Question

Three years ago Preethi' s age was 3 times the square of Swati's age will be two third of Preethi's age. Find their present ages.​

Answer 1

$\large{\bigstar{{\fbox{\large{\mathcal{\blue{Answer:-}}}}}}}$

Let swati's present age be x years

Three years ago Swati's age was (x-3) years

$\sf {\red{Preethi's \:age \:was\: 3(x - 3 ){}^{2} }}$

$\sf {\red{So \:Preethi's\: age \:is \:3(x - 3 ){}^{2} + 3 }}$

--------(1)

Six years hence, Swati's age will be x + 6 years and Preethi's age will be

$\sf {\purple{[3(x - 3 ){}^{2} + 9 ] years}}$

$\sf {\purple{(x + 6) = \frac{2}{3} [3(x - 3 ){}^{2} + 9]}}$

$\sf{\purple {(x + 6) = 2( {x}^{2} - 6x + 18)}}$

$\sf{\purple{2 {x}^{2} - 13x + 15 = 0}}$

------(2)

{Solving equation (2) we get x (Swati's age) as 5 and substituting it in equation (1) we get Preethi's age as 15 years.

Answer 2

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For Solution See Attachment.

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