Question

The ratio of the ages of A and B ten years before was $3:5$. The ratio of their present ages is $2:3$ . Their ages are respectively

• A. $30,50$
• B. $20,30$
• C. $40,60$
• D. $16,24$

Answer 1

The correct option is C $40,60$

Let the present ages of $A$ and $B$ are $x$ and $y$ years respectively
$\therefore \frac{x-10}{y-10}=\frac{3}{5}$ .....(i)
or $5x-50=3y-30$ ......(ii)
and $\frac{x}{y}=\frac{2}{3}$or $3x=2y$ or $y=\frac{3x}{2}$
putting the value of y in equation (i) we get
$5x-50=$$\frac{9x}{2}-30$
$10x-100=9x-60$
or $x=40$ $\therefore y=\frac{3\times 40}{2}=60$