Question

7 years ago Nitin age was five times the square of varshas Age. 3 years hence varshas age will be two fifth of Nithin age. find their present ages.

Answer 1

Answer: Nitin's age = 18.25 or 27 years and Varsha's age = 5.5 or 9 years.

Step-by-step explanation:  Let 'x' years and 'y' years be the present ages of Nitin and Varsha respectively.

Then, according to the given information, we have

$x-7=5(y-7)^2~~~~~~~~~~~~~~(A)\\\\y+3=\dfrac{2}{5}(x+3)\\\\\Rightarrow 5y+15=2x+6\\\\\Rightarrow 2x=5y+9\\\\\Rightarrow x=\dfrac{5y+9}{2}.~~~~~~~~~~~(B)$

Substituting the value of 'x' from equation (B) in equation (A), we have\

$\dfrac{5y+9}{2}-7=5(y^2-14y+49)\\\\\Rightarrow \dfrac{5y-5}{2}=5(y^2-14y+49)\\\\\Rightarrow y-1=2(y^2-14y+49)\\\\\Rightarrow 2y^2-29y+99=0\\\\\Rightarrow 2y^2-18y-11y+99=0\\\\\Rightarrow (2y-11)(y-9)=0\\\\\Rightarrow y=5.5,~~~y=9.$

If y = 5.5, the from equation (B), we get

$x=\dfrac{5\times 5.5+9}{2}=\dfrac{36.5}{2}=18.25,$

and is y = 9, then

$x=\dfrac{5\times 9+9}{2}=\dfrac{54}{2}=27.$

Thus, the prsesnt ages of Nitin and Varsha are 27 years and 9 years OR 18.25 years and 5.5 years.