Question

40. Raja's age is four times the combined age of his two sons. One of his son is three
times as old as the other. In 24 years, the combined ages of the sons will be 12 years
less than their father's age. What are their respective ages?solve the problem ​

Answer 1

Answer:-

Let the age of younger son be "Y".

Age of the elder son = 3Y.

4 * Sum of their ages = Father's age

4 ( Y + 3Y) = Father's age

Father's age = 16Y.

given that, In 24 years the combined ages of the sons will be 12 years less than their father's age.

So,

Combined ages of Sons in 24 years = (Y + 24 + 3Y + 24) = 4Y + 48. -- equation (1)

Father's age in 24 years = 16Y + 24

Combined ages of Sons = 16Y + 24 - 12

= 16Y + 12 -- equation (2)

Equate both the situations,

4Y + 48 = 16Y + 12

48 - 12 = 16Y - 4Y

12Y = 36

Y = 3

Therefore,

Age of younger son = Y = 3 years

Age of elder son = 3Y = 3(3) = 3 years

Age of father = 16Y = 16(3) = 48 years