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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$$=\left( 5{ x }^{ 2 }+7 \right) $$ years

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

Varun'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 $$=9$$ years

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

Maths

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