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?

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 04 Jul, 2024 Shift 3)

Answer 1

Given:

10 years later, father's age = 2 × son's age

10 years ago, father's age = 6 × son's age

Formula used:

Let father's current age be F and son's current age be S.

F + 10 = 2(S + 10) ...(i)

F - 10 = 6(S - 10) ...(ii)

Calculations:

From equation (i):

⇒ F + 10 = 2S + 20

⇒ F = 2S + 10 ...(iii)

From equation (ii):

⇒ F - 10 = 6S - 60

⇒ F = 6S - 50 ...(iv)

Equating (iii) and (iv):

⇒ 2S + 10 = 6S - 50

⇒ 60 = 4S

⇒ S = 15

Substituting S in (iii):

⇒ F = 2(15) + 10

⇒ F = 40

Let the number of years from now be x:

(F + x) / (S + x) = 3/2

⇒ (40 + x) / (15 + x) = 3/2

⇒ 2(40 + x) = 3(15 + x)

⇒ 80 + 2x = 45 + 3x

⇒ 80 - 45 = 3x - 2x

⇒ 35 = x

∴ The correct answer is option (2).

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