Question

The present ages of $A$ and $B$ are in the ratio $15:8$. After ten years, their ages will be in the ratio $5:3$. Find their present ages.

• A. $A=60$ years and $B=32$ years
• B. $A=20$ years and $B=32$ years
• C. $A=70$ years and $B=42$ years
• D. $A=30$ years and $B=12$ years

Answer 1

The correct option is A $A=60$ years and $B=32$ years

Let the current A's age be $15x$, and B's age be $8x$,
After $10$ years, their ages will be $15x+10$ and $8x+10$
Given,
$\frac{15x+10}{8x+10}=\frac{5}{3}$

$=>45x+30=40x+50$

$=>5x=20$

$=>x=4$

Hence, their present ages are $A=15x=60years;=8x=32years$