Question

The denominator of a fraction is 6 more than its numerator. If the denominator is increased by 5 and the numerator is decreased by 1 ,the fraction becomes 2/3.Find the fraction.​

Answer 1

let the numerator be x

denominator be y

first condition-

y=6+x

x-y=-6...(1)

second condition-

$\frac{y + 5}{x - 1} = \frac{2}{3}$

3(y+5)= 2(x-1)

3y+15= 2x-2

3y-2x=-2-15

-2x-+3y=-17....(2)

multiplying (1) by 2

x-y=-6

2x-2y=-12

adding

2x-2y=-12

-2x-+3y=-17

y= -29

x-y= -6

x+29=-6

x=-6-29

x=-35

hence the fraction is

$\frac{35}{ 29}$