Question

The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction? • Kindly Don’t Spam :)​

Answer 1

Let Numerator and Denominator of Original Fraction be :

Numerator = x

As Per the question numerator of the fraction is 8 less than the denominator so,

Denominator should be = x + 8

So ,

$original \: fraction = \frac{x}{x + 8}$

❒ When 3 is added to the numerator and 3 is subtracted from the denominator :

$fraction \: becomes = \frac{x + 3}{x + 5}$

According To Question :

$\frac{x + 3}{x + 5} = \frac{3}{4} \\ 4(x + 3) = 3(x + 5) \\ 4x + 12 = 3x + 15 \\ 4x - 3x = 15 - 12 \\ x = 3$

$numerator \: of \: origional \: fraction \\ = 3$

☆ As numerator of the fraction is 8 less than the denominator

$therefore \: denominator = 3 + 8 \\ denominator \: of \: original \\ \: fraction = 11$

Therefore,

$original \: fraction = \frac{3}{11}$

Answer 2

ANSWER

3/11

STEP BY STEP

Let denominator of fraction be X.

Numerator = ( X - 8 )

Fraction = Numerator/Denominator = ( X -8)/X.

According to question,

When 3 is added to numerator and 3 is subtracted from denominator the fraction obtained is 3/4

X - 8 + 3 / X - 3 =3 /4

X-5/X-3 = 3/4

4X-20 = 3X-9

X = 11

NOW 

(X-8)/X = (11-8)/11

Answer is

3/11