Question

seven years ago varun's age was five times the square of vasanth age. three years hence, vasanth age will be two fifth of varun's age. find the present age​

Answer 1

let the present age of varun and vasanth are x and y years respectively

given- 7year ago
x-7=5(y-7)power2.........(1)
also given -3year hence
y+3=2/5(x+3)
5y+15=2x+6
2x=5x+9
x=(5y+9)/2..........(2)
substitute the value of x in equation 1
(5y+9)/2-7= 5(y-7)power 2
5y+9 -14 = 10(y power 2 -14y+49)
5y-5= 10ypower 2-140y+490
10ypower 2-145y+495=0
dividing the equation by 5
2ypower2-29y+99=0
solving above quadratic equation to find y


y=(-b+sqrt(bpower 2 -4ac))/4ac or y=(-b-sqrt(bpower2-4ac))/4ac

get y=9 and y=11/2
consider age as a whole num6

therefore y=9year
substitute the value of y in equation 2
therefore, x=(5*9+9)/2=27 years
Answer :The present age of varun is 27 year and present age of vasanth is 9 year

Answer 2

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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