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.


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Answer 1

$\large \dag$ 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,

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

Answer 2

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.

EXPLANATION-:

Let the numerator be x

and the denominator will be x+8

Number so formed-:

$\dashrightarrow \boxed{\bf\; \frac{x}{x+8}}$

After adding 3 to numerator

Numerator x+3

After subtracting 3 from the denominator

Denominator x+8-3 > x+5

Number for formed-:

$\dashrightarrow \boxed{\bf\; \frac{x}{x+5}}$

A.T.Q

$\rightarrow \bf\; \frac{x+3}{x+5}=\frac{3}{4}\\\\\rightarrow \bf\; 4(x+3)=3(x+5)\\\\\rightarrow \bf\;4x+12=3x+15\\\\\rightarrow \bf\; 4x-3x=15-12\\\\\longrightarrow \underline{\boxed{\bf\; x=3 }}$

So-:

Numerator=3

Denominator=8+3

Denominator=11

Original fraction=3/11

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