Seven years ago Varun's age was five times the square of Swati's age.

1.	Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati'sage will be two-fifth of Varun's age. Find their present ages.
Answer» 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 yearsAnswer – The present age of Varun is 27 years and presentage of Swati is 9 years.

Seven years ago Varun's age was five times the square of Swati's age. Three years hence Swati'sage will be two-fifth of Varun's age. Find their present ages.

Answer»

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 yearsAnswer – The present age of Varun is 27 years and presentage of Swati is 9 years.