The sum of the present ages of Hari and Mohan is double the difference of their present ages. Four years ago this relation became one-and-a-half times. The ratio of their ages after $12$ years is:

Question

The sum of the present ages of Hari and Mohan is double the difference of their present ages. Four years ago this relation became one-and-a-half times. The ratio of their ages after $12$ years is:

Option A

7:5

Option B

8:5

Option C — Correct answer

9:5

Correct choice.

Option D

11:7

Explanation

Let present ages be $x$ and $y$ with $x+y=2(x-y)$, giving $x=3y$. Four years ago, $x+y-8=\frac32[(x-4)-(y-4)]$, which gives $5y-x=16$. Solving yields $x=24$, $y=8$. After $12$ years they are $36$ and $20$, so the ratio is $9:5$.

Chapter Mock 6: Average and Ages