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.

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Solution

Seven years ago. let Swati's age be $x$ years. Then, seven years ago Varun's age was $5 x^{2}$ years.

Swati's present age $= (x + 7)$ years, Varun's present age $= (5 x^{2} + 7)$ years

Three years hence, we have
Swati's age $(x + 7 + 3)$ years $= (x + 10)$ years

Varun's age $= (5 x^{2} + 7 + 3) = (5 x^{2} + 10)$

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

$∴ x + 10 = \frac{2}{5} (5 x^{2} + 10)$

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

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

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

$\Rightarrow x - 2 = 0 \Rightarrow x = 2$

Hence Swati's present age $= (2 + 7)$ years $= 9$ years

Varun's present age $= (5 \times x^{2} + 7)$ years $= 27$ years

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