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?

Q: 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?

Let Nuri's present age = $x$ years\nLet Sonu's present age = $y$ years Five years ago: Nuri's age = $(x - 5)$ years Sonu's age = $(y - 5)$ years \nAccording to the problem: $$x - 5 = 3(y - 5)$$ $$x - 5 = 3y - 15$$ $$x - 3y = -10 \quad \text{--- (1)}$$ Ten years later: Nuri's age = $(x + 10)$ years Sonu's age = $(y + 10)$ years \nAccording to the problem: $$x + 10 = 2(y + 10)$$ $$x + 10 = 2y + 20$$ $$x - 2y = 10 \quad \text{--- (2)}$$ Solving the equations:\nSubtract equation (1) from equation (2): $$(x - 2y) - (x - 3y) = 10 - (-10)$$ $$y = 20$$ \nSubstitute $y = 20$ 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.

Question

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.

CBSE · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesFive 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?