Question

six years from now aamir's age will be three-seventh of his father's age. ten years ago the ratio of their ages was 1:5. what is aamir's father's age at present?

Answer 1

let Aamir father's age at present = X
and Aamir age =y
10 years ago,
$\frac{y - 10}{x - 10 } = \frac{1}{5}$
it means , 5y-x=40 ----eq. 1
after 6years,
$y + 6 = (x + 6) \times \frac{3}{7}$
it means 7y-3x= -24 ------eq. 2
solving equations. 1 and 2 , we get, y=18 and X= 50

Answer 2

Let the common ratio be 'x'.

10 years ago:

⇒ Age of Aamir = x + 10.

⇒ Age of his father = 5x + 10.

6 years hence:

⇒ Age of aamir = x + 16.

⇒ Age of his father = 5x + 16.

Now,

Given that Aamir's age will be three-seventh of his father's age.

⇒ x + 16 = (3/7)[5x + 16]

⇒ 7x + 16 = 3[5x + 16]

⇒ 7x + 112 = 15x + 48

⇒ 8x = 64

⇒ x = 8

Then:

⇒ 5x + 10

⇒ 50.

Therefore:

⇒ Aamir's present age = 8 years.

⇒ Age of his father = 50 years.

Hope it helps!