Question
Fri March 01, 2013 By:

# At present Asha's age is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Sat March 02, 2013
Let Asha's age be x and Nisha's age be y

so, x = 2+y2
After N years, which is equal to (x - y) years, Asha's age would be x+(x-y) = 2x-y
while Nisha's age would be y+(x-y) = x

And, so, 2x-y = 10y-1
2x = 11y -1
Substituting for x
2(2+y2) = 11y-1
4+2y2 = 11y -1
2y2-11y +5 = 0
(2y-1)(y-5) = 0
y = 1/2 or y = 5 years
x = 9/4 or y = 27 years

Since, ages would preferentially be in whole numbers, Asha's and Nisha's present ages are 25 and 5 years respectively.
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