Question

Raja's age is one fifth of his father's age. After 6 years ,his age will be one third his father's age .how old they are now?

Answer 1

Let the age of Raja be a

Father's age = 5a

After 6 years

Raja's age = a + 6

Father's age = 5a + 6


According to question

3(a+6) = 5a + 6

=> 3a + 18 = 5a +6

=> 18-6 = 5a - 3a

=> 2a = 12

=> a = 6

Raja's age = 6 years

Father's age = 30 years

Answer 2

Let the Raja's age be x
and Father's age be y


x = y/5 ....( i )


After 6 years

Raja's age :- x + 6
Father's age :- y + 6


x + 6 = ( y + 6 )/3

3x + 18 = y + 6

3x - y = 6 - 18

3x - y = - 12 ....( ii )


Putting value of x in ( ii )

3x - y = - 12

3 × y/5 - y = - 12

3y /5 - y = - 12

( 3y - 5y )/5 = - 12

- 2y = - 60

y = 30


Putting in ( i )

x = y /5

x = 30/5

x = 6

Raja's age is 6 years
and his father's age 30 years.