Question

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces
to 1. It becomes 1
/2 if we only add 1 to the denominator, find the fraction?
​

Answer 1

Let the numerator be x and denominator be y....

Let the numerator be x and denominator be y....then the fraction will be x/y

now,

according to question

case1)

(x+1)/(y-1)=1

x+1=y-1

x-y=-2.......i)

case2)

x/(y+1)=1/2

2x=y+1

2x-y=1.......ii)

now,.subtract I) from ii)

x=3

putting this value in ii)

we get

y=5

Hence the fraction is 3/5

Answer 2

Answer:

$let \: the \: fraction \: be \: \frac{x}{y} \\ atq \\ \frac{x + 1}{y - 1} = 1 \\ x + 1 = y - 1 \\ x - y = - 2 \: \: \: \: \: \: ........(1)\\ also \: \\ \frac{x}{y + 1} = \frac{1}{2} \\ 2x = y + 1 \\ 2x - y = 1 \: \: \: \: \: \: .........(2) \ \\ : on \: substracting \: (2) \: from \: (1) \\ - x = - 3 \\ and \: putting \: the \: vlue \: of \: x \: in \: (1) \\ - y = - 2 - x \\ y = 2 + 3 \\ y = 5 \\ hence \: the \: required \: fraction \: is \: \frac{3}{5}$