Question

A says to B "I am twice as old as you were when i was as old as you are". The sum of their ages is $63$ years. Find the difference of their ages.

• A. $27$
• B. $12$
• C. $9$
• D. $6$
• E. $3$

Answer 1

The correct option is C $9$

Let $\text{age of A}=a$

$\text{age of B}=b$

When, age of $A=b$ , age of $B=b-(a-b)$

$=2b-a$

$\text{Age of A}=2\times \text{Age of B in past}$

$a=2(2b-a)$

$3a=4b$

$a+b=63$

$\frac{2b}{3}=63$

$b=27$, $a=36$

Difference in ages $=36-27=9$