(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