Ratio and Proportion Questions & Answers

Question 31

Easy

A mixture of 112 litres contains milk and water in the ratio 3 : 5. How much water does it contain?

A 42 litres

B 84 litres

C 70 litres

D 56 litres

Correct Answer: C

Explanation:

Step 1: Total parts = 3 + 5 = 8. Step 2: 1 part = 112 ÷ 8 = 14 litres. Step 3: Water = 5 parts = 5 × 14 = 70 litres.

Question 32

Medium

What number must be subtracted from each of 23, 32, 19 and 25 so that the remainders are in proportion?

A 12

B 10

C 13

D 11

Correct Answer: D

Explanation:

Step 1: For proportion, (23 − x) : (32 − x) :: (19 − x) : (25 − x), so (23 − x)(25 − x) = (32 − x)(19 − x). Step 2: Expand; the x² terms cancel: 575 − 48x = 608 − 51x. Step 3: (48 − 51)x = 575 − 608 → x = -33/-3 = 11. Check: 12, 21, 8, 14 are in proportion.

Question 33

Easy

What is the duplicate ratio of 5 : 9?

A 5 : 9

B 81 : 25

C 26 : 81

D 25 : 81

Correct Answer: D

Explanation:

Step 1: The duplicate ratio of a : b is obtained when you square each term. Step 2: 5² : 9² = 25 : 81. Step 3: 25 : 81 is already in its simplest form.

Question 34

Easy

If A : B = 7 : 5 and B : C = 7 : 5, find A : B : C.

A 49 : 35 : 25

B 7 : 5 : 5

C 7 : 7 : 5

D 25 : 35 : 49

Correct Answer: A

Explanation:

Step 1: B is 5 in the first ratio and 7 in the second; make it equal by multiplying the first ratio by 7 and the second by 5. Step 2: A : B = 49 : 35 and B : C = 35 : 25. Step 3: A : B : C = 49 : 35 : 25 = 49 : 35 : 25.

Question 35

Medium

If (a + b) : (a − b) = 11 : 5, find a : b.

A 11 : 5

B 3 : 8

C 8 : 3

D 3 : 1

Correct Answer: C

Explanation:

Step 1: Cross-multiply: 5(a + b) = 11(a − b) → 5a + 5b = 11a − 11b. Step 2: Collect terms: 16b = 6a. Step 3: a/b = 16/6, so a : b = 8 : 3.

Ratio and Proportion Practice Questions