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

Framing of equation: 2 Marks
Calculations: 1 Mark
Answer: 1 Mark

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

Three years hence, we have

Swati's age $= (x + 7 + 3) y e a r s = (x + 10) y e a r s$

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

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

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

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

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

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

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

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

$\Rightarrow x - 2 = 0$ $[∵ 2 x + 3 \neq 0 a s x > 0]$

$\Rightarrow x = 2$

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

Varun's present age $= (5 \times 2^{2} + 7) y e a r s$ = 27 years.

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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]

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]