Question

10. The sum of the numerator and denominator of a certain positive fraction is 8 If 2 is
added to both the numerator and denominator, the fraction is increased by 4/35 . Find the fraction.​

Answer 1

Let the denominator be 'x' So the numerator will be '8-x'

The obtained dfraction is (8−x)/x

So according to the question,

x+2/8−x+2= x/8−x + 35/4

x+2/10−x= x8−x + 35/4

x+2/10−x−x/8−x=35/4

By taking LCM

x(x+2)/10x−x2−8x+x2−16+2x=35/4

x2+2x4x−16=35/4

By cross Multiplying,

35(4x−16)=4(x2+2x)

140x−560=4x2+8x

4x2+8x−140x+560=0

4x2−132x+560=0

Divide by 4, we get

x2−33x+140=0

let us factorize,

x2−28x−5x+140=0

x(x−28)−5(x−28)=0

(x−28)(x−5)=0

So

(x−28)=0 or (x−5)=0

x=28 or x=5

So the value of x=5[ since, x=28 is not possible as sum of numerator and denominator is 8

When substitute the value of x=5 in the dfraction (8−x)/x, we get (8−5)/5=3/5

∴ The required dfraction is =3/5