Ratio and Proportion MCQs: Practice Questions and Answers

Ratio and proportion is one of the most reliable scoring areas in the quantitative section of SSC CGL, SSC CHSL, RRB NTPC and banking prelims — the question patterns repeat, and almost every question can be solved in under a minute with the ratio-unit method. Below are 15 practice MCQs with worked solutions. Attempt each before reading the answer.

Key Concepts in 30 Seconds

• Ratio units: if a quantity is split in ratio a:b, call the parts ax and bx and solve for x from the given total or difference.
• Combining ratios: to get a:c from a:b and b:c, multiply so the b terms match — (a:b) × (b:c) term-wise gives a:c.
• Similar figures: lengths scale by k, areas by k², volumes by k³.

Practice Questions

Q1. The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?

(a) 30 (b) 35 (c) 36 (d) 40

Answer: (d) 40. Let the numbers be 3x and 4x. Then 7x = 70, so x = 10. The larger number is 4x = 40.

Q2. If a:b = 5:7 and b:c = 4:9, what is a:c?

(a) 20:63 (b) 5:9 (c) 35:36 (d) 4:7

Answer: (a) 20:63. Multiply term-wise: a:c = (5×4):(7×9) = 20:63.

Q3. The ratio of boys to girls in a class is 2:3. If there are 30 girls, how many boys are there?

(a) 15 (b) 20 (c) 24 (d) 45

Answer: (b) 20. 3x = 30 gives x = 10, so boys = 2x = 20.

Q4. The present ages of A and B are in the ratio 4:7. If the sum of their ages is 66, what is B''s age?

(a) 24 (b) 28 (c) 36 (d) 42

Answer: (d) 42. 11x = 66, so x = 6; B = 7x = 42 years.

Q5. The prices of two products are in the ratio 3:5. If the first costs ₹45, what does the second cost?

(a) ₹27 (b) ₹60 (c) ₹75 (d) ₹90

Answer: (c) ₹75. 3x = 45 gives x = 15, so the second price is 5x = ₹75.

Q6. The ages of a father and son are in the ratio 7:1. After 8 years the sum of their ages will be 56. The father''s present age is:

(a) 35 (b) 40 (c) 42 (d) 49

Answer: (a) 35. Present sum = 8x; after 8 years the sum is 8x + 16 = 56, so 8x = 40 and x = 5. Father = 7x = 35 years.

Q7. Boys and girls in a school are in the ratio 3:4. If the school has 210 students, how many are girls?

(a) 90 (b) 105 (c) 120 (d) 140

Answer: (c) 120. 7x = 210 gives x = 30; girls = 4x = 120.

Q8. The ages of two friends are in the ratio 5:8. If the sum of their ages is 65, the younger friend''s age is:

(a) 25 (b) 30 (c) 35 (d) 40

Answer: (a) 25. 13x = 65, x = 5; younger = 5x = 25 years.

Q9. The areas of two similar triangles are in the ratio 4:9. If the first triangle''s area is 36 sq units, the second''s is:

(a) 54 (b) 64 (c) 72 (d) 81

Answer: (d) 81 sq units. 4x = 36 gives x = 9; second area = 9x = 81.

Q10. A rectangle''s sides are in the ratio 5:3 and its perimeter is 64 units. The longer side is:

(a) 12 (b) 16 (c) 20 (d) 30

Answer: (c) 20 units. Perimeter = 2(5x + 3x) = 16x = 64, so x = 4. Longer side = 5x = 20.

Q11. Two brothers'' ages are in the ratio 4:9. If the difference of their ages is 10 years, the elder brother''s age is:

(a) 16 (b) 18 (c) 25 (d) 27

Answer: (b) 18. 9x − 4x = 5x = 10, so x = 2. Elder = 9x = 18 years.

Q12. The prices of two books are in the ratio 7:10. If the second book costs ₹70, the first costs:

(a) ₹49 (b) ₹56 (c) ₹63 (d) ₹100

Answer: (a) ₹49. 10x = 70 gives x = 7; first book = 7x = ₹49.

Q13. The weights of two objects are in the ratio 5:9. If the first weighs 20 kg, the second weighs:

(a) 25 kg (b) 36 kg (c) 40 kg (d) 45 kg

Answer: (b) 36 kg. 5x = 20 gives x = 4; second = 9x = 36 kg.

Q14. The sides of two similar triangles are in the ratio 2:5. If the first triangle''s perimeter is 18 cm, the second''s is:

(a) 36 cm (b) 40 cm (c) 45 cm (d) 50 cm

Answer: (c) 45 cm. Perimeters scale like sides: 2x = 18 gives x = 9, so the second perimeter is 5x = 45 cm.

Q15. Marbles and candies in a jar are in the ratio 3:7. If there are 84 candies, how many marbles are there?

(a) 24 (b) 36 (c) 42 (d) 63

Answer: (b) 36. 7x = 84 gives x = 12; marbles = 3x = 36.

Practice More

Attempt timed, exam-style ratio and proportion sets — with per-question solutions and analysis — in Pareeksha practice sets, or take a full-length mock in the mock test section.