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
Age of Swati = x
So, age of Varum = 5x2
Now, present age of Swati = x + 7
and present age of Varun = 5x2 + 7
Again given that 3 years hence, age of Swati will be 2/5 of age of Varun
x + 7 + 3 = (2/5)*(5x2 + 7 + 3)
=> x + 10 = (2/5)*(5x2 + 10)
=> 5(x + 10) = 2(5x2 + 10)
=> 5x + 50 = 10x2 + 20
=> 10x2 + 20 - 5x - 50 = 0
=> 10x2 - 5x - 30 = 0
=> 2x2 - x - 6 = 0 {divided by 5}
=> 2x2 - 4x + 3x - 6 = 0
=> 2x(x - 2) + 3(x - 2) = 0
=> (x - 2)*(2x + 3) = 0
=> x = 2, -3/2
Since age can not be negative,
So, x = 2
Now, present age of Swati = x + 7 = 2 + 7 = 9 years
and present age of Varun = 5x2 + 7 = 5*22 + 7 = 5*4 + 7 = 20 + 7 = 27 years
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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