Question

Seven years ago, the ratio of the ages of A and B was 4 ∶ 5. Eight years hence, the ratio of the ages of A and B will be 9 ∶ 10. What is the sum of their present ages in years?
1. 32 years
2. 41 years 
3. 56 years
4. 82 years 

Answer 1

Correct Answer - Option 2 : 41 years 

Given:

Seven years ago the ratio of ages of A and B = 4 : 5

After 8 years from present the ratio of ages of A and B = 9 : 10

Calculation:

Seven years ago the ratio of ages of A and B

⇒ 4x : 5x

Ratio of Present ages of A and B

⇒ 4x + 7 : 5x + 7

After 8 years the ratio of ages of A and B

⇒ (4x + 7 + 8) : (5x + 7 + 8) = 9 : 10

⇒ 40x + 150 = 45x + 135

⇒ 5x = 15

⇒ x = 3

Sum of present ages of A and B

⇒ (4 × 3 + 7) + (5 × 3 + 7)

⇒ 41 years

∴ The sum of present ages of A and B is 41 years.