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Six years ago, a man was three times as old as his son. In 6 years time, he will be twice as old as his son. Find their present ages.

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30, 15

40, 20

42, 18

41, 19

answer is C.

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Detailed Solution

Let the present age of man and his son be x years and y years respectively.
Six years ago,
The age of man

= x - 6

The age of his son

= y - 6

According to the question,
x - 6 = 3(y – 6)
x – 6 = 3y – 18
x – 3y = -12 ….(i)
Six year later,
The age of man =

x + 6

The age of his son =

y + 6

⇒

x + 6 = 2 (y + 6)

x + 6 = 2y + 12
x – 2y = 6 …(ii)
Subtracting eq (i) from (ii), we get
x – 2y – x + 3y = 6 + 12
y = 18
Thus, x = 6 + 2(18) = 42
Hence, the age of man is 42 years and age of son is 18 years.
Therefore, 3 is the correct option.

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