Question

Th denominator of a rational number is greater than its numerator by 3 if numerator is increased by 14 and denominator is decreased by 3 the new number becomes 11 by 4 what is the rational number

Answer 1

$\large \dag$ Question :-

The denominator of a rational number is greater than its numerator by 3, if numerator is increased by 14 and denominator is decreased by 3 the new number becomes 11 by 4 what is the rational number ?

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{The   \: Original \:  Number  \: is \:  \frac{8}{11} }} }$

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

Let Numerator and Denominator of Original Rational Number be :

• Numerator = x

As Per the question denominator of the rational number is greater than its numerator by 3 so,

• Denominator should be = x + 3

Hence,

$\text{Original Number = } \frac{\text x}{\text x + 3}$

❒ When numerator is increased by 14 and denominator is decreased by 3 :

$\rm \text{Number Becomes } :  \frac{x + 14}{x}$

⏩ According To Question :

$\large \blue \bigstar \: \: \red{ \bf \frac{ x + 14 }{x} = \frac{11}{4} }$

$\maltese \:$ On Cross Multiplying ;

$:\longmapsto \rm11x = 4(x + 14)$

$:\longmapsto \rm 11x = 4x + 56$

$:\longmapsto \rm 11x - 4x = 56$

$:\longmapsto \rm 7x = 56$

$:\longmapsto \rm x = \cancel \frac{56}{7}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 8} }}}$

$\blue\dashrightarrow\underline{\underline{\sf  \orange{Numerator  \: of \:  Original  \: Number = 8 }} }$

☆ As The denominator of the rational number is greater than its numerator by 3

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

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

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{ Original  \: Fraction  =  \dfrac{8}{11} }}}}}$

Answer 2

QUESTION-:

The  denominator of a rational number is greater than its numerator by 3 if numerator is increased by 14 and denominator is decreased by 3 the new number becomes 11/4 what is the rational number .

EXPLANATION-:

Let the numerator =x

According to the condition in the question -:

Denominator=x+3

So the numbers so formed-:

$\rightarrow \bf\;\frac{x}{x+3}$

----------------------------------------------

Now ,Is numerator is increased by 14 -:

Numerator=x+14

And denominator is decreased by 3-:

Denominator=x+3-3

Denominator=x

Number so formed-:

$\rightarrow \bf\;\frac{x+14}{x}$

A,T,Q,

$\rightarrow \bf\;\frac{x+14}{x}=\frac{11}{4} \\\\\rightarrow \bf\;11x=4x+56\\\\\rightarrow \bf\;7x=56\\\\\rightarrow \bf\;x=\frac{56}{4}\\\\\longrightarrow \boxed{\bf\;x=8}$

So-:

Numerator =8

Denominator=8+3

Denominator=11

Rational numbers(ORIGINAL FRACTION) is 8/11