Question

Raman’s age is three times the sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman.

Answer 1

Let Raman’s age be “x” years and the sum of the ages of two sons be “y” years.

By the given first condition

x = 3y

x – 3y = 0 → (1)

After 5 years Raman’s age is x + 5 years

Sum of sons age is (y + 10) years ...(each son age increases by 5 years)

By the given second condition

x + 5 = 2(y + 10)

x + 5 = 2y + 20

x – 2y = 20 – 5

x – 2y = 15 → (2)

Equation (1) becomes

x = 3y

Substitute the value of x in (2)

3y – 2y = 15

y = 15

Substitute the value of y = 15 in x = 3y

x = 3(15)

x = 45

∴ Raman’s age = 45 years