Question

Three years ago Preethi ‘s age was 3 times the square of Swati’s age. Six years hence, Swati’s age will be two – third of Preethi’s age. Find their Present ages.

Answer 1

Let Swati’s present age be x yrs

Three years ago Swati’s age was (x-3) yrs and Preethi's age was $3(x-3{)}^2$

So, Preethi ‘s age is $3(x-3{)}^2+3$ ---(1)

Six years hence, Swati’s age will be x+6 yrs and Preeti’s age will be $\left[3\right(x-3{)}^2+9]$ yrs.

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

$(x+6)=2(x^2–6x+18)$

$2x^2–13x+15=0$ ---(2)

Solving equation (2) we get x (Swati’s age) as 5 yrs and substituting it in equation (1) we get Preeti’s age as 15 yrs.