  • D ₹2,024
Show answer
Answer: ₹2,260
Why:

CP = SP ÷ 0.9 = 2,034 ÷ 0.9 = ₹2,260. Taking 10% of the SP is the trap.

Q27 By selling an electric iron for ₹918, Sunita loses 15%. What was the cost price? advanced
  • A ₹780.3
  • B ₹1,080
  • C ₹903
  • D ₹1,055.7
Show answer
Answer: ₹1,080
Why:

CP = SP ÷ 0.85 = 918 ÷ 0.85 = ₹1,080. Taking 15% of the SP is the trap.

Q28 Selling a watch for ₹1,140 gives a loss of 5%. At what price should it be sold to get a gain of 5%? intermediate
  • A ₹1,197
  • B ₹1,254
  • C ₹1,260
  • D ₹1,150
Show answer
Answer: ₹1,260
Why:

CP = 1,140 ÷ 0.95 = ₹1,200; new SP = 1,200 × 1.05 = ₹1,260.

Q29 Selling a ceiling fan for ₹850 gives a loss of 15%. At what price should it be sold to get a gain of 10%? intermediate
  • A ₹935
  • B ₹1,062.5
  • C ₹875
  • D ₹1,100
Show answer
Answer: ₹1,100
Why:

CP = 850 ÷ 0.85 = ₹1,000; new SP = 1,000 × 1.1 = ₹1,100.

Q30 Selling a bicycle for ₹2,800 gives a gain of 12%. At what price should it be sold to get a gain of 15%? advanced
  • A ₹2,875
  • B ₹2,827
  • C ₹3,220
  • D ₹2,884
Show answer
Answer: ₹2,875
Why:

CP = 2,800 ÷ 1.12 = ₹2,500; new SP = 2,500 × 1.15 = ₹2,875.

Q31 Selling a desk lamp for ₹684 gives a loss of 10%. At what price should it be sold to get a gain of 15%? advanced
  • A ₹786.6
  • B ₹874
  • C ₹855
  • D ₹709
Show answer
Answer: ₹874
Why:

CP = 684 ÷ 0.9 = ₹760; new SP = 760 × 1.15 = ₹874.

Q32 A shopkeeper sells two bicycles for ₹3,000 each. On one he gains 20% and on the other he loses 20%. What is his overall loss percent? intermediate
  • A 10%
  • B 8%
  • C 4%
  • D 2%
Show answer
Answer: 4%
Why:

Same SP with ±20%: loss = 20² ÷ 100 = 4%. (CPs ₹2,500 and ₹3,750.)

Q33 A shopkeeper sells two televisions for ₹9,900 each. On one he gains 10% and on the other he loses 10%. What is his overall loss percent? intermediate
  • A 1.5%
  • B 5%
  • C 2%
  • D 1%
Show answer
Answer: 1%
Why:

Same SP with ±10%: loss = 10² ÷ 100 = 1%. (CPs ₹9,000 and ₹11,000.)

Q34 Two used scooters are sold for ₹3,000 each, one at 25% profit and the other at 25% loss. What is the overall profit or loss in rupees? advanced
  • A Loss of ₹400
  • B Loss of ₹800
  • C No profit, no loss
  • D Profit of ₹400
Show answer
Answer: Loss of ₹400
Why:

CPs: 3,000 ÷ 1.25 = ₹2,400 and 3,000 ÷ 0.75 = ₹4,000. Total CP ₹6,400, SP ₹6,000: loss ₹400.

Q35 The cost price of 20 pens is equal to the selling price of 16 pens. What is the profit percent? intermediate
  • A 4%
  • B 25%
  • C 11 1/9%
  • D 20%
Show answer
Answer: 25%
Why:

Take each pen to cost ₹1: CP of 16 = ₹16, SP of 16 = ₹20. Profit = 4 ÷ 16 × 100 = 25%.

Q36 The cost price of 12 notebooks is equal to the selling price of 10 notebooks. What is the profit percent? beginner
  • A 2%
  • B 9 1/11%
  • C 20%
  • D 16 2/3%
Show answer
Answer: 20%
Why:

Take each notebook to cost ₹1: CP of 10 = ₹10, SP of 10 = ₹12. Profit = 2 ÷ 10 × 100 = 20%.

Q37 The cost price of 11 mangoes is equal to the selling price of 10 mangoes. What is the profit percent? intermediate
  • A 9 1/11%
  • B 1%
  • C 15%
  • D 10%
Show answer
Answer: 10%
Why:

Take each mango to cost ₹1: CP of 10 = ₹10, SP of 10 = ₹11. Profit = 1 ÷ 10 × 100 = 10%.

Q38 The cost price of 16 toys is equal to the selling price of 20 toys. What is the loss percent? advanced
  • A 20%
  • B 4%
  • C 11 1/9%
  • D 25%
Show answer
Answer: 20%
Why:

Take each toy to cost ₹1: CP of 20 = ₹20, SP of 20 = ₹16. Loss = 4 ÷ 20 × 100 = 20%.

Q39 A vendor buys bananas at 6 for ₹10 and sells them at 4 for ₹10. What is the profit percent? intermediate
  • A 60%
  • B 50%
  • C 33 1/3%
  • D 10%
Show answer
Answer: 50%
Why:

On 12 bananas: CP = ₹20, SP = ₹30. Profit % = 10 ÷ 20 × 100 = 50%.

Q40 A vendor buys oranges at 3 for ₹20 and sells them at 2 for ₹15. What is the profit percent? advanced
  • A 11 1/9%
  • B 50%
  • C 12.5%
  • D 25%
Show answer
Answer: 12.5%
Why:

On 6 oranges: CP = ₹40, SP = ₹45. Profit % = 5 ÷ 40 × 100 = 12.5%.

Q41 A vendor buys toffees at 5 for ₹4 and sells them at 4 for ₹5. What is the profit percent? advanced
  • A 66.25%
  • B 36%
  • C 25%
  • D 56.25%
Show answer
Answer: 56.25%
Why:

On 20 toffees: CP = ₹16, SP = ₹25. Profit % = 9 ÷ 16 × 100 = 56.25%.

Q42 A vendor buys lemons at 4 for ₹3 and sells them at 5 for ₹3. What is the loss percent? intermediate
  • A 20%
  • B 25%
  • C 10%
  • D 30%
Show answer
Answer: 20%
Why:

On 20 lemons: CP = ₹15, SP = ₹12. Loss % = 3 ÷ 15 × 100 = 20%.

Q43 If an article is sold at 15% profit instead of 10% profit, the seller gets ₹60 more. What is its cost price? intermediate
  • A ₹400
  • B ₹1,200
  • C ₹240
  • D ₹200
Show answer
Answer: ₹1,200
Why:

The two SPs differ by 5% of CP, and that is ₹60. CP = 60 × 100 ÷ 5 = ₹1,200.

Q44 If an article is sold at 12% profit instead of 8% profit, the seller gets ₹36 more. What is its cost price? intermediate
  • A ₹180
  • B ₹144
  • C ₹900
  • D ₹300
Show answer
Answer: ₹900
Why:

The two SPs differ by 4% of CP, and that is ₹36. CP = 36 × 100 ÷ 4 = ₹900.

Q45 A man sold a watch at a loss of 10%. Had he sold it for ₹90 more, he would have gained 5%. Find the cost price. advanced
  • A ₹450
  • B ₹700
  • C ₹1,800
  • D ₹600
Show answer
Answer: ₹600
Why:

The two SPs differ by 15% of CP, and that is ₹90. CP = 90 × 100 ÷ 15 = ₹600.

Q46 A man buys a second-hand phone for ₹4,500 and spends ₹500 on a new screen. He sells it for ₹5,500. What is his profit percent? beginner
  • A 10%
  • B 11 1/9%
  • C 9 1/11%
  • D 22 2/9%
Show answer
Answer: 10%
Why:

Effective CP = 4,500 + 500 = ₹5,000; profit = ₹500; 500 ÷ 5,000 × 100 = 10%.

Q47 A man buys an old scooter for ₹18,000 and spends ₹2,000 on repairs. He sells it for ₹23,000. What is his profit percent? intermediate
  • A 16 2/3%
  • B 15%
  • C 20%
  • D 27 7/9%
Show answer
Answer: 15%
Why:

Effective CP = 18,000 + 2,000 = ₹20,000; profit = ₹3,000; 3,000 ÷ 20,000 × 100 = 15%.

Q48 A man buys a load of potatoes for ₹700 and spends ₹100 on transport. He sells it for ₹1,000. What is his profit percent? intermediate
  • A 28 4/7%
  • B 20%
  • C 25%
  • D 42 6/7%
Show answer
Answer: 25%
Why:

Effective CP = 700 + 100 = ₹800; profit = ₹200; 200 ÷ 800 × 100 = 25%.

