Question

the numerator of a fraction is 4 less than the denominator if 1 is added to both its numerator and denominator it become 1 by 2 find the fraction

Answer 1

let fraction be x/y,
numerator (x)= 4-y,

on adding 1,
numerator=x+1;
denominator=y+1;
(x+1)/(y+1)=1/2;


on solving, we get,
x=1;
y=3;

so fraction is 1/3;
hope answer helps you....^_^
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Answer 2

GIVEN :-

Tʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴏғ ᴀ ғʀᴀᴄᴛɪᴏɴ ɪs 4 ʟᴇss ᴛʜᴀɴ ᴛʜᴇ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ .

Iғ 1 ɪs ᴀᴅᴅᴇᴅ ᴛᴏ ʙᴏᴛʜ ɴᴜᴍᴇʀᴀᴛᴏʀ ᴀɴᴅ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ, ᴛʜᴇɴ ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ʙᴇᴄᴏᴍᴇs 1/2 .

TO FIND :-

Tʜᴇ ᴏʀɪɢɪɴᴀʟ ғʀᴀᴄᴛɪᴏɴ .

SOLUTION :-

Lᴇᴛ,

Nᴜᴍᴇʀᴀᴛᴏʀ ʙᴇ "X" .

Aɴᴅ Dᴇɴᴏᴍɪɴᴀᴛᴏʀ ʙᴇ "Y" .

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ,

ᴄᴀsᴇ - 1 :-

$➪ X = Y - 4 -----(1)$

ᴄᴀsᴇ - 2 :-

$\huge\red\checkmark✓ \bf{\dfrac{X\:+\:1}{Y\:+\:1}\:=\:\dfrac{1}{2}\:}$

$\rm{:\implies\:2X\:+\:2\:=\:Y\:+\:1\:}:$

Putting the value of X in the above equation .

$\rm{:\implies\:2\times(Y\:-\:4)\:+\:2\:=\:Y\:+\:1\:}$

$\rm{:\implies\:2Y\:-\:8\:+\:2\:=\:Y\:+\:1\:}:$

$\rm{:\implies\:2Y\:-\:Y\:-\:6\:-\:1\:=\:0\:}$

$\rm{:\implies\:Y\:-\:7\:=\:0\:}$

$\bf \huge\green{:\implies\:Y\:=\:7\:}$

Now, putting the value of Y in the equation (1) .

$➳ X = 7 - 4 \\ </p><p></p><p>➳ X = 3</p><p>$

$\huge\blue\ Tʜᴇ \: ᴏʀɪɢɪɴᴀʟ \: ғʀᴀᴄᴛɪᴏɴ \: is \:$

$\bf{\dfrac{X}{Y},\:i.e.\:\pink{\dfrac{3}{7}}\:.}$