seven years ago varun's age was five times the square of swati's age. three years hence swati's age will be two-fifth of varun's age. find their present age
Answers
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:
Step-by-step explanation:
Solution :-
Let Swati's age 7 years ago be x years.
Then, Varun's age 7 years ago is 5x² years.
Swati's present age = x + 7 years
Varun's present age = 5x² + 7 years.
3 years hence :-
Swati's age = x + 7 + 3 = x + 10 years.
Varun's age = 5x² + 7 + 3 = 5x² + 10 years.
According to the Question,
⇒ (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, - 3/2 (As x can't be negative)
⇒ x = 2
Swati's present age = x + 7 = 2 + 7 = 9 years.
Varun's present age = 5x² + 7 = 27 years.
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