Seven years ago Varuns age was five times the square of Swatis age. Three years hence Swatis age will be two fifth of Varuns age. Find their present ages.

Explanation

Let Swati's age 7 years ago be x years.
Then, Varun's age 7 years ago `=5x^(2)` years.
Swati's present age `=(x+7)` years.
Varun's present age `=(5x^(2)+7)` years.
Swati's age 3 years hence `=(x+7+3)" years"=(x-10)` years.
Varun's age 3 years hence `=(5x^(2)+7+3)` years
`=(5x^(2)+10)` years.
`:." "(x+10)=(2)/(5)(5x^(2)+10)`
`implies" "5x+50=10x^(2)+20implies10x^(2)-5x-30=0`
`implies" "2x^(2)-x-6=0implies2x^(2)-4x+3x-6=0`
`implies" "2x(x-2)+3(x-2)=0implies(x-2)(2x+3)=0`
`implies" "x-2=0" or "2x+3=0impliesx=2" or "x=(-3)/(2)`
`implies" "x=2" "[because" age cannot be negative"]`
`:." ""Swati's present age "=(2+7)" years = 9 years."`
Varun's present age `=(5xx2^(2)+7)` years =27 years.