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Solution


Q.

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

Ans.

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

⇒ x + 10 = 2y + 20

⇒ x = 2y + 10 ...(ii)

From eqs (i) and (ii), we get 3y – 6 = 2y + 10

⇒ y = 16

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

x = 3 × 16 – 6 = 48 – 6 = 42

Thus, the age of Rashmi is 42 years and age of Nazma is 16 years.