Q49 A trader calculates his profit as 20% of the selling price. What is his real profit percent on the cost price? advanced
  • A 20%
  • B 16 2/3%
  • C 40%
  • D 25%
Show answer
Answer: 25%
Why:

Let SP = 100: profit = 20, CP = 80. Profit on CP = 20 ÷ 80 × 100 = 25%.

Q50 A trader calculates his profit as 37.5% of the selling price. What is his real profit percent on the cost price? advanced
  • A 60%
  • B 75%
  • C 37.5%
  • D 27 3/11%
Show answer
Answer: 60%
Why:

Let SP = 100: profit = 37.5, CP = 62.5. Profit on CP = 37.5 ÷ 62.5 × 100 = 60%.

Q51 The table lists four items. Which one gives the highest profit percent? ![Table: pen CP 40 SP 50; bag CP 600 SP 720; watch CP 1,200 SP 1,560; lamp CP 800 SP 960.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-items-table.svg) intermediate
  • A Pen
  • B Watch
  • C Bag
  • D Lamp
Show answer
Answer: Watch
Why:

Pen 10/40 = 25%, bag 120/600 = 20%, watch 360/1200 = 30%, lamp 160/800 = 20%. The watch is highest even though the pen looks cheap and easy.

Q52 The arrow shows a 25% profit on the cost price. What is the cost price? ![Cost price unknown, an arrow labelled +25% profit, selling price ₹750.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-chain-cp.svg) beginner
  • A ₹725
  • B ₹625
  • C ₹600
  • D ₹562.50
Show answer
Answer: ₹600
Why:

CP = 750 ÷ 5/4 = 750 × 4/5 = ₹600. (750 − 25% of 750 = ₹562.50 is the trap.)

Q53 Read the chain. What is the selling price? ![Cost price ₹1,500, an arrow labelled −12% loss, selling price unknown.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-chain-loss.svg) beginner
  • A ₹1,488
  • B ₹1,339.29
  • C ₹1,680
  • D ₹1,320
Show answer
Answer: ₹1,320
Why:

SP = 1500 × 0.88 = ₹1,320.

Q54 The chart shows the cost and selling prices of two items. What is the overall profit percent on both items together? ![Bar chart: item A cost ₹400 and sold for ₹500; item B cost ₹600 and sold for ₹660.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-cp-sp-bars.svg) advanced
  • A 16%
  • B 15%
  • C 13.79%
  • D 17.5%
Show answer
Answer: 16%
Why:

Total CP = ₹1,000, total SP = ₹1,160, profit = 16%. (Averaging 25% and 10% gives 17.5%, the wrong way.)

Q55 Profit percent is calculated on beginner
  • A the selling price
  • B the cost price
  • C the marked price
  • D the profit itself
Show answer
Answer: the cost price
Why:

Unless a question says otherwise, profit and loss percents are on CP.

Q56 An article is sold at 20% loss. The selling price is what fraction of the cost price? beginner
  • A 5/4
  • B 1/5
  • C 4/5
  • D 6/5
Show answer
Answer: 4/5
Why:

20% loss leaves 80% = 4/5 of CP.

Q57 If the selling price is doubled, the profit triples. What is the profit percent? advanced
  • A 200%
  • B 33 1/3%
  • C 50%
  • D 100%
Show answer
Answer: 100%
Why:

2S − C = 3(S − C) gives S = 2C, so profit = C, which is 100%.

Q58 A seller has neither profit nor loss when beginner
  • A SP equals CP
  • B SP equals twice CP
  • C SP is 100% of profit
  • D CP is zero
Show answer
Answer: SP equals CP
Why:

Profit = SP − CP = 0 only when the two prices are equal.

Q59 Which multiplier gives the SP for a 37.5% profit? intermediate
  • A 5/8
  • B 11/8
  • C 3/8
  • D 8/11
Show answer
Answer: 11/8
Why:

100% + 37.5% = 137.5% = 11/8.

Q60 A man buys an item and sells it at a 10% loss. If he had bought it 10% cheaper and sold it at the same price, his profit percent would be intermediate
  • A 10%
  • B 1%
  • C 0%
  • D 11 1/9%
Show answer
Answer: 0%
Why:

Let CP = 100: SP = 90. New CP = 90 and SP = 90, so no profit.

Q61 Assertion (A): Buying at ₹80 and selling at ₹100 gives a 25% profit. Reason (R): Profit percent is measured on the cost price. beginner
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: Both A and R are true, and R is the correct explanation of A
Why:

Both true, and R explains A: 20 ÷ 80 = 25%.

Q62 Assertion (A): Selling two items at the same price with 15% gain on one and 15% loss on the other is break-even. Reason (R): The item sold at a loss had a larger cost price. intermediate
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: A is false but R is true
Why:

A is false: there is a loss of 15² ÷ 100 = 2.25%. R is true and is the reason the loss is bigger.

Q63 An article costs ₹500. Which of these statements is/are true? 1. Selling it for ₹600 gives a 20% profit. 2. Selling it for ₹400 gives a 25% loss. beginner
  • A 1 only
  • B 2 only
  • C Both 1 and 2
  • D Neither 1 nor 2
Show answer
Answer: 1 only
Why:

100 ÷ 500 = 20%, so 1 is true. 100 ÷ 500 = 20% loss, not 25%, so 2 is false.

Q64 Which of these statements is/are true? 1. If the CP of 10 items equals the SP of 8 items, the profit is 25%. 2. A profit of 20% on SP is a profit of 25% on CP. advanced
  • A 1 only
  • B 2 only
  • C Both 1 and 2
  • D Neither 1 nor 2
Show answer
Answer: Both 1 and 2
Why:

1: (10 − 8) ÷ 8 = 25%. 2: SP 100, profit 20, CP 80, so 20 ÷ 80 = 25%. Both true.

Important short questions (4)

A cycle bought for ₹2,400 is sold for ₹2,760. Find the profit percent.

Profit = ₹360; 360 ÷ 2400 × 100 = 15%.

By selling a fan for ₹1,380, a dealer gains 15%. Find the CP.

CP = 1380 ÷ 1.15 = ₹1,200.

If the CP of 15 bulbs equals the SP of 12 bulbs, find the profit percent.

(15 − 12) ÷ 12 × 100 = 25%.

A watch sold at 8% loss would fetch ₹120 more at 4% gain. Find its CP.

8% + 4% = 12% of CP = ₹120, so CP = ₹1,000.

Long answer questions (1)

A shopkeeper buys 50 kg of rice at ₹40 per kg and pays ₹100 for transport. 5 kg is spoilt. At what price per kg must he sell the rest to gain 20% on his total outlay?

Outlay = 50 × 40 + 100 = ₹2,100. Needed SP = 2100 × 1.2 = ₹2,520. Rice left = 45 kg, so the price = 2520 ÷ 45 = ₹56 per kg.

Flashcards (14)

Profit %?
Profit ÷ CP × 100
Loss %?
Loss ÷ CP × 100
SP at p% profit?
CP × (100 + p) ÷ 100
CP from SP at p% profit?
SP × 100 ÷ (100 + p)
Multiplier for 25% profit?
5/4
Multiplier for 12.5% loss?
7/8
Same SP, x% gain and x% loss?
Loss of x² ÷ 100 %
CP of x = SP of y: profit %?
(x − y) ÷ y × 100
Where do repair costs go?
Into the cost price
Bought at ₹50, sold at ₹40: loss %?
20%
Profit 20% on SP is what on CP?
25%
5% more profit means ₹40 more: CP?
₹800
Buy 4 for ₹3, sell 3 for ₹4: profit?
77 7/9%
SP = CP means?
No profit, no loss

Play this topic

  • Profit or trap?

Marked Price and Discounts

Read a price tag: find the selling price after a discount, the discount percent, and the marked price. Then link cost, marked and selling prices: the profit after a mark-up and a discount, how much to mark to earn a target profit, and "buy x get y free" offers.

What you will be able to do

  • I can find the selling price, discount percent or marked price when the other two are given.
  • I can find the profit percent after a mark-up and a discount.
  • I can find how much above cost a seller must mark to earn a profit after a discount.
  • I can turn "buy x get y free" into a discount percent.

Key points

  • Marked price (MP) or list price is the price printed on the tag. MRP is the highest price allowed by law.

  • Discount is always calculated on the marked price: SP = MP − discount.

  • SP = MP × (100 − d) ÷ 100 and MP = SP × 100 ÷ (100 − d).

  • Discount % = (MP − SP) ÷ MP × 100. Profit % is still on CP.

  • If goods are marked m% above CP and sold at d% discount, SP = CP × (1 + m/100)(1 − d/100).

  • To earn p% profit after d% discount, mark MP = CP × (100 + p) ÷ (100 − d).

  • "Buy x get y free" is a discount of y ÷ (x + y) × 100 %.

Full explanation

Meera's Diwali sale

A shirt on a hanger with a blank sale tag.

