Question

If twice the age of son is added to age of mother, the sum is 56. But if twice the age of the mother is added to the age of son, the sum is 82. Find the ages of mother and son.

• A. 36 and 10 years
• B. 32 and 10 years
• C. 34 and 10 years
• D. 31 and 10 years

Answer 1

The correct option is A 36 and 10 years

Let the mothers current age be x and sons current age be y.

As per the given statement form equations,

$x+2y=56$ ----- (1)

$2x+y=82$ ----- (2)

Multiplying the equation (2) by 2 and then subtract the equations:

$x+2y=56$

$4x+2y=164$

_____________

$-3x=-108$

$x=\frac{-108}{-3}=36$

Substitute the value of x in equation (1),

$x+2y=56$

$36+2y=56$

$2y=56-36$

$y=\frac{20}{2}=10$

Therefore, the mothers age is 36 and sons age is 10 years.