The product of the ages of Swati and Aparna is 120. If thrice the age of Aparna is more than Swati’s age by 2 years, find the age of Swati.

Let the ages of Swati and Aparna be x and y respectively.

The product of the ages of Swati and Aparna = xy = 120 ----- (1)

According to the given information,

3y = x + 2

⇒ x = 3y – 2

Substitute the above value of x in (1).

⇒ (3y – 2) × y = 120

⇒ 3y2 – 2y – 120 = 0

⇒ 3y2 + 18y – 20y – 120 = 0

⇒3y(y + 6) – 20(y + 6) = 0

⇒ (y + 6)(3y – 20) = 0

⇒ y = -6 or y = 20/3

(? Age can’t be negative)

⇒ y = 20/3

x = 3 × (20/3) – 2 = 20 – 2 = 18

∴ Age of Swati = 18 years