The denominator of a rational number is greater than its numerator by 4. If the numerator is increased by 7 and denominator is decreased by 2 ,the new number brcomes 6/5. Find the original number
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Question :-
The denominator of a rational number is greater than its numerator by 4. If the numerator is increased by 7 and denominator is decreased by 2 , the new number becomes 6/5. Find the original number.
\large \dag† Answer :-
\begin{gathered}\red\dashrightarrow\underline{\underline{\sf \green{The \: Original \: Number \: is \: \frac{23}{27} }} }\\\end{gathered}
⇢
The Original Number is
27
23
\large \dag† Step by step Explanation :-
Let Numerator and Denominator of Original Fraction be :
Numerator = x
As Per the question denominator of the rational number is greater than its numerator by 4 so,
Denominator should be = x + 4
So ,
\begin{gathered}\text{Original Fraction = } \frac{\text x}{\text x + 4} \\ \\\end{gathered}
Original Fraction =
x+4
x
❒ When numerator is increased by 7 and denominator is decreased by 2 :
\begin{gathered}\\ \rm \text{Fraction Becomes } : \frac{x +7}{x + 2} \\ \\\end{gathered}
Fraction Becomes :
x+2
x+7
⏩ According To Question :
\begin{gathered} \\ \large \blue \bigstar \: \red{ \bf \frac{x +7}{x + 2} = \frac{6}{5} } \\ \\\end{gathered}
★
x+2
x+7
=
5
6
\begin{gathered}:\longmapsto \rm 6(x + 2) = 5(x + 7) \\ \\ \end{gathered}
:⟼6(x + 2)=5(x+7)
\begin{gathered}:\longmapsto \rm 6x + 12 = 5x + 35 \\ \\ \end{gathered}
:⟼6x +12=5x+35
\begin{gathered}:\longmapsto \rm 6x - 5x = 35-12 \\ \\ \end{gathered}
:⟼6x − 5x=35−12
\begin{gathered}\purple{ \large :\longmapsto \underline {\boxed{{\bf x = 23} }}}\\\\\end{gathered}
:⟼
x=23
\begin{gathered}\blue\dashrightarrow\underline{\underline{\sf \orange{Numerator \: of \: Original \: Fraction = 23}} }\\ \end{gathered}
⇢
Numerator of Original Fraction=23
☆ As denominator of the rational number is greater than its numerator by 4
\begin{gathered}\rm\therefore \: Denominator = 23 + 4\\ \end{gathered}
∴ Denominator =23 +4
\begin{gathered}\blue\dashrightarrow\underline{\underline{\sf \orange{Denominator \: of \: Original \: Fraction = 27}} }\\ \end{gathered}
⇢
Denominator of Original Fraction=27
Therefore,
\large\underline{\pink{\underline{\frak{\pmb{ Original \: Fraction = \dfrac{23}{27} }}}}}
Original Fraction =
27
23
Original Fraction =
27
23
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