Sunita's age at present is 2 years less than 6 times the age of her daughter Anita. The product of their ages 5 years later will be 330. What was the age of Sunita when her daughter Anita was born?

Let present age of Anita be x yrs.

∵ sunita’s age is 2 yrs less than 6 times age of Anita.

⇒ Present age of Anita = (6x – 2) yrs.

∴ five yrs later age of Anita will be – (x + 5)yrs.

And age of Sunita = (6x – 2) + 5 yrs

= 6x + 3 years.

⇒ (x + 5)(6x + 3) = 330

⇒ 6x² + 33x + 15 = 330

⇒6x² + 33x – 315 = 0

Dividing the whole equation by 3, we get –

⇒2x² + 11x – 105 = 0

⇒2 + (21 – 10)x – 105 = 0

⇒2x² + 21x – 10x – 105 = 0

⇒x(2x + 21) – 5(2x + 21) = 0

⇒ (2x + 21)(x – 5) = 0

⇒ 2x + 21 = 0 or x – 5 = 0

But age cannot be negative

⇒ x = 5 years.

∴ present age of Anita = 5 yrs.

And present age of Sunita = 6x – 2

= 6(5) – 2

= 28 years.

And, ∵ Anita was born five years ago,

⇒ Age of Sunita at that time = 28 – 5 yrs.

= 23 yrs.