Question

The present ages of Ramesh and his elder brother are in the ratio $5:7$. After five year. the ratio of their ages will be $3:4$. Find their present ages.

Answer 1

Ratio of present ages of Ramesh and his elder brother $=5:7$

Let the present ages of Ramesh and his elder brother be $5x$ and $7x$.

After five years,

Age of Ramesh $=5x+5$ and Age of elder Brother $=7x+5$

According to question, then the ratio of their ages $=3:4$

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

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

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

$\Rightarrow 20x+20=21x+15$

$\Rightarrow 21x-20x=20-15$

$\Rightarrow x=5$

Thus, Present age of Ramesh $=5x=5\times 5=25$years

Present age of his elder brother $=7x=7\times 5=35$years.