Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Given :
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu.
To do :
We have to find the present ages of Nuri and Sonu.
Solution :
Let the ages of Nuri and Sonu be $x$ and $y$ respectively.
This implies,
Age of Nuri 5 years ago $= x-5$ years.
Age of Sonu 5 years ago $= y-5$ years.
Age of Nuri after 10 years $= x+10$ years.
Age of Sonu after 10 years $= y+10$ years.
According to the question,
$x+10=2(y+10)$
$x+10=2y+20$
$x=2y+20-10$
$x=2y+10$.....(i)
$x-5=3(y-5)$
$x-5=3y-15$
$3y=(2y+10)+15-5$ (From (i))
$3y=2y+10+10$
$3y-2y=20$
$y=20$
$\Rightarrow x=2(20)+10=40+10=50$
The present ages of Nuri and Sonu are 50 years and 20 years respectively.
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