Question: If twice the son's age in years is added to the father's age, the sum is 70. But twice the father's age is added to the son's age, the sum is 95, find the present ages of the father and his son.


Solution:

Let the present ages of the father and son be 'x' years and 'y' years respectively.

According to the question,

Condition I,
Twice the son's age in years is added to the father's age, the sum is 70.
$or, x + 2y = 70$
$or, x = 70-2y$ - (i)

Condition II,
Twice the father's age in years is added to the son's age, the sum is 95.
$or, 2x + y = 95$
$or, 2x = 95 - y$ - (ii)

Put the value of x from equation (i) in equation (ii), we get,
$2(70 - 2y) = 95 - y$
$or, 140 - 4y = 95 - y$
$or, 140 - 95 = 4y -y$
$or, 45 = 3y$
$or, 3y = 45$
$or, y = \frac{45}{3}$
$\therefore y = 15$

Put value of y in equation (i), we get,

$or, x = 70 - 2×15$
$or, x = 70 - 30$
$\therefore x = 40$

So, (x,y) = (40,15)

Therefore, the required present age of the father is 40 years and the present age of the son is 15 years.