# Ratio and Proportions problems made easy

Published: Published Date - 11:45 PM, Wed - 14 September 22

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic that will help you in your preparation for the State government recruitment jobs.

**1. The ratio of the ages of A and B at present is 3:1. Four years earlier the ratio was 4:1. The present age of A is?**

a) 44 years b) 24 years c) 34 years d) 36 years

**Ans**: d

**Solution**: A’s present age = 3x years

B’s present age = x years

4 years ago,

3x – 4/ x – 4 = 4/1

==>; 4x – 16 = 3x – 4

==>; 4x – 3x = 16 – 4

==>; x = 12

A’s present age

= 3x = 3 × 12 = 36 years

**2. Eighteen years ago, the ratio of A’s age to B’s age was 8:13. Their present ratios are 5:7. What is the present age of A?**

a) 40 years b) 50 years c) 60 years d) 70 years

**Ans**: b

**Solution**: 18 years ago,

A’s age = 8x years

B’s age = 13x years

At present,

8x 18/ 13x 18 = 5/7

==>; 56x 126 = 65x 90

==>; 65x – 56x = 126 – 90

==>; 9x = 36 ==>; x = 36/9 = 4

A’s present age = 8x 18

= 8 × 4 18 = 50 years

**3. The present ages of A and B are in the ratio 5:6 respectively. After seven years this ratio becomes 6:7. Then the present age of A in years is?**

a) 30 years b) 31 years c) 34 years d) 35 years

**Ans**: d

**Solution**: A’s present age = 5x years

B’s present age = 6x years

According to the question,

After 7 years,

5x 7/ 6x 7 = 6/7

==>; 36x 42 = 35x 49

==>;36x – 35x = 49 – 42

==>; x = 7

A’s present age = 5x = 35 years

**4. The present ages of A and B are in the ratio 3:4. Ten years ago, this ratio was 4:7. The present ages of A and B are respectively:**

a) 32 years, 40 years b) 24 years, 18 years

c) 27 years, 36 years d) 18 years, 24 years

**Ans**: d

**Solution**: A’s present age = 3x years (let)

B’s present age = 4x years

According to the question,

10 years ago,

3x – 10/ 4x – 10 = 4/7

==>; 21x – 70 = 16x – 40

==>; 21x – 16x = 70 – 40

==>; 5x = 30

==>; x = 30/5 = 6

A’s present age

= 3x = 3x × 6 = 18 years

B’s present age

= 4x = 4 × 6 = 24 years

**5. The ratio of the age of Rahul and Rohit 10 years ago was 1:3. The ratio of their age five years hence will be 2:3. Then the ratio of their present age is?**

a) 3:1 b) 3:4 c) 3:5 d) 3:2

**Ans**: c

**Solution**: Let the age of Rahul and Rohit 10 years ago be x and 3x years respectively.

After 5 years from now,

x 15/ 3x 15 = 2/3

==>; 6x 30 = 3x 45

==>; 3x = 45 – 30 = 15

==>; x = 5

Ratio of their present age

= (x 10) : (3x 10)

= 15 : 25 = 3 : 5

**To be continued….**