Question

Form the pair of linear equation in the following problem, and find its solutions (if they exist) by the elimination method:

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?

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?

Answer 1

Let, present the age of Nuri = x years

Let, Sonu's present age = y years

five years ago

Nuri’s age = x - 5 years

Sonu's age = y - 5 years

x - 5 = 3(y - 5)

x – 3y = -10          ...(1)

ten years later

Nuri’s age = x + 10 years

Sonu's age = y + 10 years

x + 10 = 2(y + 10)

x – 2y = 10         ...(2)

By subtracting equation (2) from equation (1)

(x – 3y = -10) – (x – 2y = 10)

y = 20

Putting the value of y in equation (1)

x = 50

Hence, the present age of Nuri is 50 years and the present age of Sonu is 20 years.