Question

Seven years ago, Varun's age was 5 times the square of swatis age. Three years hence swatis age will be two fifth of Varun's age. Find their present ages if Varun's present age is x and swatis present age is y.

Answer 1

Let the present age of Varun and Swati are x and y years respectively.

Given – 7 years ago

x – 7 = 5(y-7)^2 ----------------1

Also given – 3 years hence

y + 3 = 2/5 (x + 3)

5y + 15 = 2x + 6

2x = 5y + 9

x = (5y + 9)/2 ------------------2

Substitute the value of x in equation 1

(5y + 9)/2 – 7 = 5 (y-7)^2

5y + 9 – 14 = 10 (y^2 – 14y + 49)

5y – 5 = 10y^2 – 140y + 490

10y^2 – 145y + 495 = 0

Dividing the equation by 5

2y^2 – 29y + 99 = 0

Solving above quadratic equation to find y

y = (-b + sqrt (b^2 – 4ac))/4ac or y = (-b - sqrt (b^2 – 4ac))/4ac

get y = 9 and y = 11/2

consider age as a whole number

Therefore, y = 9 years

Substitute the value of y in equation 2

Therefore, x = (5 * 9 + 9)/ 2 = 27 years
Answer – The present age of Varun is 27 years and present
age of Swati is 9 years.