Question

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Nuri's age is _____

• A. $50$
• B. $60$
• C. $40$
• D. $30$

Answer 1

The correct option is A $50$

Let the age of Sonu be $x$ and the age of Nuri be $y$.
Age of Nuri five years ago $\Rightarrow (x-5)$
Age of Sonu five years ago $\Rightarrow (y-5)$
Age of Nuri ten years later $\Rightarrow (x+10)$
Age of Sonu ten years later $\Rightarrow (y+10)$
Given:
Five years ago Nuri was thrice as old as Sonu. This implies,
$3(x-5)=y-5$
$\Rightarrow 3x-15=y-5$
$\Rightarrow 3x-y=10......\left(1\right)$
Also, given:
Ten years later Nuri will be twice as old as Sonu. This implies,
$2(x+10)=y+10$
$\Rightarrow 2x+20=y+10$
$\Rightarrow 2x-y=-10......\left(2\right)$
$\left(1\right)-\left(2\right)\Rightarrow x=20$
Substitute the value of $x$ in $\left(1\right)$
$\Rightarrow 3\left(20\right)-y=10$
$\Rightarrow 60-y=10$
$\Rightarrow y=50$
Therefore, the age of Nuri is $50$ years.