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Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

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28

years

30

years

32

years

34

years

answer is B.

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Detailed Solution

It is given a man's age will be three times the age of his son and three years ago he was nine times as old as his son.
Let the present age of man be

x

years and the present age of son be

y

years,
After six years,
Man's age =

(x + 6)

years
Son's age =

(y + 6)

years
According to the condition,

\Rightarrow x + 6 = 3 (y + 6)

\Rightarrow x - 3 y = 12

\Rightarrow x = 12 + 3 y

. . . (1)

Three years ago,
Man's age =

(x - 3)

years
Son's age =

(y - 3)

years
According to the condition

\Rightarrow x - 3 = 9 (y - 3)

\Rightarrow x - 9 y = - 24

. . . (2)

Put the value of

x

(2),

\Rightarrow 12 + 3 y - 9 y = - 24

\Rightarrow y = 6

Put the value of

y

(1)

x - 3 \times 6 = 12

\Rightarrow x = 30

So, Man's age = 30 years.
Therefore, the present age of man is 30 years.
Hence, correct option is 2.

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