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After five years the age of a father will be thrice the age of his son whereas five years ago, he was seven times old as his son was.What is father's present age?30 years40 years50 yearsNone of these

Question

After five years the age of a father will be thrice the age of his son whereas five years ago, he was seven times old as his son was.What is father's present age?30 years40 years50 yearsNone of these

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Solution

Let's denote the present age of the father as F and the present age of the son as S.

From the problem, we have two conditions:

  1. After five years the age of a father will be thrice the age of his son. This can be written as: F + 5 = 3 * (S + 5)

  2. Five years ago, he was seven times old as his son was. This can be written as: F - 5 = 7 * (S - 5)

Now we have a system of two equations. We can solve it step by step.

First, let's simplify both equations:

  1. F + 5 = 3S + 15 => F - 3S = 10
  2. F - 5 = 7S - 35 => F - 7S = -30

Now we can subtract the second equation from the first one:

(F - 3S) - (F - 7S) = 10 - (-30)

This simplifies to:

4S = 40

So, S = 40 / 4 = 10 years old.

Substitute S = 10 into the first equation:

F - 3 * 10 = 10 => F = 10 + 30 = 40 years old.

So, the father's present age is 40 years.

This problem has been solved

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