7 years ago Varun's age was five times the square of Swati's age. 3 years hence, Swati's age will be two-fifth of Varun's age. Find their present ages.
Answers
➠ AnSwer :-
Let Swati's age 7 years ago be x years.
Then, Varun's age 7 years ago = 5x² years.
Swati's present age = (x + 7) years.
Varun's present age = (5x² + 7) years.
Swati's age 3 years hence = (x + 7 + 3) years =
(x + 10) years.
Varun's age 3 years hence =
➝(5x² + 7 + 3) years
➝(5x²+ 10) years.
➝(x + 10) = 2/5(5x² + 10)
➝5x + 50 = 10x² + 20 = 10x² – 5x - 30 = 0
➝2x² - x - 6= 0 = 2x² - 4x + 3x - 6 = 0
➝2x (x - 2) + 3(x - 2) = 0 = (x - 2)(2x + 3) = 0
➝x - 2 = 0 or 2x +3= 0 x = 2 or x = -3/2
➝x=2 [: age cannot be negative ]
Swati's present age = (2 + 7) years = 9 years.
Varun's present age = (5 x 22 + 7) years = 27 years.
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 years
Answer – The present age of Varun is 27 years and present age of Swati is 9 years.
Step-by-step explanation: