Question

Sum of the ages of $X$ and $Y$, $12$ years, ago, was $48$ years and sum of the ages of $X$ and $Y$, $12$ years hence will be $96$ years. Present age of $X$ is _____

• A. $55$
• B. $72$
• C. Cannot be determined
• D. None of these

Answer 1

The correct option is C Cannot be determined

Sum of the ages of $X$ and $Y$, $12$ years ago was $48$ years implies,
$(X-12)+(Y-12)=48$
$\Rightarrow X+Y-24=48$
$\Rightarrow X+Y=72......\left(1\right).$
Sum of the ages of X and Y after 12 years implies,
$(X+12)+(Y+12)=96$
$\Rightarrow X+Y+24=96$
$\Rightarrow X+Y=72......\left(2\right)$
$\left(1\right)-\left(2\right)\Rightarrow 0=0$
Therefore, the age of $X$ cannot be determined.