Question

7.Represent the following situation in the form of quadratic equation: 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 . Consider Swati's present age be x years *
2 points​

Answer 1

Answer:

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Step-by-step explanation:

let the present age of swati be x years and varun be y years

according to the first condition

y-7=5(x-7)square

ie y-7=5(x square+49-14x)

ie y-7=5x.square+245-70x

so y=5x.square+252-70x (1)

according to the second condition

x+3=2/5×(y+3)

ie 5(x+3)=2(y+3)

ie 5x+15=2y+6

ie 2y=5x+9 (2)

substitute value of y in (2) from (1)

we get

2(5x.square+252-70x)=5x+9

ie 10x.square+504-140x=5x+9

so 10x.square-145x+495=0

dividing throughout by 2

we get

2x.square-29x+99=0

so 2x.square-18x-11x+99=0

ie 2x(x-9)-11(x-9)=0

(2x-11)(x-9)=0

so x=11/2 or x=9

ie x=5.5 or x=9

but as ages of any person are never in decimal

x=5.5 is absurd

hence x=9

now substitute value of x in any of two equations

we get

y=27

hence present age of swati is 9 years and that of varun is 27 years