At present Asha's age (in years) 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.

Explanation

Let Nisha's present age be `x` yr.
Then, Asha's present age `=x^(2)+2` [by given condition]
Now, when Nisha grows to her mother's present age i.e. after `{(x^(2)+2)-x}`yr. Then,
Asha's age also increased by `[(x^(2)+2)-x]yr`.
Again by given condition
Age of Asha `=` One years less than 10 times the present age of Nisha
`(x^(2)=2)+{(x^(2)+2)-x}=10x-1`
`implies 2x^(2)-x+4=10x-1`
`implies 2x^(2)-1x+5=0`
`implies 2x^(2)-11x+5=0`
`implies 2x^(2)-10x-x+5=0`
`implies 2x(x-5)-1(x-5)=0`
`implies(x-5)(2x-1)=0`
`:. x=5`
[here `x=1/2` cannot be possible because at `x=1/2`. Asha's age is `2 1/4` yr which is not possible]
Hence required age of Nisha `=5` yr
and required age of Asha `=x^(2)+2=(5)^(2)+2=25+2=27`yr