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At present Asha's age(in years) is …

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At present Asha's age(in years) is 2 more than thesquare 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 their present ages?
  • 1 answers

Sia ? 5 years, 6 months ago

Let the present age of Nisha be x years.
Then, as per given condition
Asha's age (in years) is 2 more than the square of her daughter Nisha's age.
So, Asha's age = x2 + 2
Difference in their ages = x2 + 2 - x
And,  Asha's age when Nisha's age will be (x2 + 2) years  = ( x2 + 2) + (x2 + 2 - x)
If Asha's age is one year less than 10 times the present age of Nisha = 10x - 1
So, As per given condition
(x2 + 2 - x) + (x2 + 2) = 10x - 1
{tex}\Rightarrow{/tex} 2x2 - x + 4 = 10x - 1
{tex}\Rightarrow{/tex} 2x2 - 11x + 5 = 0
{tex}\Rightarrow{/tex} 2x2 - 10x - x + 5 = 0
{tex}\Rightarrow{/tex} 2x(x - 5) - 1(x - 5) = 0
{tex}\Rightarrow{/tex} (x - 5)(2x - 1) = 0
{tex}\Rightarrow{/tex} x - 5 = 0 or 2x - 1 = 0
{tex}\Rightarrow{/tex} x = 5 or {tex}x = \frac{1}{2}{/tex}
{tex}\Rightarrow{/tex} x = 5 [as age can't be a fraction]
{tex}\Rightarrow{/tex} x2 + 2 = 52 + 2 = 27
Hence, Nisha's age is 5 years and Asha's age is 27 years.

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