Correct Answer - Option 2 : 25, 10; 4 ∶ 3
Given∶
Before 5 years’ father was 4 times as old as his son.
After 5 years father will be 2 times as old as his son.
Formula Used∶
Concept of Linear Equations, Elimination Method.
Calculation∶
Let father’s present age be ‘x’ years and son’s present age be ‘y’ years.
Five years’ ago,
Father’s age = (x – 5) years
Son’s age = (y – 5) years
So, (x – 5) = 4(y – 5)
⇒ x – 4y = - 15 ----(1)
Five years later, father’s age = (x + 5) years and son’s age = (y + 5) years
So, (x + 5) = 2(y + 5)
⇒ x – 2y = 5 (2)
Subtracting eq. (2) from (1), we get
-2y = -20
⇒ y = 10
put y = 10 in eq (1)
x – 4(10) = - 15
⇒ x = 40 – 15
⇒ x = 25
After 35 years father’s age will be 60 years = 25 + 35 = 60 years
So, Son’s age after 35 years = 10 + 35 = 45 years
Hence, Ratio of their ages when father’s age will be 60 years = 60/45 = 4 ∶ 3
∴ Father’s present age is 25 years and Son’s age is 10 years and the required ratio is 4 ∶ 3.