Meera owns a saree shop in Lucknow. A silk saree costs her ₹1,250. She prints ₹2,000 on its tag and, for Diwali, announces 20% off. A customer pays ₹1,600 and walks away happy. Meera is happy too.

How can both win? Because there are three prices here, not two.

Marked price and discount

The marked price (MP) is printed on the tag. The discount is a cut on that MP, and what the customer pays is the SP.

$$SP = MP \times \frac{100 - d}{100} = 2000 \times 0.8 = ₹1600$$

A price tag for a silk saree: MRP ₹2,000 struck through, 20% off, pay ₹1,600.

Discount percent and finding the MP

Discount % $= \frac{MP - SP}{MP} \times 100$. A ₹2,400 kurta sold for ₹1,920 has a discount of $480 \div 2400 = 20%$.

Finding MP: a bag sold for ₹1,360 after 15% off had $MP = 1360 \div 0.85 = ₹1600$. Divide, do not add 15%.

Three prices in a row

The seller marks up on CP, then gives a discount on MP. Multiply the two multipliers to get from CP to SP.

Chain of three boxes: cost price ₹1,250, marked 60% higher at ₹2,000, then 20% off to a selling price of ₹1,600; profit ₹350, which is 28% of CP.

Profit after a mark-up and a discount

$$\text{Profit}% = \left[\left(1 + \frac{m}{100}\right)\left(1 - \frac{d}{100}\right) - 1\right] \times 100$$

Equal mark-up and discount always lose: 20% up and 20% off gives $1.2 \times 0.8 = 0.96$, a 4% loss.

Table: marked 50% up with 20% off gives 1.2, 20% profit; 40% up with 10% off gives 1.26, 26% profit; 25% up with 20% off gives 1, no profit; 20% up with 25% off gives 0.9, 10% loss.

How much should the seller mark?

To keep a profit of $p%$ after a discount of $d%$:

$$MP = CP \times \frac{100 + p}{100 - d}$$

Example: CP ₹800, wanted profit 20%, discount 20%: $MP = 800 \times \frac{120}{80} = ₹1200$. That is 50% above cost.

"Buy x, get y free"

You take $x + y$ items and pay for $x$. The discount is $\frac{y}{x + y} \times 100%$.

Two tags: buy 3 get 1 free, pay for 3 and take 4, equals a 25% discount; buy 4 get 1 free, pay for 4 and take 5, equals a 20% discount.

Back to Meera

Meera's saree: CP ₹1,250, MP ₹2,000, SP ₹1,600. The customer saved ₹400, which is 20% of MP. Meera earned ₹350, which is 28% of CP. Both percents are right, on different bases.

Exam summary: discount on MP, profit on CP, multiply the multipliers, and mark $CP \times \frac{100 + p}{100 - d}$.

Mind map of discounts: SP from MP, discount percent, mark-up, profit after mark-up and discount, buy x get y free, and what price to mark.

Concepts and terms

Discount

A reduction on the marked price. A ₹2,000 saree at 20% off sells for ₹1,600.

Mark-up

How far the marked price is above the cost price, as a percent of CP.

Three prices

CP (paid by the seller) → MP (on the tag) → SP (paid by the buyer). Mark-up is on CP, discount is on MP.

Free-item offer

Paying for 3 and taking 4 means you pay 3/4 of the marked value: a 25% discount.

Did you know

In India, it is illegal to sell a packaged product above the MRP printed on it, but shops may sell below it.

Many festival sales raise the marked price first, so a "50% off" tag may be a much smaller real discount.

Memory tricks

Bases — Profit on Cost, Discount on Mark — Two different bases. Mixing them up is the most common error in this topic.

What to mark — Profit up, discount down — MP ÷ CP = (100 + profit) ÷ (100 − discount): profit goes on top, discount at the bottom.

Practice MCQs with answers (53)

Q1 The marked price of a pair of shoes is ₹1,200. The shop gives a discount of 15%. How much does a customer pay? beginner
  • A ₹1,020
  • B ₹1,185
  • C ₹1,380
  • D ₹180
Show answer
Answer: ₹1,020
Why:

SP = 1,200 × 0.85 = ₹1,020. Discount = ₹180.

Q2 The marked price of a mixer-grinder is ₹2,500. The shop gives a discount of 12%. How much does a customer pay? beginner
  • A ₹300
  • B ₹2,200
  • C ₹2,488
  • D ₹2,800
Show answer
Answer: ₹2,200
Why:

SP = 2,500 × 0.88 = ₹2,200. Discount = ₹300.

Q3 The marked price of a school bag is ₹850. The shop gives a discount of 20%. How much does a customer pay? beginner
  • A ₹1,020
  • B ₹170
  • C ₹680
  • D ₹830
Show answer
Answer: ₹680
Why:

SP = 850 × 0.8 = ₹680. Discount = ₹170.

Q4 The marked price of an air cooler is ₹3,600. The shop gives a discount of 35%. How much does a customer pay? intermediate
  • A ₹4,860
  • B ₹1,260
  • C ₹3,565
  • D ₹2,340
Show answer
Answer: ₹2,340
Why:

SP = 3,600 × 0.65 = ₹2,340. Discount = ₹1,260.

Q5 The marked price of a desk lamp is ₹760. The shop gives a discount of 25%. How much does a customer pay? beginner
  • A ₹570
  • B ₹190
  • C ₹608
  • D ₹735
Show answer
Answer: ₹570
Why:

SP = 760 × 0.75 = ₹570. Discount = ₹190.

Q6 The marked price of a television is ₹15,000. The shop gives a discount of 12.5%. How much does a customer pay? intermediate
  • A ₹16,875
  • B ₹13,125
  • C ₹1,875
  • D ₹14,987.5
Show answer
Answer: ₹13,125
Why:

SP = 15,000 × 0.875 = ₹13,125. Discount = ₹1,875.

Q7 A watch marked at ₹1,500 is sold for ₹1,275. What is the rate of discount? beginner
  • A 20%
  • B 10%
  • C 15%
  • D 85%
Show answer
Answer: 15%
Why:

Discount = ₹225; on MP: 225 ÷ 1,500 × 100 = 15%.

Q8 A saree marked at ₹2,400 is sold for ₹1,800. What is the rate of discount? beginner
  • A 33 1/3%
  • B 75%
  • C 30%
  • D 25%
Show answer
Answer: 25%
Why:

Discount = ₹600; on MP: 600 ÷ 2,400 × 100 = 25%.

Q9 An electric iron marked at ₹650 is sold for ₹546. What is the rate of discount? intermediate
  • A 16%
  • B 21%
  • C 11%
  • D 84%
Show answer
Answer: 16%
Why:

Discount = ₹104; on MP: 104 ÷ 650 × 100 = 16%.

Q10 A bicycle marked at ₹8,000 is sold for ₹7,000. What is the rate of discount? intermediate
  • A 14 2/7%
  • B 12.5%
  • C 87.5%
  • D 17.5%
Show answer
Answer: 12.5%
Why:

Discount = ₹1,000; on MP: 1,000 ÷ 8,000 × 100 = 12.5%.

Q11 A chair marked at ₹320 is sold for ₹256. What is the rate of discount? beginner
  • A 80%
  • B 15%
  • C 20%
  • D 25%
Show answer
Answer: 20%
Why:

Discount = ₹64; on MP: 64 ÷ 320 × 100 = 20%.

Q12 After a discount of 15%, a school bag is sold for ₹1,360. What was its marked price? intermediate
  • A ₹1,375
  • B ₹1,700
  • C ₹1,564
  • D ₹1,600
Show answer
Answer: ₹1,600
Why:

MP = SP ÷ 0.85 = 1,360 ÷ 0.85 = ₹1,600.

Q13 After a discount of 10%, a mobile phone is sold for ₹2,250. What was its marked price? intermediate
  • A ₹2,500
  • B ₹2,600
  • C ₹2,475
  • D ₹2,260
Show answer
Answer: ₹2,500
Why:

MP = SP ÷ 0.9 = 2,250 ÷ 0.9 = ₹2,500.

Q14 After a discount of 15%, a ceiling fan is sold for ₹918. What was its marked price? intermediate
  • A ₹1,055.7
  • B ₹1,080
  • C ₹933
  • D ₹1,180
Show answer
Answer: ₹1,080
Why:

MP = SP ÷ 0.85 = 918 ÷ 0.85 = ₹1,080.

Q15 After a discount of 30%, a table is sold for ₹4,200. What was its marked price? advanced
  • A ₹4,230
  • B ₹6,100
  • C ₹6,000
  • D ₹5,460
Show answer
Answer: ₹6,000
Why:

MP = SP ÷ 0.7 = 4,200 ÷ 0.7 = ₹6,000.

Q16 An article costs Ramesh ₹800. What price should be marked on it so that after a discount of 20% there is still a profit of 20%? intermediate
  • A ₹960
  • B ₹1,152
  • C ₹1,120
  • D ₹1,200
Show answer
Answer: ₹1,200
Why:

MP = 800 × 120 ÷ 80 = ₹1,200. Check: ₹1,200 × 0.8 = ₹960 = 800 + 20%.

