Question

If 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. Find the ages of father and son.

Answer 1

Let the age of the father be x and that of the son be y.

According to the conditions,
2y+x=70 ..............(1)
2x+y=95 ..............(2)

Multiplying equation (1) by 2, we get
4y+2x=140 .........(3)

Subtracting equation (2) from equation (3),
3y = 45
$\Rightarrow$ y=15 ..................(4)
substituting (4) in (2) we get
15 +2x=95
$\Rightarrow$ 2x=80
$\Rightarrow$ x=40
Therefore, the age of the father is 40 years and that of the son is 15 years.