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Q.

A man is thrice as old as his son. Five years ago, the man was four times as old as his son. What are the present ages of the son and the man respectively?

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a

13 years, 40 years

b

15 years, 45 years

c

16 years, 46 years

d

17 years, 50 years

answer is B.

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Detailed Solution

It is given that, a man is thrice as old as his son and five years ago, the man was four times as old as his son.
Let x years be the present age of the son.
Then, 3x years is the present age of the man.
Five years ago, the age of the son = (x – 5) years.
Five years ago, the age of the man = (3x – 5) years.
Given that,
3x – 5 = 4(x – 5)
On simplifying,
3x – 5 = 4x – 20
3x – 4x = – 20 + 5
– x = – 15
x = 15
Therefore,
3x = 3×15 = 45
Hence, 15 years is the present age of the son and 45 years is the present age of the father.
Therefore, option 2 is correct.

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A man is thrice as old as his son. Five years ago, the man was four times as old as his son. What are the present ages of the son and the man respectively?