Q17 An article costs Sunita ₹1,500. What price should be marked on it so that after a discount of 5% there is still a profit of 14%? intermediate
  • A ₹1,800
  • B ₹1,710
  • C ₹1,795.5
  • D ₹1,785
Show answer
Answer: ₹1,800
Why:

MP = 1,500 × 114 ÷ 95 = ₹1,800. Check: ₹1,800 × 0.95 = ₹1,710 = 1,500 + 14%.

Q18 An article costs a shopkeeper ₹2,400. What price should be marked on it so that after a discount of 20% there is still a profit of 25%? advanced
  • A ₹3,600
  • B ₹3,750
  • C ₹3,480
  • D ₹3,000
Show answer
Answer: ₹3,750
Why:

MP = 2,400 × 125 ÷ 80 = ₹3,750. Check: ₹3,750 × 0.8 = ₹3,000 = 2,400 + 25%.

Q19 An article costs Imran ₹600. What price should be marked on it so that after a discount of 10% there is still a profit of 8%? intermediate
  • A ₹648
  • B ₹712.8
  • C ₹720
  • D ₹708
Show answer
Answer: ₹720
Why:

MP = 600 × 108 ÷ 90 = ₹720. Check: ₹720 × 0.9 = ₹648 = 600 + 8%.

Q20 An article costs a dealer ₹1,800. What price should be marked on it so that after a discount of 10% there is still a profit of 17%? advanced
  • A ₹2,316.6
  • B ₹2,286
  • C ₹2,106
  • D ₹2,340
Show answer
Answer: ₹2,340
Why:

MP = 1,800 × 117 ÷ 90 = ₹2,340. Check: ₹2,340 × 0.9 = ₹2,106 = 1,800 + 17%.

Q21 A shopkeeper wants a profit of 20% even after giving a discount of 20%. By what percent above the cost price should he mark his goods? intermediate
  • A 50%
  • B 55%
  • C 40%
  • D 44%
Show answer
Answer: 50%
Why:

MP ÷ CP = 120 ÷ 80 = 1.5, so mark 50% above cost (not 20% + 20%).

Q22 A shopkeeper wants a profit of 10% even after giving a discount of 12%. By what percent above the cost price should he mark his goods? advanced
  • A 23.2%
  • B 25%
  • C 20%
  • D 22%
Show answer
Answer: 25%
Why:

MP ÷ CP = 110 ÷ 88 = 1.25, so mark 25% above cost (not 10% + 12%).

Q23 A shopkeeper wants a profit of 17% even after giving a discount of 10%. By what percent above the cost price should he mark his goods? advanced
  • A 28.7%
  • B 6 4/11%
  • C 30%
  • D 27%
Show answer
Answer: 30%
Why:

MP ÷ CP = 117 ÷ 90 = 1.3, so mark 30% above cost (not 17% + 10%).

Q24 A shopkeeper wants a profit of 8% even after giving a discount of 10%. By what percent above the cost price should he mark his goods? intermediate
  • A 18.8%
  • B 16%
  • C 18%
  • D 20%
Show answer
Answer: 20%
Why:

MP ÷ CP = 108 ÷ 90 = 1.2, so mark 20% above cost (not 8% + 10%).

Q25 Ramesh marks goods 40% above the cost price and then allows a discount of 20%. What is the profit percent? beginner
  • A 12%
  • B 28%
  • C 8%
  • D 20%
Show answer
Answer: 12%
Why:

1.4 × 0.8 = 1.12, so profit = 12%.

Q26 Sunita marks goods 50% above the cost price and then allows a discount of 20%. What is the profit percent? beginner
  • A 40%
  • B 20%
  • C 10%
  • D 30%
Show answer
Answer: 20%
Why:

1.5 × 0.8 = 1.2, so profit = 20%.

Q27 A shopkeeper marks goods 25% above the cost price and then allows a discount of 10%. What is the profit percent? intermediate
  • A 2.5%
  • B 15%
  • C 12.5%
  • D 17.5%
Show answer
Answer: 12.5%
Why:

1.25 × 0.9 = 1.125, so profit = 12.5%.

Q28 Imran marks goods 30% above the cost price and then allows a discount of 30%. What is the loss percent? intermediate
  • A 13%
  • B 9.5%
  • C 10%
  • D 9%
Show answer
Answer: 9%
Why:

1.3 × 0.7 = 0.91, so loss = 9%.

Q29 A dealer marks goods 80% above the cost price and then allows a discount of 25%. What is the profit percent? intermediate
  • A 35%
  • B 20%
  • C 55%
  • D 75%
Show answer
Answer: 35%
Why:

1.8 × 0.75 = 1.35, so profit = 35%.

Q30 Lakshmi marks goods 20% above the cost price and then allows a discount of 25%. What is the loss percent? advanced
  • A 14%
  • B 10%
  • C 5%
  • D 6%
Show answer
Answer: 10%
Why:

1.2 × 0.75 = 0.9, so loss = 10%.

Q31 A store offers "Buy 3 soaps, get 1 free". What is the effective discount percent? beginner
  • A 75%
  • B 33 1/3%
  • C 25%
  • D 20%
Show answer
Answer: 25%
Why:

You take 4 and pay for 3: discount = 1 ÷ 4 × 100 = 25%.

Q32 A store offers "Buy 4 shirts, get 1 free". What is the effective discount percent? beginner
  • A 16 2/3%
  • B 80%
  • C 25%
  • D 20%
Show answer
Answer: 20%
Why:

You take 5 and pay for 4: discount = 1 ÷ 5 × 100 = 20%.

Q33 A store offers "Buy 3 pens, get 2 free". What is the effective discount percent? intermediate
  • A 40%
  • B 66 2/3%
  • C 33 1/3%
  • D 60%
Show answer
Answer: 40%
Why:

You take 5 and pay for 3: discount = 2 ÷ 5 × 100 = 40%.

Q34 A store offers "Buy 7 biscuit packets, get 1 free". What is the effective discount percent? intermediate
  • A 11 1/9%
  • B 12.5%
  • C 87.5%
  • D 14 2/7%
Show answer
Answer: 12.5%
Why:

You take 8 and pay for 7: discount = 1 ÷ 8 × 100 = 12.5%.

Q35 A store offers "Buy 5 juice bottles, get 3 free". What is the effective discount percent? advanced
  • A 60%
  • B 33 1/3%
  • C 37.5%
  • D 62.5%
Show answer
Answer: 37.5%
Why:

You take 8 and pay for 5: discount = 3 ÷ 8 × 100 = 37.5%.

Q36 An article marked at ₹1,500 is sold at a discount of 20%, and the seller still gains 20%. What is the cost price? intermediate
  • A ₹960
  • B ₹1,250
  • C ₹900
  • D ₹1,000
Show answer
Answer: ₹1,000
Why:

SP = 1,500 × 0.8 = ₹1,200; CP = SP ÷ 1.2 = ₹1,000.

Q37 An article marked at ₹2,400 is sold at a discount of 10%, and the seller still gains 20%. What is the cost price? intermediate
  • A ₹1,800
  • B ₹1,680
  • C ₹1,728
  • D ₹2,000
Show answer
Answer: ₹1,800
Why:

SP = 2,400 × 0.9 = ₹2,160; CP = SP ÷ 1.2 = ₹1,800.

Q38 An article marked at ₹880 is sold at a discount of 25%, and the seller still gains 10%. What is the cost price? advanced
  • A ₹572
  • B ₹600
  • C ₹594
  • D ₹800
Show answer
Answer: ₹600
Why:

SP = 880 × 0.75 = ₹660; CP = SP ÷ 1.1 = ₹600.

Q39 When a trader gives a discount of 10%, he makes a profit of 17%. What would his profit percent be if he gave a discount of 20% instead? advanced
  • A 15 1/9%
  • B 4.5%
  • C 4%
  • D 7%
Show answer
Answer: 4%
Why:

MP ÷ CP = 117 ÷ 90 = 1.3. New SP ÷ CP = 1.3 × 0.8 = 1.04, so profit = 4%.

Q40 When a trader gives a discount of 20%, he makes a profit of 20%. What would his profit percent be if he gave a discount of 10% instead? advanced
  • A 22.5%
  • B 30%
  • C 38%
  • D 35%
Show answer
Answer: 35%
Why:

MP ÷ CP = 120 ÷ 80 = 1.5. New SP ÷ CP = 1.5 × 0.9 = 1.35, so profit = 35%.

Q41 When a trader gives a discount of 25%, he makes a profit of 5%. What would his profit percent be if he gave a discount of 15% instead? advanced
  • A 19%
  • B 15%
  • C 20%
  • D 22%
Show answer
Answer: 19%
Why:

MP ÷ CP = 105 ÷ 75 = 1.4. New SP ÷ CP = 1.4 × 0.85 = 1.19, so profit = 19%.

