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.

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$$=\left( 5{ x }^{ 2 }+7 \right)$$ yearsThree years hence, we haveSwati's age $$(x+7+3)$$ years $$=(x+10)$$ yearsVarun's age $$=\left( 5{ x }^{ 2 }+7+3 \right) =\left( 5{ x }^{ 2 }+10 \right)$$It is given that three years hence Swati's age wil be $$\cfrac{2}{5}$$ of Varun's age$$\quad \therefore x+10=\cfrac { 2 }{ 5 } \left( 5{ x }^{ 2 }+10 \right)$$$$\Rightarrow x+10=2{ x }^{ 2 }+4$$$$\Rightarrow 2{ x }^{ 2 }-x-6=0$$$$\Rightarrow 2{ x }^{ 2 }-4x+3x-6=0$$$$\Rightarrow (2x+3)(x-2)=0$$$$\Rightarrow x-2=0\Rightarrow x=2$$Hence Swati's present age $$=(2+7)$$ years $$=9$$ yearsVarun's present age $$=\left( 5\times { x }^{ 2 }+7 \right)$$ years $$=27$$ yearsMaths

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