Question

The sum of ages of a Father and his son is 60 years . Ten years from now , ratio of their ages would be 5:11. Find their present ages

Answer 1

please refer to the attachment

Hope it will help you

Answer 2

The Main Answer is: The present age of the son is 15 years

                                   The present age of the father is 45 years

Given: Sum of the present ages of the father and son is 60 years.

           After 10 years, the ratio of their ages is 5:11

To Find: The present ages of the father and son

Solution:

Let the present age of the son be 'x' years.

Let the present age of the father be 'y' years.

According to the question:

x  + y = 60

y = 60 - x -------(1)

After 10 years-

Age of the son = x + 10 years

Age of the father = y + 10 years

According to the question-

$\frac{x + 10}{y + 10} = \frac{5}{11}$ ----- (2)

⇒ 11(x+10) = 5(y+10)

⇒ 11x + 110 = 5y + 50

⇒ 11x - 5y = -60 --------(3)

Put (1) in (3)

⇒ 11x - 5(60-x) = -60

⇒ 11x - 300 + 5x = -60

⇒ 16x = 240

⇒ x = 15 --------(4)

Put (4) in (1)

y = 60 - 15 = 45

⇒ y = 45 -------(5)

From (4) and (5)

∴ The Present age of the son is 15 years

  The Present age of the father is 45 years

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