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A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.

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Present age of father is

44

years and Present age of son is

20

years

Present age of father is

42

years and Present age of son is

18

years

Present age of father is

60

years and Present age of son is

36

years

Present age of father is

48

years and Present age of son is

24

years

answer is B.

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Detailed Solution

It is given a man 24 years older than his son.
Let the present age of father and son be

x

and

y

years respectively.
According to question,

x = y + 24

\Rightarrow x - y = 24 . . . . . . (1)

12

years ago,

(x - 12) = 5 (y - 12)

\Rightarrow x - 12 = 5 y - 60

\Rightarrow x - 5 y = - 60 + 12

\Rightarrow x - 5 y = - 48 . . . . . . (2)

On subtracting

(1)

from

(2)

, we get,

(x - x) + (- 5 y + y) = - 24 - 48

\Rightarrow - 4 y = - 72

\Rightarrow y = 18

Substituting this value of

y

(1)

, we get,

x - 18 = 24

\Rightarrow x = 24 + 18 = 42

Therefore, the present age of the father is

42

years and the present age of the son is

18

years.
Hence, correct option is 2.

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A man is 24 years older than his son. 12 years ago, he was five times as old as his son. Find the present ages of both.

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