Question

If twice the son's age in years is added to the father's age; the sum is $70$ years. But, if twice the father's age is added to the son's age, the sum is $95$ years. Find the ages of father and the son.

• A. $70$ years and $25$ years
• B. $30$ years and $5$ years
• C. $20$ years and $35$ years
• D. $40$ years and $15$ years

Answer 1

Answer: (D)

$40$ years and $15$ years

Currently, if father's age is $x$ and son's age is $y$,

then given, $x+2y=70$ --- $\left(1\right)$

$2x+y=95$ --- $\left(2\right)$
Multiplying equation $\left(1\right)$ with $2$ we get, $2x+4y=140$ --- $\left(3\right)$

Subtracting equation $\left(2\right)$ from $\left(3\right)$, we get $3y=45\Rightarrow y=15$

Substituting $y=15$ in the equation $\left(2\right)$, we get

$2x+15=95\Rightarrow x=40$

Hence, the father is $40$ years old and the son is $15$ years old.