Question

At present age of father and his son are in the ratio 7:3 and they will in the ratio 2:1 after 10 years then present age of father is
a)42
b)56
c)70
d)77

Answer 1

Solution :

Ratio of present age of father and his son = 7 : 3

Let the age of fathere be 7x years and the age of son be 3x years

After 10 years :

• Age of father = (7x + 10) years
• Age of son = (3x + 10) years

Ratio of ages of father and his son after 10 years = 2 : 1

$\implies \dfrac{7x + 10}{3x + 10} = \dfrac{2}{1}$

By cross multiplication

⇒ 1(7x + 10) = 2(3x + 10)

⇒ 7x + 10 = 6x + 20

⇒ 7x - 6x = 20 - 10

⇒ x = 10

Present age of father = 7x = 7 * 10 = 70 years

Hence, the present age of father is (C) 70 years.

Answer 2

The present age of father is 70 years. (Option c)

Given: Ratio of present ages of father and his son = 7 : 3

          Ratio of their ages after 10 years = 2 : 1

To find: Present age of father

Let: Present age of father be $7x$ and present age of son be $3x$

Solution: According to the given question and assumption made,

If present ages of father and son are  $7x$ and $3x$ respectively, then

father's age after 10 years =   $7x$ + 10

son's age after 10 years =  $3x$ + 10

Given that ratio of their ages after 10 years is 2 : 1

i.e.,

⇒ $\frac{7x + 10}{3x + 10} = \frac{2}{1}$

Using cross multiplication:

⇒ $1(7x + 10) = 2 (3x + 10)$

⇒ $7x + 10 = 6x + 20$

⇒ $7x - 6x = 20 - 10$

⇒ $x = 10$

Hence,

Present age of father ( $7x$ ) = 7*10 = 70 years

Present age of son ( $3x$ ) = 3*10 = 30 years

Project code - #SPJ3