Question

The ratio of the ages of father and son at
present is 6:1. After 5 years, the ratio will
become 7:2. The present age of the son is:
​

Answer 1

Given:

The ratio of the ages of father and son at present is 6:1.

After 5 years the ratio of the ages of the father and the son will be 7:2.

To find:

The present age of the son.

Solution:

The ratio of the ages of father and son at present is 6:1.

Let, the common multiple of the ratio be, 'n'.

∴ The present age of the father = (n×6)

                                                    = 6n.

The present age of the son = (n×1)

                                             = n

After 5 years the age of the father will be_

(6n+5)

= 6n+5

After 5 years the age of the son will be_

(n+5)

= n+5

After 5 years the ratio of the ages of the father and the son will be 7:2.

∴ According to the problem:

(6n+5) : (n+5) = 7:2

$or, \dfrac{6n+5}{n+5} = \dfrac{7}{2}$

or, (6n+5)× 2 = (n+5)×7

or, (12n+10) =( 7n+35)

or, (12n-7n) = (35-10)

or, 5n = 25

or, n =(25÷5)

or, n = 5

∴ The present age of the son is 5 years.

Answer:

            The present age of the son is 5 years.