Question

Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now? 

Answer 1

Let the age of Rashmi = x years

and the age of Nazma = y years

Three years ago,

Rashmi's age = (x − 3) years

Nazma's age = (y − 3) years

According to the question,

(x − 3) = 3(y − 3)

⇒ x − 3 = 3y − 9

⇒ x = 3y − 6      ...(i)

Ten years later,

Rashmi's age = x + 10

Nazma's age= y + 10

According to the question,

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

x + 10 = 2y + 20

x = 2y + 10      ...(ii)

From eq. (i) and (ii), we get

3y − 6 = 2y + 10

y = 16

Substituting the value of y in eq. (i), we get

x = 3 × 16 − 6 = 48 − 6 = 42

Thus, Rashmi is 42 years old, and Nazma is 16 years old.