Question

The ratio between the present ages of $M$ and $N$ is $5:3$ respectively The ratio between $M$'s age $4$ years ago and $N$'s age after $4$ years is $1:1$. What is the ratio between $M$'s age after $4$ years and $N$'s age $4$ years ago?

• A. $2:1$
• B. $1:3$
• C. $4:1$
• D. $3:1$

Answer 1

Answer: (D)

$3:1$

Let the present ages of $M$ and $N$ be $5x$ years and $3x$ years respectively.
Given $(5x-4):(3x+4)=1:1$ $\Rightarrow$ $5x-4=3x+4$
$\Rightarrow 2x=8\Rightarrow x=4$
$\therefore$ Present ages of $M$ and $N$ respectively are $(5\times 4)$ years and $(3\times 4)$ years i.e., $20$ years and $12$ years
$\therefore$ Required ratio $=\frac{20+4}{12-4}=\frac{24}{8}=\frac{3}{1}=3:1$