Question

Arun’s age is one third the age of his father. 15 years hence, he will be one half of the age of his father. Determine their present ages.

Answer 1

SOLUTION:-

Let x be the age of Arun and y be the of his father.

According to 1st Condition:-

Arun’s age is one third the age of his father.

=> x = 1/3 × y .....1

According to the 2nd condition:-

15 years hence, he will be one half of the age of his father.

After 15 year

Aruns age = (x + 15) = (y/3 + 15)...2..from 1

farhers age = (y + 15)

•°• y/3 + 15 = 1/2 × (y + 15)

•°• (45 + y)/3 = (y + 15)/2

=> 2(45 + y) = 3(y + 15)

=> 90 + 2y = 3y + 45

=> 90 - 45 = 3y - 2y

=> 45 = y

•°• y = 45

Substituting y = 45 in eq 1

•°• x = 1/3 × 45

=> x = 15

The present age of arun is 15 years and present age of his father is 45 years .