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

Let Anita's age be x. Sunita's age is 6x - 2. Five years later, their ages are x+5 and 6x+3. Their product is (x+5)(6x+3) = 330. Solving 6x^2 + 33x + 15 = 330 leads to 6x^2 + 33x - 315 = 0, or 2x^2 + 11x - 105 = 0. Factoring gives (2x + 21)(x - 5) = 0, so x = 5. Sunita's present age is 6(5) - 2 = 28. When Anita was born (5 years ago), Sunita was 28 - 5 = 23.