Q42 Read the price tag. How much does the customer pay for the kurta? ![Price tag: cotton kurta, MRP ₹1,800, 25% off.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-tag-kurta.svg) beginner
  • A ₹450
  • B ₹1,350
  • C ₹1,440
  • D ₹1,775
Show answer
Answer: ₹1,350
Why:

1800 × 0.75 = ₹1,350 (₹450 is the discount, not the price).

Q43 The tag shows the old price struck out and the sale price. What discount percent is being given? ![Price tag: pressure cooker, MRP ₹2,400 struck through, sale price ₹1,920.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-tag-sale.svg) beginner
  • A 80%
  • B 25%
  • C 20%
  • D 48%
Show answer
Answer: 20%
Why:

Discount ₹480 on MP ₹2,400 = 20%. (480 ÷ 1920 = 25% uses the wrong base.)

Q44 Amit takes 4 shirts under this offer. What does he effectively pay per shirt? ![Tag: any shirt ₹450, buy 3 get 1 free.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-tag-bogo.svg) intermediate
  • A ₹300
  • B ₹450
  • C ₹360
  • D ₹337.50
Show answer
Answer: ₹337.50
Why:

He pays 3 × 450 = ₹1,350 for 4 shirts, so ₹337.50 each, a 25% discount.

Q45 Follow the chain from cost price to selling price. What is the profit percent? ![Cost price ₹1,500, marked 40% higher, then 10% off on the marked price; marked and selling prices are hidden.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-chain-mark.svg) intermediate
  • A 26%
  • B 30%
  • C 36%
  • D 24%
Show answer
Answer: 26%
Why:

MP = ₹2,100, SP = 2100 × 0.9 = ₹1,890; profit ₹390 on ₹1,500 = 26%.

Q46 Discount is always calculated on beginner
  • A the selling price
  • B the marked price
  • C the profit
  • D the cost price
Show answer
Answer: the marked price
Why:

Discount is a reduction on the tag price, the MP.

Q47 A shopkeeper marks goods 20% above cost and gives a 20% discount. He intermediate
  • A neither gains nor loses
  • B gains 4%
  • C loses 4%
  • D loses 20%
Show answer
Answer: loses 4%
Why:

1.2 × 0.8 = 0.96, a 4% loss.

Q48 If the SP of an item equals its MP, the discount is beginner
  • A equal to the profit
  • B 100%
  • C 50%
  • D 0%
Show answer
Answer: 0%
Why:

No reduction from the tag means no discount: 0%.

Q49 Which offer gives the largest discount? intermediate
  • A Buy 2 get 1 free
  • B Buy 3 get 1 free
  • C 30% off
  • D Buy 4 get 1 free
Show answer
Answer: Buy 2 get 1 free
Why:

Buy 2 get 1 is 1 ÷ 3 = 33 1/3%, more than the flat 30%; buy 3 get 1 is 25%; buy 4 get 1 is 20%.

Q50 A seller wants the same profit percent as the discount percent he gives. Compared with the cost price, the marked price must be advanced
  • A exactly double that percent above CP
  • B more than double that percent above CP
  • C exactly that percent above CP
  • D equal to CP
Show answer
Answer: more than double that percent above CP
Why:

MP/CP = (1 + x)/(1 − x), which is above 1 + 2x. For x = 10%: 110/90 ≈ 1.222, so 22.2% above, more than 20%.

Q51 Assertion (A): A 20% discount on a ₹2,000 tag and a 28% profit can happen on the same sale. Reason (R): Discount is on the marked price but profit is on the cost price. intermediate
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: Both A and R are true, and R is the correct explanation of A
Why:

With CP ₹1,250: SP ₹1,600 is 20% below MP and 28% above CP. R explains A.

Q52 Assertion (A): "Buy 3 get 1 free" is a 25% discount. Reason (R): The free item is one-third of the items paid for. advanced
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: Both A and R are true, but R is not the correct explanation of A
Why:

Both statements are true, but the discount is 1 out of 4 taken (25%), not 1 out of 3 paid. R does not explain A.

Q53 An item is marked ₹1,000 and sold for ₹850. Which of these statements is/are true? 1. The discount is 15%. 2. If the CP is ₹680, the profit is 25%. intermediate
  • A 1 only
  • B 2 only
  • C Both 1 and 2
  • D Neither 1 nor 2
Show answer
Answer: Both 1 and 2
Why:

150 ÷ 1000 = 15%. Profit = 170 ÷ 680 = 25%. Both true.

Important short questions (3)

A TV marked ₹15,000 is sold at 12.5% discount. Find the SP.

15000 × 7/8 = ₹13,125.

A trader marks goods 40% above CP and gives 25% discount. Find his profit or loss percent.

1.4 × 0.75 = 1.05, so a 5% profit.

At what price should an item costing ₹720 be marked to gain 25% after 10% discount?

MP = 720 × 125 ÷ 90 = ₹1,000.

Long answer questions (1)

A shop buys mixers at ₹2,000 each. (a) It wants a 17% profit after a 10% discount: find the marked price. (b) In a clearance sale it gives 20% off on that marked price instead: find the new profit percent.

(a) MP = 2000 × 117 ÷ 90 = ₹2,600.

(b) SP = 2600 × 0.8 = ₹2,080; profit = 80 ÷ 2000 = 4%.

Flashcards (13)

Discount is on?
Marked price
SP after d% discount?
MP × (100 − d) ÷ 100
MP from SP and d%?
SP × 100 ÷ (100 − d)
Discount %?
(MP − SP) ÷ MP × 100
Marked m% up, d% off: profit?
(1 + m)(1 − d) − 1
MP for p% profit after d% off?
CP × (100 + p) ÷ (100 − d)
Buy 3 get 1 free?
25% discount
Buy 4 get 1 free?
20% discount
20% up, 20% off?
4% loss
50% up, 20% off?
20% profit
MRP ₹800, SP ₹680: discount?
15%
Can a shop sell above MRP?
No
Mark-up % is on?
Cost price

Play this topic

  • Tag check

Successive Discounts and Dishonest Dealers

Apply two or three discounts one after another, turn them into a single equivalent discount, compare shop offers, and catch dishonest dealers who use false weights, add water, or cheat while buying and selling.

What you will be able to do

  • I can find the selling price after two or three successive discounts.
  • I can find the single discount equal to successive discounts, and compare offers.
  • I can find the net change when a price rises and then falls.
  • I can find the gain of a dealer who uses false weights, mixes water or cheats both ways.

Key points

  • Successive discounts are applied one after another; the second is on the already reduced price.

  • Two discounts a% and b% equal a single discount of (a + b − ab/100)%.

  • For three or more, multiply the factors (1 − a)(1 − b)(1 − c) and subtract from 1.

  • The order of successive discounts does not change the final price.

  • A rise of a% followed by a fall of b% is a net change of (a − b − ab/100)%.

  • A dealer who sells at cost but gives w grams for 1 kg gains (1000 − w) ÷ w × 100 %.

  • With false weight and a price change together, multiply: SP ÷ CP = (price factor) × (1000 ÷ w).

Full explanation

Neha's two shops

A weighing scale with a hidden magnet under one pan.

Neha wants headphones with a marked price of ₹5,000. Shop A offers a flat 30% off. Shop B offers 20% off and then another 10% off. "Same thing," says her brother, "20 plus 10 is 30." Neha is not so sure.

This topic settles it, and then looks at sellers who cheat with the scale itself.

Successive discounts

The second discount is taken on the price after the first. At shop B: $5000 \times 0.8 = 4000$, then $4000 \times 0.9 = 3600$.

Chain: marked price ₹5,000, minus 20% gives ₹4,000, minus 10% of 4,000 gives ₹3,600; total cut ₹1,400, which is 28%.

The single equivalent discount

$$\text{Single discount} = a + b - \frac{ab}{100}$$

For 20% and 10%: $20 + 10 - 2 = 28%$. So shop A (30%) is cheaper by ₹100.

Two price tags for ₹5,000 headphones: shop A flat 30% off, pay ₹3,500; shop B 20% plus 10% off, pay ₹3,600.

Three or more discounts

Multiply the factors. 10%, 20% and 25%: $0.9 \times 0.8 \times 0.75 = 0.54$, so the buyer pays 54% and the single discount is 46%. The order does not matter, because multiplication can be done in any order.

Table: 10% and 10% give 0.81, single 19%; 20% and 10% give 0.72, single 28%; 25% and 20% give 0.60, single 40%; 10%, 20% and 25% give 0.54, single 46%.

A rise, then a fall

The same idea works for any two percent changes. A rise of $a%$ then a fall of $b%$ gives a net change of $a - b - \frac{ab}{100}$.

