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Question
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
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Solution
Let the present age of the Mother be M years and her daughter age be D years.
Then, as per the question description,
M = D2 ...... (i)
(M + 4) = 4(D + 4) ...... (ii)
Putting (ii) in (i) above, we get
D2 + 4 = 4D +16
⇒ D2 - 4D -12 = 0
⇒ D2 - 6D + 2D - 12 = 0
⇒ D(D-6 )+ 2(D-6)=0
⇒ (D+ 2)(D-6)=0
⇒ D= -2, D = 6 (Age cannot be negative)
⇒ D =6 years and hence, M =36 years
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