At the time of marriage the average age of a couple was 28 years and the age of husband was 30 years at the time of marriage. The age ratio of father and son’s age to the age ratio of Mother and Son’s age is 17 : 15. How many years after the marriage son was born?

At the time of marriage the average age of a couple was 28 years and the age of husband was 30 years at the time of marriage. The age ratio of father and son’s age to the age ratio of Mother and Son’s age is 17 : 15. How many years after the marriage son was born? Correct Answer 2 years

GIVEN:

(i) Average age at the time of marriage was 28 years

(ii) Age of husband at the time of marriage was 30 years

(iii) (Father + son) : (Mother + son) = 17 : 15

CONCEPT:

(i) Addition of P people’s age after N years increase by = P × N

(ii) The difference of age never changes along with the time.

FORMULA USED:

(i) Average = Sum of terms/number of terms

CALCULATIONS:

At the time of marriage the average age of the couple was 28 years and the age of husband (A) was 30 years,

Let the age of wife at the time of marriage be B

⇒ Average = sum of terms/number of terms

⇒ 28 = (30 + B)/2

⇒ 28 × 2 = 30 + B

⇒ 56 = 30 + B

⇒ B = 56 – 30 = 26 years at the time of marriage.

⇒ Difference of age = 30 – 26 = 4 years. This won’t be changed over time.

Let the age of their son be P years now

⇒ (A + P) : (B + P) = 17 : 15,

⇒ (A + P) = 17x,

⇒ (B + P) = 15X,

⇒ (A + P) – (B + P) = (A – B) = 4

⇒ 17x – 15x = 2x

⇒ 2x = 4,

⇒ x = 2

⇒ (A + P) = 17x = 34 years

Which mean

(A) After 1 year of marriage they will have a 3 year Son.

(B) After 2 years of marriage they will have a 2 year Son.

(C) After 3 years of marriage they will have a 1 year Son.

⇒ Conclusion (A) and (B) is practically not possible. So after 3 years, they will have 1 year Son.