Question

Four years ago, the ages of Ritu and Reena were in the ratio $5:6$ respectively. Eight years from now the respective ratio of their ages will be $8:9$. What is the sum of their ages at present?

• A. $52$ years
• B. $50$ years
• C. $60$ years
• D. $62$ years

Answer 1

The correct option is A $52$ years

Let the present age of Ritu and Reena will be x and y respectively.
four years ago,
$\frac{x-4}{y-4}=\frac{5}{6}$
$6x-24=5y-20$
$6x-5y=4$...............(i)
After eight years,
$\frac{x+8}{y+8}=\frac{8}{9}$
$9x-8y=-8$ ................(ii)
from equation (i) and (ii)
we get $x=24$ and $y=28$
So, sum of their ages at present $=(24+28)$
$=52$ years.