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?

Question

Form the pair of linear equations for the following problems and find their solution by 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?

Answer 1

Let the present age of Nuri = x yr

And the present age of Sonu = y yr

Five years ago,

Nuri’s age = (x – 5)yr

Sonu’s age = (y – 5)yr

According to the question,

(x – 5) = 3(y – 5)

⇒ x – 5 = 3y – 15

⇒ x – 3y = – 10 …(i)

After ten years,

Aftab’s age = (x + 10)yr

Daughter’s age = (y + 10)yr

According to the question,

(x + 10) = 2(y + 10)

⇒ x + 10 = 2y + 20

⇒ x – 2y = 10 …(ii)

Now, we can solve this by an elimination method

On subtracting Eq. (ii) from (i) we get

x – 2y – x + 3y = 10 – ( – 10)

⇒ – 2y + 3y = 10 + 10

⇒ y = 20

On putting y = 20 in Eq. (i) we get

x – 3(20) = – 10

⇒ x – 60 = – 10

⇒ x = 50

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