Question

The sum of the numerator and the denominator of a certain positive fraction is 8. If 2 is added to both the numerator and denominator, the fraction is increased by 435. Find the fraction.

Answer 1

let the numerator be x and denominator be y.

The fraction is x/y.

Given that their sum = 8.

x + y = 8   ------ (1)

y = 8 - x  --------- (2)

Given that if 2 is added to both numerator and denominator, the fraction is increased by 4/35.

35(x + 2)(8-x) = 35x(10-x)+4(8-x)(10-x)

-35x^2 +210x + 560 = -31x^2 +278x + 320

-35x^2 -68x +240=-31x^2

-4x^2 -68x + 240 = 0

x^2 + 17x -60=0

x^2 - 3x +20x - 60 = 0

x(x - 3) + 20(x - 3) = 0

x = 3 (or) x = -20.

Since x cannot be -ve, so x = 3.

Then y = 8 - x

            = 8 - 3

            = 5.

Therefore the fraction = 3/5.

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