The ages of Hari and Harry are in the ratio $5:7$. Four years from now, the ratio of their ages will be $3:4$. Find their present ages.

Given:

The ages of Hari and Harry are in the ratio $5:7$

Let the common ratio between their ages be $x$.

$\Rightarrow$ Hari’s age $=5x$ years

Harry’s $=7x$ years.

After four years,

Hari’s age $=5x+4$ years

Harry’s $=7x+4$ years

It is given that, four years later, their ages in the ratio $3:4$.

$\Rightarrow \frac{5x+4}{7x+4}=\frac{3}{4}$

$\Rightarrow 4(5x+4)=3(7x+4)$

$\Rightarrow 20x+16=21x+12$

$\Rightarrow 16-12=21x-20x$

$\Rightarrow 4=x$

Now,

Hari’s age $=5x=5\times 4=20$ years

Harry’s $=7x=7\times 4=28$ years.

Therefore, Hari’s age and Harry’s age are $20$ years and $28$ years, respectively.