Question

Four years ago, the ratio of the ages of A and B was 9 : 13. Eight years hence, the ratio of the ages of A and B will be 3 : 4. What will be the ratio of their ages 4 years hence?

• A. 11 : 15
• B. 9 : 11
• C. 5 : 7
• D. 7 : 9

Answer 1

Answer:

A. 11 : 15

Solution:

Given:

Four year ago the ratio of age of A and B is 9 : 13

Calculation:

Let the age of A and B, 4 years ago = 9x and 13x

So, the present age of A and B, respectively = 9x + 4 and 13x +4

Eight years hence, the ratio of the ages of A and B =$\frac{3}{4}$

⇒$\frac{(9x + 4 + 8)}{(13x + 4 + 8)} = \frac{3}{4}$

⇒ $36x + 48 = 39x + 36$

⇒$x = 4$

⇒ Present age of A $= 9\times{4} + 4 = 40$

⇒ Present age of B $= 13\times{4}+ 4 = 56$

⇒ The ratio after 4 years $=\frac{(40 + 4)}{(56 + 4)} = \frac{44}{60} = \frac{11}{15}$

∴ The required result will be $\frac{11}{15}.$