Question

At present Asha's age (in years) is two more than the square of her daughter Nisha's age (in years). 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 age of Asha and Nisha

Answer 1

Asha's present age is 27 years and Nisha's present age is 5 years.

Explanation:

Let the present age of Nisha be
`x` years.

As per question, Asha's present age is 2 more than the square of Nisha's age.

`\therefore` Asha's present age =
`x^2+2`

Now, Nisha will reach her mother's age after
`x^2+2-x` years.

Therefore, age of Asha after
`x^2+2-x` years will be =
`x^2+2+x^2+2-x=2x^2-x+4`

Now, as per question,

`2x^2-x+4=10x-1\\2x^2-x-10x+4+1=0\\2x^2-11x+5=0\\2x^2-x-10x+5=0\\x(2x-1)-5(2x-1)=0\\(2x-1)(x-5)=0\\x=(1)/(2)\ or\ x=5`

As age can't be in fraction, we consider the present age of Nisha as 5 years. So, Asha's present age is
`x^2+2=5^2+2=25+2=27` years.

Therefore, Asha's present age is 27 years and Nisha's present age is 5 years.