Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri

1.	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» Given: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. To find: The age of Nuri and Sonu. Solution: Let the present age of Nuri and his son be ‘a’ and ‘b’ respectively. Given, Five years ago, Nuri was thrice as old as Sonu. This implies age of Nuri and Sonu five years ago was a - 5 and b - 5. ⇒ a – 5 = 3(b – 5) ⇒ a - 5 = 3b – 15 ⇒ a = 3b – 15 + 5 ⇒ a = 3b – 10 ------- (1) Ten years later, Nuri will be twice as old as Sonu. This implies after ten years the age of Nuri and Sonu will be a + 10 and b + 10. ⇒ a + 10 = 2(b + 10) ⇒ a + 10 = 2b + 20 ⇒ a = 2b + 20 - 10 ⇒ a = 2b + 10 -------- (2) Equating (1) and (2), we get 3b – 10 = 2b + 10 ⇒ 3b - 2b = 10 + 10 b = 20 Thus, a = 60 – 10 = 50 Hence, Nuri's present age is 50 years and Sonu's age is 20 years.

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»

Given:

Five years ago, Nuri was thrice as old as Sonu.

Ten years later, Nuri will be twice as old as Sonu.

To find:

The age of Nuri and Sonu.

Solution:

Let the present age of Nuri and his son be ‘a’ and ‘b’ respectively.

Given,

Five years ago, Nuri was thrice as old as Sonu.

This implies age of Nuri and Sonu five years ago was

a - 5 and b - 5.

⇒ a – 5 = 3(b – 5)

⇒ a - 5 = 3b – 15

⇒ a = 3b – 15 + 5

⇒ a = 3b – 10 ------- (1)

Ten years later, Nuri will be twice as old as Sonu.

This implies after ten years the age of Nuri and Sonu will be

a + 10 and b + 10.

⇒ a + 10 = 2(b + 10)

⇒ a + 10 = 2b + 20

⇒ a = 2b + 20 - 10

⇒ a = 2b + 10 -------- (2)

Equating (1) and (2), we get

3b – 10 = 2b + 10

⇒ 3b - 2b = 10 + 10

b = 20

Thus,

a = 60 – 10 = 50

Hence, Nuri's present age is 50 years and Sonu's age is 20 years.