The sum of the age of a father and his son is 38 years. If the father is 22 years older than his son, find their present ages.

Solution:

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

According to the question,

Condition I,

Sum of the age of a father and his son is 38 years.
$or, x + y = 38$
$or, x = 38 - y$ - (i)

Condition II,

The father is 22 years older than his son.
$or, x = y +22$ - (ii)

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

$or, 38 - y = y +22$
$or, 38 -22 = y + y$
$or, 16 = 2y$
$or, y = \frac{16}{2}$
$\therefore y = 8$

Now,

Put the value of y in equation (i), we get,
$x = 38 - 8$
$\therefore x = 30$

So, (x,y) = (30,8)

Hence, the present ages of the father and the son are 30 years and 8 years respectively.

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