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in Quadratic Equations by (46.1k points)
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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

1 Answer

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Best 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

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