Up 20% then down 20%: $20 - 20 - 4 = -4$, a 4% fall. Up 25% then down 20%: $25 - 20 - 5 = 0$, back where it started.

The dishonest dealer

A grocer sells at cost price but his scale gives 800 g when it shows 1 kg. He is paid for 1,000 g but his cost is only 800 g.

A shop balance: one pan shows what the customer is told, 1 kg paid for as 1,000 g; the other shows what the customer gets, 800 g; gain = 200 ÷ 800 = 25%.

The false-weight formula

$$\text{Gain}% = \frac{\text{true weight} - \text{false weight}}{\text{false weight}} \times 100$$

With 900 g for a kilogram: $\frac{100}{900} \times 100 = 11\frac{1}{9}%$. The same rule works for a metre stick that is 90 cm long.

Cheating on price and weight together

Multiply the two effects. Selling 10% above cost and giving 880 g per kg:

$$\frac{SP}{CP} = 1.1 \times \frac{1000}{880} = 1.25$$

so the gain is 25%. Even a seller who "loses 4%" on price but gives 800 g gains: $0.96 \times 1.25 = 1.2$, a 20% gain.

Back to Neha

Neha buys from shop A and saves ₹100, because 20% + 10% is only a 28% discount. On the way home she notices the fruit seller's scale has no stamp, and now she knows how much a missing 100 g is worth to him.

Exam summary: multiply factors for successive changes; for false weights, divide by what is actually given.

Mind map: two discounts a + b − ab/100, many discounts multiply, rise then fall, false weight gain, weight and price together, and order does not matter.

Concepts and terms

Successive discounts

20% then 10% on ₹5,000: ₹4,000, then ₹3,600. The total cut is 28%, not 30%.

Single equivalent

One discount that gives the same final price: a + b − ab/100.

False weight gain

Charging for 1,000 g but giving 800 g gains 200 on a cost of 800: 25%.

Combined cheating

Price and weight effects multiply: 10% above cost and 880 g for a kg gives 1.1 × 1000/880 = 1.25, a 25% gain.

Did you know

Shop scales in India must carry a stamp from the Legal Metrology department, checked every year, to stop false weighing.

Online stores often stack offers: a sale discount, then a bank-card discount. These are successive, not added.

Memory tricks

Two discounts — Add, then take the product away — 20 and 10: 20 + 10 = 30, minus 20 × 10 ÷ 100 = 2, gives 28.

False weight — Error over what is given — Gain % = (shortfall ÷ actual weight given) × 100.

Practice MCQs with answers (55)

Q1 What single discount is equivalent to two successive discounts of 20% and 10%? beginner
  • A 28%
  • B 15%
  • C 30%
  • D 32%
Show answer
Answer: 28%
Why:

20 + 10 − (20 × 10)/100 = 28%.

Q2 What single discount is equivalent to two successive discounts of 25% and 20%? beginner
  • A 22.5%
  • B 40%
  • C 45%
  • D 50%
Show answer
Answer: 40%
Why:

25 + 20 − (25 × 20)/100 = 40%.

Q3 What single discount is equivalent to two successive discounts of 15% and 10%? intermediate
  • A 26.5%
  • B 12.5%
  • C 23.5%
  • D 25%
Show answer
Answer: 23.5%
Why:

15 + 10 − (15 × 10)/100 = 23.5%.

Q4 What single discount is equivalent to two successive discounts of 30% and 20%? intermediate
  • A 56%
  • B 25%
  • C 50%
  • D 44%
Show answer
Answer: 44%
Why:

30 + 20 − (30 × 20)/100 = 44%.

Q5 What single discount is equivalent to two successive discounts of 12% and 5%? intermediate
  • A 16.4%
  • B 17%
  • C 17.6%
  • D 8.5%
Show answer
Answer: 16.4%
Why:

12 + 5 − (12 × 5)/100 = 16.4%.

Q6 What single discount is equivalent to two successive discounts of 40% and 25%? beginner
  • A 65%
  • B 55%
  • C 75%
  • D 32.5%
Show answer
Answer: 55%
Why:

40 + 25 − (40 × 25)/100 = 55%.

Q7 What single discount is equivalent to two successive discounts of 10% and 10%? beginner
  • A 20%
  • B 21%
  • C 19%
  • D 10%
Show answer
Answer: 19%
Why:

10 + 10 − (10 × 10)/100 = 19%.

Q8 The marked price of a television is ₹5,000. It is sold after successive discounts of 20% and 10%. What is the selling price? beginner
  • A ₹3,700
  • B ₹3,500
  • C ₹1,400
  • D ₹3,600
Show answer
Answer: ₹3,600
Why:

5,000 × 0.8 × 0.9 = ₹3,600. (Adding the discounts would give ₹3,500.)

Q9 The marked price of a pair of shoes is ₹1,200. It is sold after successive discounts of 25% and 10%. What is the selling price? beginner
  • A ₹810
  • B ₹390
  • C ₹834
  • D ₹780
Show answer
Answer: ₹810
Why:

1,200 × 0.75 × 0.9 = ₹810. (Adding the discounts would give ₹780.)

Q10 The marked price of an air cooler is ₹8,000. It is sold after successive discounts of 15% and 10%. What is the selling price? intermediate
  • A ₹1,880
  • B ₹6,120
  • C ₹6,280
  • D ₹6,000
Show answer
Answer: ₹6,120
Why:

8,000 × 0.85 × 0.9 = ₹6,120. (Adding the discounts would give ₹6,000.)

Q11 The marked price of a mixer-grinder is ₹2,500. It is sold after successive discounts of 20% and 20%. What is the selling price? intermediate
  • A ₹900
  • B ₹1,650
  • C ₹1,600
  • D ₹1,500
Show answer
Answer: ₹1,600
Why:

2,500 × 0.8 × 0.8 = ₹1,600. (Adding the discounts would give ₹1,500.)

Q12 The marked price of a desk lamp is ₹640. It is sold after successive discounts of 25% and 12.5%. What is the selling price? advanced
  • A ₹432.8
  • B ₹400
  • C ₹220
  • D ₹420
Show answer
Answer: ₹420
Why:

640 × 0.75 × 0.875 = ₹420. (Adding the discounts would give ₹400.)

Q13 The marked price of a used scooter is ₹12,000. It is sold after successive discounts of 10% and 5%. What is the selling price? intermediate
  • A ₹10,260
  • B ₹1,740
  • C ₹10,500
  • D ₹10,200
Show answer
Answer: ₹10,260
Why:

12,000 × 0.9 × 0.95 = ₹10,260. (Adding the discounts would give ₹10,200.)

Q14 Find the single discount equivalent to three successive discounts of 10%, 20%, 25%. intermediate
  • A 54%
  • B 46%
  • C 49%
  • D 55%
Show answer
Answer: 46%
Why:

Buyer pays 0.9 × 0.8 × 0.75 = 0.54 of MP, so the discount = 46%.

Q15 Find the single discount equivalent to three successive discounts of 10%, 10%, 10%. advanced
  • A 30%
  • B 72.9%
  • C 27.1%
  • D 30.1%
Show answer
Answer: 27.1%
Why:

Buyer pays 0.9 × 0.9 × 0.9 = 0.729 of MP, so the discount = 27.1%.

Q16 Find the single discount equivalent to three successive discounts of 20%, 10%, 5%. advanced
  • A 68.4%
  • B 34.6%
  • C 35%
  • D 31.6%
Show answer
Answer: 31.6%
Why:

Buyer pays 0.8 × 0.9 × 0.95 = 0.684 of MP, so the discount = 31.6%.

Q17 An item marked ₹5,000 is offered at shop A with a flat 30% discount and at shop B with successive discounts of 20% and 10%. Which shop is cheaper, and by how much? intermediate
  • A Shop A, by ₹100
  • B Shop A, by ₹200
  • C Shop A, by ₹50
  • D Shop B, by ₹100
Show answer
Answer: Shop A, by ₹100
Why:

A: 5,000 × 0.7 = ₹3,500. B: 5,000 × 0.8 × 0.9 = ₹3,600. Difference ₹100.

Q18 An item marked ₹12,000 is offered at shop A with a flat 35% discount and at shop B with successive discounts of 20% and 15%. Which shop is cheaper, and by how much? advanced
  • A Shop B, by ₹360
  • B Shop A, by ₹360
  • C Shop A, by ₹720
  • D Shop A, by ₹180
Show answer
Answer: Shop A, by ₹360
Why:

A: 12,000 × 0.65 = ₹7,800. B: 12,000 × 0.8 × 0.85 = ₹8,160. Difference ₹360.

Q19 An item marked ₹2,000 is offered at shop A with a flat 25% discount and at shop B with successive discounts of 15% and 10%. Which shop is cheaper, and by how much? intermediate
  • A Shop A, by ₹15
  • B Shop B, by ₹30
  • C Shop A, by ₹30
  • D Shop A, by ₹60
Show answer
Answer: Shop A, by ₹30
Why:

A: 2,000 × 0.75 = ₹1,500. B: 2,000 × 0.85 × 0.9 = ₹1,530. Difference ₹30.

