Question

The ages of $A$ and $B$ are in the ratio $7:5$. Ten years hence, the ratio of their ages will be $9:7$, find their ages.

• A. $35$ years and $25$ years
• B. $45$ years and $23$ years
• C. $42$ years and $21$ years
• D. $39$ years and $29$ years

Answer 1

The correct option is A $35$ years and $25$ years

Let the present age of $A=$ $7x$ years

The present age of $B=$ $5x$ years

After $10$ years, their ages will be
$A=7x+10$ years and
$B=5x+10$ years

The ratio of their ages after $10$ years is $9:7$.
$\therefore \frac{7x+10}{5x+10}=\frac{9}{7}$
$\Rightarrow 49x+70=45x+90$

$\Rightarrow 49x-45x=90-70$
$\Rightarrow 4x=20$

$\Rightarrow x=5$

$\therefore$ Present age of $A=$ $7\times 5=35$ years and present

age of $B=$ $5\times 5=25$ years.