Question

The denominator of a fraction is 4 more than the numerator if both are decreased by 3 the simplified result is 6/7 find original fraction

Answer 1

The denominator of a fraction is 4 more than the numerator. The original fraction is
`(27)/(31)`

Solution:

Given that

Denominator of fraction is 4 more than the numerator.

Let’s say numerator of fraction be represented by variable x.

So denominator of a faction as it is four more that numerator will be x + 4

Also given if both decreased by three than simplified result is
`(6)/(7)`

`=>((x-3))/(((x+4)-3))=(6)/(7)`

Solving above equation for x

=> 7(x – 3 ) = 6 ( x + 1 )

=> 7x – 21 = 6x + 6

=> 7x – 6x = 6 + 21

=> x = 27

Numerator of fraction = x = 27

Denominator of fraction = x + 4 = 27 + 4 = 31

`\text {required fraction}=\frac{\text {numerator}}{\text {denominator}}`

`= (27)/(31)`

Hence the original fraction is
`(27)/(31)`