Q20 An item marked ₹8,000 is offered at shop A with a flat 28% discount and at shop B with successive discounts of 20% and 12%. Which shop is cheaper, and by how much? advanced
  • A Shop B, by ₹256
  • B Shop B, by ₹320
  • C Shop A, by ₹128
  • D Shop B, by ₹128
Show answer
Answer: Shop B, by ₹128
Why:

A: 8,000 × 0.72 = ₹5,760. B: 8,000 × 0.8 × 0.88 = ₹5,632. Difference ₹128.

Q21 A shop marks a jacket at ₹1,000, gives a discount of 20%, and then a second discount, so that the customer pays ₹720. What is the second discount percent? intermediate
  • A 10%
  • B 8%
  • C 28%
  • D 11 1/9%
Show answer
Answer: 10%
Why:

After the first discount: ₹800. Second cut = 80 ÷ 800 × 100 = 10%.

Q22 A shop marks a jacket at ₹2,500, gives a discount of 10%, and then a second discount, so that the customer pays ₹1,800. What is the second discount percent? intermediate
  • A 28%
  • B 20%
  • C 25%
  • D 18%
Show answer
Answer: 20%
Why:

After the first discount: ₹2,250. Second cut = 450 ÷ 2,250 × 100 = 20%.

Q23 A shop marks a jacket at ₹800, gives a discount of 25%, and then a second discount, so that the customer pays ₹510. What is the second discount percent? advanced
  • A 11.25%
  • B 36.25%
  • C 15%
  • D 20%
Show answer
Answer: 15%
Why:

After the first discount: ₹600. Second cut = 90 ÷ 600 × 100 = 15%.

Q24 Ramesh sells pulses at the cost price but uses a false weight of 800 g in place of 1 kg. What is the gain percent? beginner
  • A 125%
  • B 27%
  • C 20%
  • D 25%
Show answer
Answer: 25%
Why:

The buyer gets 800 g but pays for 1000 g: gain = 200 ÷ 800 × 100 = 25%.

Q25 Sunita sells pulses at the cost price but uses a false weight of 900 g in place of 1 kg. What is the gain percent? intermediate
  • A 11 1/9%
  • B 111 1/9%
  • C 13 1/9%
  • D 10%
Show answer
Answer: 11 1/9%
Why:

The buyer gets 900 g but pays for 1000 g: gain = 100 ÷ 900 × 100 = 11 1/9%.

Q26 A shopkeeper sells pulses at the cost price but uses a false weight of 960 g in place of 1 kg. What is the gain percent? intermediate
  • A 104 1/6%
  • B 4 1/6%
  • C 6 1/6%
  • D 4%
Show answer
Answer: 4 1/6%
Why:

The buyer gets 960 g but pays for 1000 g: gain = 40 ÷ 960 × 100 = 4 1/6%.

Q27 Imran sells pulses at the cost price but uses a false weight of 750 g in place of 1 kg. What is the gain percent? advanced
  • A 25%
  • B 133 1/3%
  • C 33 1/3%
  • D 35 1/3%
Show answer
Answer: 33 1/3%
Why:

The buyer gets 750 g but pays for 1000 g: gain = 250 ÷ 750 × 100 = 33 1/3%.

Q28 A cloth merchant sells cloth at the cost price but uses a measuring rod of 80 cm in place of 1 metre. What is his gain percent? beginner
  • A 27%
  • B 20%
  • C 125%
  • D 25%
Show answer
Answer: 25%
Why:

The buyer gets 80 cm but pays for 100 cm: gain = 20 ÷ 80 × 100 = 25%.

Q29 A cloth merchant sells cloth at the cost price but uses a measuring rod of 90 cm in place of 1 metre. What is his gain percent? intermediate
  • A 11 1/9%
  • B 10%
  • C 111 1/9%
  • D 13 1/9%
Show answer
Answer: 11 1/9%
Why:

The buyer gets 90 cm but pays for 100 cm: gain = 10 ÷ 90 × 100 = 11 1/9%.

Q30 A shopkeeper sells rice at 10% above the cost price and also gives only 880 g for every kilogram. What is his total gain percent? advanced
  • A 23 7/11%
  • B 25%
  • C 13 7/11%
  • D 22%
Show answer
Answer: 25%
Why:

SP ÷ CP = 1.1 × 1000/880 = 1.25, so the gain is 25%. Multiply the effects; do not add them.

Q31 A shopkeeper sells rice at 20% above the cost price and also gives only 800 g for every kilogram. What is his total gain percent? intermediate
  • A 45%
  • B 25%
  • C 50%
  • D 40%
Show answer
Answer: 50%
Why:

SP ÷ CP = 1.2 × 1000/800 = 1.5, so the gain is 50%. Multiply the effects; do not add them.

Q32 A shopkeeper sells rice at 8% above the cost price and also gives only 900 g for every kilogram. What is his total gain percent? advanced
  • A 11 1/9%
  • B 18%
  • C 19 1/9%
  • D 20%
Show answer
Answer: 20%
Why:

SP ÷ CP = 1.08 × 1000/900 = 1.2, so the gain is 20%. Multiply the effects; do not add them.

Q33 A dealer claims to sell sugar at a loss of 4%, but he gives only 800 g for every kilogram. What is his actual gain percent? advanced
  • A 20%
  • B 21%
  • C 25%
  • D 16%
Show answer
Answer: 20%
Why:

SP ÷ CP = 0.96 × 1000/800 = 1.2, so the gain is 20%. Multiply the effects; do not add them.

Q34 A dealer claims to sell sugar at a loss of 12%, but he gives only 800 g for every kilogram. What is his actual gain percent? advanced
  • A 25%
  • B 10%
  • C 8%
  • D 13%
Show answer
Answer: 10%
Why:

SP ÷ CP = 0.88 × 1000/800 = 1.1, so the gain is 10%. Multiply the effects; do not add them.

Q35 A trader cheats by 10% both while buying and while selling: he takes 10% more when buying and gives 10% less when selling, using false weights. What is his total gain percent? advanced
  • A 20%
  • B 21%
  • C 22 2/9%
  • D 25 2/9%
Show answer
Answer: 22 2/9%
Why:

For the price of 100 g he gets 110 g and gives 90 g: gain = (110 ÷ 90 − 1) × 100 = 22 2/9%.

Q36 A trader cheats by 20% both while buying and while selling: he takes 20% more when buying and gives 20% less when selling, using false weights. What is his total gain percent? advanced
  • A 40%
  • B 44%
  • C 45%
  • D 50%
Show answer
Answer: 50%
Why:

For the price of 100 g he gets 120 g and gives 80 g: gain = (120 ÷ 80 − 1) × 100 = 50%.

Q37 A milkman mixes water and milk in the ratio 1 : 4 and sells the mixture at the cost price of pure milk. What is his gain percent? intermediate
  • A 25%
  • B 30%
  • C 20%
  • D 80%
Show answer
Answer: 25%
Why:

He pays for 4 parts of milk and sells 5 parts: gain = 1 ÷ 4 × 100 = 25%.

Q38 A milkman mixes water and milk in the ratio 1 : 9 and sells the mixture at the cost price of pure milk. What is his gain percent? intermediate
  • A 90%
  • B 11 1/9%
  • C 16 1/9%
  • D 10%
Show answer
Answer: 11 1/9%
Why:

He pays for 9 parts of milk and sells 10 parts: gain = 1 ÷ 9 × 100 = 11 1/9%.

Q39 A milkman mixes water and milk in the ratio 3 : 17 and sells the mixture at the cost price of pure milk. What is his gain percent? advanced
  • A 22 11/17%
  • B 15%
  • C 17 11/17%
  • D 85%
Show answer
Answer: 17 11/17%
Why:

He pays for 17 parts of milk and sells 20 parts: gain = 3 ÷ 17 × 100 = 17 11/17%.

Q40 The price of an item is first increased by 20% and then decreased by 20%. What is the net change in the price? beginner
  • A 6% decrease
  • B No change
  • C 4% increase
  • D 4% decrease
Show answer
Answer: 4% decrease
Why:

Net = 20 − 20 − (20 × 20)/100 = −4%. Check with 100: 100 → 120 → 96.

Q41 The price of an item is first increased by 25% and then decreased by 20%. What is the net change in the price? intermediate
  • A No change
  • B 5% increase
  • C 1% increase
  • D 2% decrease
Show answer
Answer: No change
Why:

Net = 25 − 20 − (25 × 20)/100 = 0%. Check with 100: 100 → 125 → 100.

Q42 Ravi's salary was raised by 10% and later cut by 10%. What is the net effect on his salary? beginner
  • A No change
  • B 1% decrease
  • C 1% increase
  • D 3% decrease
Show answer
Answer: 1% decrease
Why:

Net = 10 − 10 − (10 × 10)/100 = −1%. Check with 100: 100 → 110 → 99.

