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?
Let the present age of Nuri be x years and the present age of Sonu be y years.
After 10 years, Nuri’s age will be(x + 10) years and the age of Sonu will be(y + 10) years. Thus using the given information, we have
$x+10=2(y+10)$
$\Rightarrow x+10=2 y+20$
$\Rightarrow x-2 y-10=0$
Before 5 years, the age of Nuri was(x – 5)years and the age of Sonu was(y – 5)years. Thus using the given information, we have
$x-5=3(y-5)$
$\Rightarrow x-5=3 y-15$
$\Rightarrow x-3 y+10=0$
So, we have two equations
$x-2 y-10=0$
$x-3 y+10=0$
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
$\frac{x}{(-2) \times 10-(-3) \times(-10)}=\frac{-y}{1 \times 10-1 \times(-10)}=\frac{1}{1 \times(-3)-1 \times(-2)}$
$\Rightarrow \frac{x}{-20-30}=\frac{-y}{10+10}=\frac{1}{-3+2}$
$\Rightarrow \frac{x}{-50}=\frac{-y}{20}=\frac{1}{-1}$
$\Rightarrow \frac{x}{50}=\frac{y}{20}=1$
$\Rightarrow x=50, y=20$
Hence, the present age of Nuri is 50 years and the present age of Sonu is 20 years.
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