Question

The present age of Shyam and Radha are in the ratio $4:5$. Ten years ago, their ages were in the ratio $3:4$. What are their present ages?

Answer 1

Let the present age of Shyam and Radha be $4x$ and $5x$ respectively,

and ten years ago, the ages of Shyam and Radha be $(4x-10)$ years and $(5x-10)$ years respectively

Then according to the given condition,

$$\begin{gathered} \frac{(4x-10)}{(5x-10)}=\frac{3}{4} \\ 4\times (4x-10)=3\times (5x-10) \\ 16x-40=15x-30 \\ 16x-15x=40-30 \\ x=10 \end{gathered}$$

$\therefore$The present age of Shyam $=4x=4\times 10=40years$

and present age of Radha$=5x=5\times 10=50years$