Question

The ages of Leena and Heena are in the ratio $7:5$. Ten years hence, the ratio of their ages will be $9:7$. Find the present ages.

Answer 1

From question,

The ratio of the present ages of Leena and Heena $=7:5$

Let the age of Leena be $7x$ years
and Heena be $5x$ years

Ten years later,
Leena's age $=7x+10$ years
and Heena's age $=5x+10$ years

The ratio of their ages after ten years is given as $9:7$
let their ages be $9x$ and $7x$, respectively.

So, $9x+7x=7x+10+5x+10$
$\Rightarrow 9x=-7x+7x+10+5x+10$
$\Rightarrow 9x-5x=10+10$
$\Rightarrow 4x=20$
$\Rightarrow x=\frac{20}{4}=5$

Hence, Leena's present age $=7x=7\times 5=35$ years
And Heena's present age $=5x=5\times 5=25$ years