Question

A father is 8 times as old as his son. In 10 years time , he will be
three times as old as his son. Find their present ages

Answer 1

Answer :

›»› The present age of father is 24 years, and the present age of son is 4 years.

Given :

• A father is 8 times as old as his son. In 10 years time, he will be three times as old as his son.

To Find :

• Their present ages.

Solution :

Let,

The present age of father be "x" and the present age of son be "y"

A father is 8 times as old as his son.

→ x = 8y .....(❶)

According to given question,

The age of father after 10 years = x + 10

The age of son after 10 years = y + 10

Father will be three times as old as his son.

→ 3(y + 10)

Now,

→ x + 10 = 3(y + 10)

→ x + 10 = 3y + 30

→ x - 3y = 30 - 10

→ x - 3y = 20 .....(❷)

Now, put the value of equation (❶) in equation (❷)

→ 8y - 3y = 20

→ 5y = 20

→ y = 20/5

→ y = 4

Now, put the value of y in equation (1)

→ x = 8y

→ x = 8 * 4

→ x = 24

Therefore,

• Present age of father = x = 24 years
• Present age of son = y = 4 years

║Hence, the present age of father is 24 years, and the present age of son is 4 years.║