Question

The numerator of a fraction is 4 less than its denominator. if the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes 8 times its numerator. find the freaction

Answer 1

Let the numerator be x & denominator be y
Fraction = numerator/denominator = x/y
ATQ
CASE 1 :
x = y - 4
x- y = - 4 …………..(1)

CASE 2 :
8(x - 2) = y + 1
8x - 16 = y + 1
8x - y = 17………... (2)

On Subtracting eq (2) from (1)
x - y = - 4
8x - y = 17
(-) (+) (-)
----------------
-7x = -21
x = 21/7
x = 3


Put x = 3 in eq 1,
x - y = - 4
3 - y = - 4
y = 3 + 4 = 7
y = 7 

x = 3
y = 7

Fraction = x/y = 3/7
Hence, the fraction is 3/7.

HOPE THIS WILL HELP YOU...

Answer 2

ʟᴇᴛ ᴛʜᴇ ɴᴜᴍᴇʀᴀᴛᴏʀ ʙᴇ x & ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ ʙᴇ ʏ
ғʀᴀᴄᴛɪᴏɴ = ɴᴜᴍᴇʀᴀᴛᴏʀ/ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀ = x/ʏ
ᴀᴛϙ
ᴄᴀsᴇ 1 :
x = ʏ - 4
x- ʏ = - 4 …………..(1)

ᴄᴀsᴇ 2 :
8(x - 2) = ʏ + 1
8x - 16 = ʏ + 1
8x - ʏ = 17………... (2)

ᴏɴ sᴜʙᴛʀᴀᴄᴛɪɴɢ ᴇϙ (2) ғʀᴏᴍ (1)
x - ʏ = - 4
8x - ʏ = 17
(-) (+) (-)
----------------
-7x = -21
x = 21/7
x = 3

ᴘᴜᴛ x = 3 ɪɴ ᴇϙ 1,
x - ʏ = - 4
3 - ʏ = - 4
ʏ = 3 + 4 = 7
ʏ = 7 

x = 3
ʏ = 7

ғʀᴀᴄᴛɪᴏɴ = x/ʏ = 3/7
ʜᴇɴᴄᴇ, ᴛʜᴇ ғʀᴀᴄᴛɪᴏɴ ɪs 3/7.