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?​

Answer 1

Let the denominator be x

Fraction=

x

x−5

x+3

x−5+3

=

5

4

x+3

x−2

=

5

4

5(x−2)=4(x+3)

5x−4x=12+10

x=22

So, numerator=x−5=22−5=17

and denominator=22

So, the original fraction=

22

17

Answer 2

Answer:

$\large \dag$ 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.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{The   \: Original \:  Fraction  \: is \:  \frac{3}{11} }} }$

$\large \dag$ Step by step Explanation :-

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 ,

$\text{Original Fraction = } \frac{\text x}{\text x + 8}$

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

$\rm \text{Fraction Becomes } :  \frac{x + 3}{x + 5}$

⏩ According To Question :

$\large \blue \bigstar  \:   \red{ \bf  \frac{x + 3}{x + 5} =  \frac{3}{4}  }$

$:\longmapsto \rm 4(x + 3) = 3(x + 5 )$

$:\longmapsto \rm 4x + 12 = 3x + 15$

$:\longmapsto \rm 4x - 3x = 15 - 13$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 3} }}}$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Numerator  \: of \:  Original  \: Fraction = 3 }} }$

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

$\rm\therefore \:  Denominator  = 3   + 8$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Denominator  \: of \:  Original  \: Fraction = 11 }} }$

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{ Original  \: Fraction  =  \dfrac{3}{11} }}}}}$