Q43 Ravi's salary was raised by 30% and later cut by 20%. What is the net effect on his salary? intermediate
  • A 2% increase
  • B 10% increase
  • C 4% increase
  • D 4% decrease
Show answer
Answer: 4% increase
Why:

Net = 30 − 20 − (30 × 20)/100 = 4%. Check with 100: 100 → 130 → 104.

Q44 The tag shows two discounts, one after the other. How much does the customer pay? ![Price tag: MRP ₹6,000, 20% off, plus an extra 10% off at the till.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-tag-double.svg) intermediate
  • A ₹4,380
  • B ₹1,680
  • C ₹4,200
  • D ₹4,320
Show answer
Answer: ₹4,320
Why:

6000 × 0.8 × 0.9 = ₹4,320. (Adding to 30% gives ₹4,200, the trap.)

Q45 The same cycle is tagged ₹4,000 at two shops with different offers. Which statement is correct? ![Two tags: shop A ₹4,000 with a flat 35% off; shop B ₹4,000 with 20% plus 20% off.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-two-shops.svg) advanced
  • A Shop B is cheaper by ₹40
  • B Shop A is cheaper by ₹40
  • C Shop A is cheaper by ₹200
  • D Both cost the same
Show answer
Answer: Shop B is cheaper by ₹40
Why:

A: 4000 × 0.65 = ₹2,600. B: 4000 × 0.8 × 0.8 = ₹2,560, a 36% discount. B is cheaper by ₹40.

Q46 A grocer sells at the cost price using this scale. What is his gain percent? ![A balance: one pan is labelled "shows 1 kg", the other "really weighs 875 g".](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-scale-875.svg) intermediate
  • A 14%
  • B 14 2/7%
  • C 12.5%
  • D 125%
Show answer
Answer: 14 2/7%
Why:

Gain = 125 ÷ 875 × 100 = 1/7 × 100 = 14 2/7%. (125 ÷ 1000 = 12.5% uses the wrong base.)

Q47 The chain shows a sofa after each of two discounts. What single discount would give the same final price? ![Chain: marked price ₹20,000, after the first discount ₹17,000, after the second ₹15,300.](/syllabus/veda-skills-0-quantitative-aptitude-en/ch06/q-chain-two.svg) intermediate
  • A 15%
  • B 76.5%
  • C 23.5%
  • D 25%
Show answer
Answer: 23.5%
Why:

Discounts were 15% and 10%. 15,300 ÷ 20,000 = 0.765, so the single discount is 23.5%.

Q48 Two successive discounts of 20% and 30% are the same as one discount of beginner
  • A 56%
  • B 50%
  • C 46%
  • D 44%
Show answer
Answer: 44%
Why:

20 + 30 − 6 = 44%.

Q49 Which is better for a buyer: 30% then 10%, or 10% then 30%? beginner
  • A Both are the same
  • B It depends on the price
  • C 30% then 10%
  • D 10% then 30%
Show answer
Answer: Both are the same
Why:

0.7 × 0.9 = 0.9 × 0.7 = 0.63 either way.

Q50 A dealer sells at cost price using a 950 g weight for 1 kg. His gain is intermediate
  • A 50%
  • B a little more than 5%
  • C exactly 5%
  • D a little less than 5%
Show answer
Answer: a little more than 5%
Why:

50 ÷ 950 = 5 5/19%, because the base is 950, not 1,000.

Q51 A price goes up by x% and then down by x%. The final price is intermediate
  • A lower only if x > 50
  • B equal to the original
  • C lower than the original
  • D higher than the original
Show answer
Answer: lower than the original
Why:

(1 + x)(1 − x) = 1 − x², always below 1.

Q52 Assertion (A): Successive discounts of 20% and 10% equal a single discount of 28%. Reason (R): The second discount is applied to the price already reduced by the first. intermediate
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: Both A and R are true, and R is the correct explanation of A
Why:

Both true, and R explains A: 10% of 80 is only 8, so 20 + 8 = 28.

Q53 Assertion (A): A seller who gives 900 g for a kilogram at cost price gains 10%. Reason (R): False-weight gain is calculated on the weight actually given. advanced
  • A Both A and R are true, and R is the correct explanation of A
  • B Both A and R are true, but R is not the correct explanation of A
  • C A is true but R is false
  • D A is false but R is true
Show answer
Answer: A is false but R is true
Why:

A is false: 100 ÷ 900 = 11 1/9%. R is true, and it is why A is wrong.

Q54 Which of these statements is/are true? 1. Three successive discounts of 10% each equal a single discount of 27.1%. 2. A 25% rise followed by a 20% fall leaves the price unchanged. advanced
  • A 1 only
  • B 2 only
  • C Both 1 and 2
  • D Neither 1 nor 2
Show answer
Answer: Both 1 and 2
Why:

0.9³ = 0.729, so 27.1% is right. 1.25 × 0.8 = 1, so 2 is right too.

Q55 A dealer sells at 10% above cost but gives 900 g for a kilogram. Which of these statements is/are true? 1. His gain is exactly 20%. 2. His gain is more than 20%. advanced
  • A 1 only
  • B 2 only
  • C Both 1 and 2
  • D Neither 1 nor 2
Show answer
Answer: 2 only
Why:

1.1 × 1000/900 = 11/9, a gain of 22 2/9%. So 1 is false and 2 is true.

Important short questions (3)

Find the single discount equivalent to 25%, 20% and 10%.

0.75 × 0.8 × 0.9 = 0.54, so 46%.

A shopkeeper uses 840 g for 1 kg and sells at 5% above cost. Find his gain.

1.05 × 1000/840 = 1.25, so 25%.

Which is better on ₹10,000: 40% off, or 25% + 20% off?

Both give 40%: 0.75 × 0.8 = 0.6. Both cost ₹6,000.

Long answer questions (1)

A trader marks his goods 25% above cost and gives a 10% discount. He also uses a 900 g weight for 1 kg. (a) Find his gain from price alone. (b) Find his total gain.

(a) 1.25 × 0.9 = 1.125, a 12.5% gain.

(b) 1.125 × 1000/900 = 1.25, a total gain of 25%.

Flashcards (13)

Single equivalent of a% and b%?
a + b − ab/100
20% + 10%?
28%
10% + 10%?
19%
25% + 20%?
40%
Does the order of discounts matter?
No
Up 20% then down 20%?
4% fall
Gives 900 g for 1 kg at cost: gain?
11 1/9%
Gives 800 g for 1 kg at cost: gain?
25%
False weight gain formula?
(true − false) ÷ false × 100
10% above cost, 880 g per kg?
25% gain
Three discounts 10, 20, 25?
46%
Water is 1/5 of the "milk" sold at cost: gain?
25%
Cheats 10% both buying and selling: gain?
22 2/9%

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Veda Skills Quantitative Aptitude Unit 6 — frequently asked questions

A cycle bought for ₹2,400 is sold for ₹2,760. Find the profit percent.

Profit = ₹360; 360 ÷ 2400 × 100 = 15%.

By selling a fan for ₹1,380, a dealer gains 15%. Find the CP.

CP = 1380 ÷ 1.15 = ₹1,200.

If the CP of 15 bulbs equals the SP of 12 bulbs, find the profit percent.

(15 − 12) ÷ 12 × 100 = 25%.

A TV marked ₹15,000 is sold at 12.5% discount. Find the SP.

15000 × 7/8 = ₹13,125.

A trader marks goods 40% above CP and gives 25% discount. Find his profit or loss percent.

1.4 × 0.75 = 1.05, so a 5% profit.

At what price should an item costing ₹720 be marked to gain 25% after 10% discount?

MP = 720 × 125 ÷ 90 = ₹1,000.

Find the single discount equivalent to 25%, 20% and 10%.

0.75 × 0.8 × 0.9 = 0.54, so 46%.

A shopkeeper uses 840 g for 1 kg and sells at 5% above cost. Find his gain.

1.05 × 1000/840 = 1.25, so 25%.

Which is better on ₹10,000: 40% off, or 25% + 20% off?

Both give 40%: 0.75 × 0.8 = 0.6. Both cost ₹6,000.

Part of the Veda Skills Quantitative Aptitude course
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All Veda Skills Quantitative Aptitude units

1 Number System 2 Simplification and Approximation 3 Percentage 4 Ratio and Proportion 5 Averages 6 Profit, Loss and Discount You are here 7 Simple and Compound Interest 8 Time and Work 9 Pipes and Cisterns 10 Speed, Time and Distance 11 Boats and Streams 12 Mixtures and Alligation 13 Algebra 14 Geometry 15 Mensuration 16 Trigonometry 17 Data Interpretation 18 Permutation and Combination 19 Probability 20 Practice Papers and Mock Tests

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