Question

Seven years ago, Raghav's age was five times the square of Natima 's age. After three years from now , Natima ' s age will be 2/5 times of age of Raghav. Find the difference between the ages of Raghav and Natima.

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.

Answer 2

difference In. their ages is 18 yrs