Question

pls answer my question ​

Answer 1

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Answer 2

Answer:

Nisha's present age is 5 years

Asha's present age is 27 Years.

Step-by-step explanation:

Let Asha's present age is x years

and Nisha's present age is y years

ATQ

Asha's present age is 2 more than the square of Nisha's present age

So,

$x = {y}^{2} + 2 \: \: \: \: \: eq1$

We can also write present age of Asha's is

${x}^{2} + 2$

years and her daughter age is x years,so that formation of Quadratic equation in one variable be possible.

Now,when Nisha grows to her mother's present age:

Growing years taken when Nisha: approaches Asha's age: Asha's age-Nisha's age

$= {x}^{2} + 2 - x...eq2$

According to the second condition, Asha's age will be one year less than 10 times of Nisha's present age: Nisha's present age+time span of years calculated in eq2

So,

${x}^{2} + 2 + {x}^{2} + 2 - x = 10x - 1 \: ....eq2 \\ \\ 2 {x}^{2} - x - 10x + 4 + 1 = 0 \\ \\ 2{x}^{2} - 11x + 5 = 0 \\ \\ 2 {x}^{2} - 10x - x + 5 = 0 \\ \\ 2x(x - 5) - 1(x - 5) = 0 \\ \\ (2x - 1)(x - 5) = 0 \\ \\ x - 5 = 0 \\ \\ x = 5 \\ \\ or \\ \\ 2x - 1 = 0 \\ \\ 2x = 1 \\ \\ x = \frac{1}{2}$

So,the Nisha's present age is 5 years and her Mother Asha's age is 27 years.

Verification:

Nisha age after 22 years= 27 years(Asha's present age)

After 22 years Asha's age= 22+27=49 Years

I.e. Nisha's present age×10 -1

10×5-1=49

Hope it helps you.

*Note:

We have to discard the second value of x,because it is possible to be the age of daughter,but ATQ then mother's age will be 2.25 years,which is not possible.