7 years ago Sparsh's age was …

Let seven years ago arya's age be x years.
As per given condition
Seven years ago sparsh's age was five times the square of arya's age.
Then, seven years ago sparsh's age was 5x² years.
Therefore, arya's present age = (x + 7) years
And  sparsh's present age = (5x² + 7) years
Three years hence arya's age = (x + 7 + 3) years = (x + 10) years
And three years hence sparsh's age = (5x² + 7 + 3) years = (5x² + 10) years
As per given condition
Three years hence arya's age will be {tex}\frac{2}{5}{/tex} of sparsh's age.
Therefore, x + 10 = {tex}\frac{2}{5}{/tex}(5x² + 10)
{tex}\Rightarrow{/tex} x + 10 = 2(x² + 2)
{tex}\Rightarrow{/tex} x + 10 = 2x² + 4
{tex}\Rightarrow{/tex} 2x² - x - 6 = 0
{tex}\Rightarrow{/tex} 2x² - 4x + 3x - 6 = 0
{tex}\Rightarrow{/tex} 2 x ( x - 2 ) + 3 ( x - 2 ) = 0
{tex}\Rightarrow{/tex} (2x + 3) (x - 2) = 0
{tex}\Rightarrow{/tex} x - 2 = 0 [{tex}\because{/tex} 2x + 3 {tex}\neq{/tex} 0 as x > 0]
{tex}\Rightarrow{/tex} x = 2
Hence, arya's present age = (2 + 7) years = 9 years
sparsh's present age = (5 {tex}\times{/tex}2² + 7) years = 27 years