Question

Twice the son's age in years is added to the father's age, the sum is $70$. But if twice the father's age is added to the son's age, the sum is $95$. Then the ages of father and son respectively are

• A. $30$ yrs, $10$ yrs
• B. $40$ yrs, $15$ yrs
• C. $45$ yrs, $20$ yrs
• D. None of these

Answer 1

Answer: (B)

$40$ yrs, $15$ yrs

Suppose age of father (in years) be $x$ and that of son be $y$.
Then $x+2y=70$ and $2x+y=95$
And this system of equations may be written as,
$x+2y-70=0$
$2x+y-95=0$
By cross multiplying we get
$\frac{x}{2\times (-95)-(-70)}=\frac{-y}{1\times (-95)-2\times (-70)}=\frac{1}{1\times 1-2\times 2}$
$\Rightarrow \frac{x}{-190+70}=\frac{-y}{-95+140}=\frac{1}{-3}$
$\Rightarrow \frac{x}{-120}=\frac{-y}{45}=\frac{1}{-3}\Rightarrow x=\frac{-120}{-3}=40$ and $y=\frac{-45}{-3}=15$
Hence, father's age is 40 years and the son's age is 15 years