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Question

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
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B
32 years
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C
24 years
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D
42 years
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Solution

The correct option is C 24 years
Let the daughter's age be x years.
Hence, mother's age will be (x+21) years
Now, x(21+x)12=x+2118=x+3
x(21+x)=12x+36
21x+x2=12x+36
x2+9x36=0
(x3)(x+12)=0
Since age can only be positive, so x=3.
Thus mother's age is 21+3=24 years.

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