Question: The sum of the ages of a father and his son is 40 years. If they both live on till the son becomes as old as the father is now, the sum of their ages will be 96 years. Find their present ages.

Solution:

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

According to the question,

Condition I,
The sum of the ages of the father and the son is 40 years.
$or, x + y = 40$
$or, x = 40-y$ - (i)

Condition II,
If the age of the sum is equation to the father's age, the sun of the ages is 96 years.
$or, x + (x -y) + y +(x-y) = 96$
$or, x +x -y +y +x -y = 96$
$or, 3x -y = 96$

Put value of x from equation (i) in equation (ii), we get,

$or, 3(40-y) - y = 96$
$or, 120 - 3y -y = 96$
$or, 120 -4y = 96$
$or, 120 - 96 = 4y$
$or, 24 = 4y$
$or, 4×6 = 4×y$
$\therefore y = 6$

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

$or, x = 40 -6$
$\therefore x = 34$

So, (x,y) = (34,6)

Therefore, the required present ages of the father and the son are 34 years and 6 years, respectively.