Question

Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.
[4 Marks]

Answer 1

Seven years ago, let Swati's age be $x$ years, then Varun's age seven years ago will be $5x^2$ years.
[0.5 Marks]

Thus, the present age of Swati and Varun will be $x+7$ years and $5x^2+7$ years. respectively.
[0.5 Marks]

Three years hence, we have

Swati's age $=(x+7+3)$ years $=(x+10)$ years

Varun's age $=(5x^2+7+3)$ years $=(5x^2+10)$ years
[0.5 Marks]

It is given that three years hence Swati's age will be $\frac{2}{5}$ of Varun's age.

$\therefore x+10=\frac{2}{5}(5x^2+10)$ [0.5 Marks]

$\Rightarrow x+10=2x^2+4$

$\Rightarrow 2x^2-x-6=0$ [0.5 Marks]

$\Rightarrow 2x^2-4x+3x-6=0$

$\Rightarrow 2x(x-2)+3(x-2)=0$

$\Rightarrow (2x+3)(x-2)=0$ [0.5 Marks]

$\Rightarrow x-2=0$ $[\because 2x+3\ne 0asx>0]$

$\Rightarrow x=2$

Hence, Swati's pressent age = (2+7) years = 9 years

Varun's present age $=(5\times 2^2+7)years$ = 27 years.
[1 Mark]