Question

The denominator of a fraction is 8 less than its denominator if 2 is added to both numerator and denominator section become 11 upon 19 find the fraction

Answer 1

Given:-

• The numerator of a fraction is 8 less than its denominator.
• If 2 is added to both numerator as well as denominator the fraction becomes 11 upon 19.

To Find:-

• What's the Fraction?

Solution :-

$\sf \underline {Let}$

• The denominator of the fraction be x.It’s given that the numerator of a fraction is 8 less than its denominator. So, its numerator will be (x - 8) and the fraction will be (x-8)/x.

⠀⠀⠀⠀⠀$\small\underline{\pmb{\sf According \: to \: the \: question :-}}$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies \dfrac{(x - 8) + 2}{x + 2} = \dfrac{11}{19}$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies\dfrac{x - 8 + 2}{x + 2} = \dfrac{11}{19}$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies\dfrac{x - 6}{x + 2} = \dfrac{11}{19}$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19(x - 6) = 11(x + 2)$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19x - 114 = 11x + 22$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19x - 11x = 22 + 114$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies 8x = 136$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies x = \cancel\dfrac{136}{8}$

$\sf \: \: \: \: \: \: \: \: \: \:\::\implies{\underline{\boxed{\frak{\pink{x =17}}}}}\:\bigstar$

$\therefore\:\underline{\textsf{The Denominator is \textbf{17}}}.$

$\dag\underline{\sf{\sf The\: \: of \:Numerator \: of the\: fraction\: is :- }}$

$\sf:\implies x - 8 = 17 - 8.$

$\sf:\implies \boxed{ \sf Numerator = 9.}$

$\therefore\:\underline{\textsf{The fraction will be \textbf{9/17}}}.$

Answer 2

Answer:

Given:-

The numerator of a fraction is 8 less than its denominator.

If 2 is added to both numerator as well as denominator the fraction becomes 11 upon 19.

To Find:-

What's the Fraction?

Solution :-

\sf \underline {Let}Let

The denominator of the fraction be x.It’s given that the numerator of a fraction is 8 less than its denominator. So, its numerator will be (x - 8) and the fraction will be (x-8)/x.

⠀⠀⠀⠀⠀\begin{gathered}\small\underline{\pmb{\sf According \: to \: the \: question :-}}\\\end{gathered}Accordingtothequestion:−Accordingtothequestion:−

\begin{gathered}\sf \: \: \: \: \: \: \: \: \: \:\::\implies \dfrac{(x - 8) + 2}{x + 2} = \dfrac{11}{19}\\\end{gathered}:⟹x+2(x−8)+2=1911

\begin{gathered} \sf \: \: \: \: \: \: \: \: \: \:\::\implies\dfrac{x - 8 + 2}{x + 2} = \dfrac{11}{19}\\\end{gathered}:⟹x+2x−8+2=1911

\begin{gathered} \sf \: \: \: \: \: \: \: \: \: \:\::\implies\dfrac{x - 6}{x + 2} = \dfrac{11}{19}\\ \end{gathered}:⟹x+2x−6=1911

\begin{gathered}\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19(x - 6) = 11(x + 2)\\\end{gathered}:⟹19(x−6)=11(x+2)

\begin{gathered}\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19x - 114 = 11x + 22\\\end{gathered}:⟹19x−114=11x+22

\begin{gathered}\sf \: \: \: \: \: \: \: \: \: \:\::\implies 19x - 11x = 22 + 114\\\end{gathered}:⟹19x−11x=22+114

\begin{gathered}\sf \: \: \: \: \: \: \: \: \: \:\::\implies 8x = 136\\\end{gathered}:⟹8x=136

\begin{gathered} \sf \: \: \: \: \: \: \: \: \: \:\::\implies x = \cancel\dfrac{136}{8} \\\end{gathered}:⟹x=8136

\begin{gathered} \sf \: \: \: \: \: \: \: \: \: \:\::\implies{\underline{\boxed{\frak{\pink{x =17}}}}}\:\bigstar\\\\\end{gathered}:⟹x=17★

\begin{gathered}\therefore\:\underline{\textsf{The Denominator is \textbf{17}}}.\\\end{gathered}∴The Denominator is 17.

\dag\underline{\sf{\sf The\: \: of \:Numerator \: of the\: fraction\: is :- }}†TheofNumeratorofthefractionis:−

\begin{gathered}\sf:\implies x - 8 = 17 - 8.\\\end{gathered}:⟹x−8=17−8.

\begin{gathered} \sf:\implies \boxed{ \sf Numerator = 9.}\\\end{gathered}:⟹Numerator=9.

\begin{gathered}\therefore\:\underline{\textsf{The fraction will be \textbf{9/17}}}.\\\end{gathered}∴The fraction will be 9/17.