Ratio and Proportion: 18 MCQs with answers
All 18 multiple-choice questions from this kit, free and with no sign-up.
Warm-up · 6 questions
Q1. Which of the following correctly states the fundamental rule of proportion for $a:b :: c:d$?
BeginnerShow the answer
C · $ad = bc$
The product of extremes ($a \times d$) equals the product of means ($b \times c$).
Q2. A recipe uses flour and sugar in the ratio $3:2$. If 9 cups of flour are used, how many cups of sugar are needed?
BeginnerShow the answer
D · 6 cups
Direct proportion: $\dfrac{3}{2} = \dfrac{9}{x} \Rightarrow 3x = 18 \Rightarrow x = 6$.
Q3. In the proportion $4:7 :: 12:x$, what is the value of $x$?
BeginnerShow the answer
A · 21
$4x = 7 \times 12 = 84 \Rightarrow x = 21$.
Q4. If boys : girls in a class is $3:5$, what is the ratio of boys to the total number of students?
BeginnerShow the answer
C · $3:8$
Total = $3+5 = 8$ parts, so boys : total $= 3:8$.
Q5. Which of these is an example of inverse proportion?
BeginnerShow the answer
A · Number of workers and days to finish a fixed job
With fixed total work, more workers mean fewer days — the product is constant.
Q6. The fundamental property of proportion is $a:b :: c:d \iff ad = bc$ — the product of extremes equals the product of means.
BeginnerShow the answer
A · True
The fundamental property of proportion is $a:b :: c:d \iff ad = bc$ — the product of extremes equals the product of means.
Building up · 7 questions
Q7. The mean proportional between 4 and 25 is:
IntermediateShow the answer
B · 10
Mean proportional $= \sqrt{4 \times 25} = \sqrt{100} = 10$.
Q8. If $a:b = 2:3$ and $b:c = 4:5$, what is $a:b:c$?
IntermediateShow the answer
C · $8:12:15$
Make $b$ equal: $a:b = 8:12$ and $b:c = 12:15$, so $a:b:c = 8:12:15$.
Q9. ₹1,200 is divided among A, B and C in the ratio $2:3:5$. How much does B receive?
IntermediateShow the answer
D · ₹360
Total parts $= 10$, one part $= ₹120$, so B gets $3 \times 120 = ₹360$.
Q10. If 12 workers complete a job in 10 days, how many days will 15 workers take for the same job?
IntermediateShow the answer
C · 8 days
Inverse proportion: $12 \times 10 = 15 \times x \Rightarrow x = 8$ days.
Q11. The third proportional to 4 and 6 is:
IntermediateShow the answer
D · 9
Third proportional $= \dfrac{b^2}{a} = \dfrac{36}{4} = 9$.
Q12. A student writes 3 kg : 400 g as $3:400$. What is the correct ratio?
IntermediateShow the answer
B · $15:2$
Convert to the same unit: $3000:400 = 15:2$.
Q13. If $a:b = c:d$, which of the following is true by the invertendo property?
IntermediateShow the answer
B · $b:a = d:c$
Invertendo flips both ratios: $b:a = d:c$.
Topper level · 5 questions
Q14. A map has a scale of $1:50{,}000$. If two towns are 4 cm apart on the map, what is the actual distance?
AdvancedShow the answer
A · 2 km
$4 \text{ cm} \times 50{,}000 = 200{,}000 \text{ cm} = 2 \text{ km}$.
Q15. A student claims that if $a:b = c:d$, then $a+b : b = c+d : d$. Which property justifies this?
AdvancedShow the answer
B · Componendo
Componendo adds the second term to the first in both ratios.
Q16. If $\dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}$, which underlying proportion does this represent?
AdvancedShow the answer
D · $a:b = c:d$
This is the componendo–dividendo form, which holds when $a:b = c:d$.
Q17. If the ratio of boys to girls in a class is represented as $3:5$ and the total number of students is $40$, how many boys are there in the class?
AdvancedShow the answer
D · 18
The total parts in the ratio $3:5$ is $3 + 5 = 8$. Each part represents $40/8 = 5$ students. Therefore, boys = $3 imes 5 = 15$. The correct calculation shows $3:5$ means boys are $3$ parts out of $8$, resulting in $15$ boys.
Q18. A recipe requires flour and sugar in the ratio $4:1$. If you have 20 cups of flour, how many cups of sugar are needed to maintain the ratio?
AdvancedShow the answer
C · 5
The ratio $4:1$ indicates that for every 4 cups of flour, there is 1 cup of sugar. If you have 20 cups of flour, the amount of sugar needed is calculated as $20 \div 4 = 5$ cups.
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