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 ages.
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.
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Answer:
Step-by-step explanation:
Let seven years, age of Swati was x years and age of Varun was 5x² years
Present age of Swati = ( x + 7 ) years
Present age of Varun = ( 5x² + 7 ) years
Given, after 3 years swati's age will be 2 / 5 of Varun's age.
Age of Swati after 3 years = ( x + 7 + 3 ) years = ( x + 10 ) years
Age of Varun after 3 years = ( 5x² + 7 + 3 ) years = ( 5x² + 10 ) years
Given, age of Swati after 3 years = age of varun after 3 years
( x + 10 ) = 2 / 5 × ( 5x² + 10 )
( x + 10 ) = 2( x² + 2 )
x + 10 = 2x² + 4
2x² - x + 4 - 10 = 0
2x² - x - 6 = 0
2x² - 4x + 3x - 6 = 0
2x( x - 2 ) + 3( x - 2 ) = 0
x = 2 [ Age can't be negative ]
Therefore,
present age of Swati = ( 2 + 7 ) = 9 years
present age of Varun = 5(2)²+7=27 years
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