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Two years ago, a father was five times as old as his son. Two years later, his age will be 8 years more than three times the age of the son. Find the present ages of father and son.

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The father’s age is 52 and the son’s age is 15

The father’s age is 62 and the son’s age is 12

The father’s age is 42 and the son’s age is 10

The father’s age is 32 and the son’s age is 16

answer is C.

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Detailed Solution

It is given that two years ago, father was five times as old as his son.
It is also given that two years later, his age will be 8 years more than three times the age of the son.
Let the age of father be

x

years and the age of son be

y

years.
As before two years father was five times as old as his son,

⇒ x − 2 = 5 (y − 2) ⇒ x − 2 = 5 y − 10 ⇒ x − 5 y = − 8..... (1)

As after two years, his age will be 8 years more than three times the age of the son,

⇒ x + 2 = 3 (y + 2) + 8 ⇒ x + 2 = 3 y + 6 + 8 ⇒ x − 3 y = 14 − 2 ⇒ x − 3 y = 12..... (2)

Subtracting the eq. (2) from (1),

⇒ x − 5 y − (x − 3 y) = − 8 − 12 ⇒ x − 5 y − x + 3 y = − 20 ⇒ − 2 y = − 20 ⇒ y = 10

Substituting the value of y in eq. (1),

⇒ x − 5 y = − 8 ⇒ x − 5 (10) = − 8 ⇒ x − 50 = − 8 ⇒ x = 50 − 8 ⇒ x = 42

Therefore, the father’s age is 42 and the son’s age is 10.
Hence, the correct option is 3.

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