Ratio and Proportion Questions & Answers

Question 21

Medium

If (a + b) : (a − b) = 5 : 4, find a : b.

A 9 : 1

B 5 : 4

C 1 : 9

D 10 : 1

Correct Answer: A

Explanation:

Step 1: Cross-multiply: 4(a + b) = 5(a − b) → 4a + 4b = 5a − 5b. Step 2: Collect terms: 9b = a. Step 3: a/b = 9/1, so a : b = 9 : 1.

Question 22

Easy

Find the ratio of 400 g to 5 kg.

A 25 : 2

B 3 : 25

C 1 : 25

D 2 : 25

Correct Answer: D

Explanation:

Step 1: Convert to the same unit: 5 kg = 5 × 1000 = 5000 g. Step 2: Ratio = 400 : 5000. Step 3: Divide by the HCF 200: 2 : 25.

Question 23

Easy

Find the compound ratio of 2 : 9, 4 : 8 and 9 : 7.

A 5 : 8

B 1 : 7

C 7 : 1

D 2 : 7

Correct Answer: B

Explanation:

Step 1: Compound ratio = (product of antecedents) : (product of consequents). Step 2: 2 × 4 × 9 : 9 × 8 × 7 = 72 : 504. Step 3: Simplify: 1 : 7.

Question 24

Medium

If 12A = 9B = 8C, find A : B : C.

A 6 : 8 : 9

B 12 : 9 : 8

C 9 : 8 : 6

D 7 : 8 : 9

Correct Answer: A

Explanation:

Step 1: Let 12A = 9B = 8C = k. Step 2: Then A = k/12, B = k/9, C = k/8, so A : B : C = 1/12 : 1/9 : 1/8. Step 3: Multiply by the LCM of 12, 9, 8 = 72: A : B : C = 6 : 8 : 9.

Question 25

Easy

Find the third proportional to 19 and 38.

A 9.5

B 79

C 76

D 114

Correct Answer: C

Explanation:

Step 1: Let the third proportional be x, so 19 : 38 :: 38 : x. Step 2: Product of extremes = product of means: 19 × x = 38 × 38 = 1444. Step 3: x = 1444 ÷ 19 = 76.

Ratio and Proportion Practice Questions