Question

Seven years ago ratio of the ages of father and son was 4 ∶ 1. Seven years hence from now the ratio of their ages will be 2 ∶ 1. What is the ratio of their present ages?
1. 7 ∶ 2
2. 3 ∶ 1
3. 5 ∶ 2
4. 7 ∶ 3

Answer 1

Correct Answer - Option 3 : 5 ∶ 2

Given:

Ratio of ages of father and son, 7 years ago = 4 : 1

Ratio of ages of father and son, 7 years hence = 2 : 1

Calculation:

Let the age of father and son 7 years ago be 4x and x respectively

Age of father 7 years hence = 4x + 7 + 7

⇒ 4x + 14

Age of son 7 years hence = x + 7 + 7

⇒ x + 14

Now, according to question,

(4x + 14)/(x + 14) = 2/1

⇒ 4x + 14 = 2x + 28

⇒ 2x = 14

⇒ x = 7

Present age of father = 4x + 7

⇒ 4 × 7 + 7 years

⇒ 35 years

Age of son = x + 7

⇒ 7 + 7 years

⇒ 14 years

Required ratio = 35 years : 14 years

⇒ 5 : 2

∴ The ratio of their present ages is 5 : 2