The age of a father will be double the age of his son ten years later. 10 years ago, the father’s age was six times the age of the son. How many years from now, the ratio of their ages will be 3 : 2?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 35.
Let the current age of father and son be F and S respectively
Ten years later, the father's age will be double the son's age
⇒ F + 10 = 2(S + 10)
⇒ F + 10 = 2S + 20
⇒ F = 2S + 10...(1)
Now,
Ten years ago, the father's age was six times the son's age
⇒ F - 10 = 6(S - 10)
⇒ F - 10 = 6S - 60
⇒ F = 6S - 50....(2)
From eq 1 and 2
⇒ 2S + 10 = 6S - 50
⇒ 4S = 60
⇒ S = 15
Putting in eq 1
⇒ F = 2 × 15 + 10
⇒ F = 30 + 10
⇒ F = 40
Let x years from now be the time when the ratio of their ages will be 3 : 2
⇒ (40 + x)/(15 + x) = 3/2
⇒ 2(40 + x) = 3(15 + x)
⇒ 80 + 2x = 45 + 3x
⇒ 3x - 2x = 80 - 45
⇒ x = 35
The ratio of their ages will be 3 : 2, 35 years from now