Question

If the sum of the ages of a father and his son in years is $65$ and twice the difference of their ages in years is $50$, then the age of the father is:

• A. $45$ years
• B. $40$ years
• C. $50$ years
• D. $55$ years

Answer 1

The correct option is A $45$ years

Let father's age $=x$, son's age $=y$

As per question,

$x+y=65\Rightarrow y=65-x$ .....(1)

$2(x-y)=50\Rightarrow 2x-2y=50$ .......(2)
$\Rightarrow 2x-2(65-x)=50$ $[$ substituting value of $y$ from equation (1) in equation (2) $]$

$\Rightarrow 2x-130+2x=50$
$\Rightarrow x=45$

So father's age $=45\text{years}$