The difference of mother's age and her daughter's age is 21 years and

1.	The difference of mother's age and her daughter's age is 21 years and the twelfth part of the product of their ages is less than the mother's age by 18 years. The mother's age is : (a) 22 years (b) 32 years (c) 24 years (d) 42 years
Answer» (c) 24 years Let the daughter's age be x years. Then, the mother's age = (\(x\) + 21) years According to the question, (\(x\) + 21) \(-\frac1{12}\) x \(x\) x (\(x\) + 21) = 18 ⇒ 12(x + 21 ) - (x² + 21x) = 216 ⇒ 12x + 252 - x² - 21x = 216 ⇒ x² + 9x - 36 = 0 ⇒ (x + 12 )(x - 3) = 0 ⇒ x = -12 , 3 Rejecting negative value, daughter's age = 3 years ∴ Mother's age = 24 years

The difference of mother's age and her daughter's age is 21 years and the twelfth part of the product of their ages is less than the mother's age by 18 years. The mother's age is : (a) 22 years (b) 32 years (c) 24 years (d) 42 years

Answer»

(c) 24 years

Let the daughter's age be x years. Then, the mother's age = (\(x\) + 21) years

According to the question,

(\(x\) + 21) \(-\frac1{12}\) x \(x\) x (\(x\) + 21) = 18

⇒ 12(x + 21 ) - (x² + 21x) = 216

⇒ 12x + 252 - x² - 21x = 216

⇒ x² + 9x - 36 = 0

⇒ (x + 12 )(x - 3) = 0

⇒ x = -12 , 3

Rejecting negative value, daughter's age = 3 years

∴ Mother's age = 24 years