Mr. Ranjan is seven times as old as his son. 10 years hence, he will be three times as old as his son. Find their ages.
Given :
Mr. Ranjan is seven times as old as his son. 10 years hence, he will be three times as old as his son.
To find :
We have to find their present ages.
Solution :
Let the present ages of the son and the father be $x$ and $y$ respectively.
This implies,
Age of the son after 10 years $= x+10$
Age of the father after 10 years $= y+10$.
According to the question,
$y=7x$.....(i)
Therefore,
$y+10 = 3(x+10)$
$y+10 = 3x+30$
$y = 3x+30-10$
$7x = 3x+20$ [From (i)]
$7x-3x=20$
$4x=20$
$x=\frac{20}{4}$
$x=5$
$\Rightarrow y=7(5)=35$
The present age of the son is $5$ years and the present age of Mr. Ranjan is $35$ years.
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