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Question

A father tells his son, five years ago, I was seven times as old as you were. After five years from the present time, I will be three times as old as you will be. Find their present ages.

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Solution

Let x be the age of the son before 5 years.

Then age the father 5 years ago =7x

At present,

Age of son =x+5

Age of father =7x+5

5 years later from the present time:

Age of son =x+5+5=x+10

Age of father =7x+5+5=7x+10

It is given that, father is 3 times as old as his son after 5 years from the present time.

⇒7x+10=3(x+10)

⇒7x+10=3x+30

⇒7x−3x=30−10

⇒4x=20

x=204

⇒x=5

The present age of son =x+5=5+5=10 years

The present age of father =7x+5=7(5)+5=40 years

∴ The father's age is 40 years and the son's age is 10 years old.

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