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

Question

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 now?

Accepted Answer

Let Nuri's present age = $x$ years
Let Sonu's present age = $y$ years Five years ago: Nuri's age = $(x - 5)$ years Sonu's age = $(y - 5)$ years 
According to the problem: $$x - 5 = 3(y - 5)$$ $$x - 5 = 3y - 15$$ $$x - 3y = -10 \quad 	ext{--- (1)}$$ Ten years later: Nuri's age = $(x + 10)$ years Sonu's age = $(y + 10)$ years 
According to the problem: $$x + 10 = 2(y + 10)$$ $$x + 10 = 2y + 20$$ $$x - 2y = 10 \quad 	ext{--- (2)}$$ Solving the equations:
Subtract equation (1) from equation (2): $$(x - 2y) - (x - 3y) = 10 - (-10)$$ $$y = 20$$ 
Substitute $y = 20$ into equation (2): $$x - 2(20) = 10$$ $$x - 40 = 10$$ $$x = 50$$ Final Answer: Nuri's present age is 50 years and Sonu's present age is 20 years.

Pair of Linear Equations in Two Variables

❓ Sibling Questions in this Chapter