Correct Answer - Option 4 : 54
Given :
The sum of ages of a father and son = 45 years
Five years ago, the product of their ages was four times the father's age at that time.
calculation :
Let the age of father be (a) years and age of his son be (45 - a) years,
Five years ago,
Age of father = (a - 5) years
Age of his son = (45 - a - 5) years = (40 -a) years
According to the question,
Product of their ages five years ago = 4 × father's age five years ago
⇒ (a - 5) (40 - a) = 4(a - 5)
⇒ (a - 5) (40 - a) = 4(a - 5)
⇒ 40 - a = 4
⇒ 40 - 4 = a
⇒ 36 = a
Hence,
Present age of father = a years = 36 years
Present age of his son = (45 - a) = (45 -36) = 9 years
Difference between of father's age and son's age = 36 - 9 = 27
∴ The twice the difference, of father and son's age is 2 × 27 = 54
