Question

Example 25: The numerator of a fraction is 6 less than the denominator. If 3 is added to the 2 numerator,the fraction is equal to 2/3 ,find the original fraction 3​

Answer 1

⚘ Given :

• The numerator of a fraction is 6 less than the denominator.

• If 3 is added to the 2 numerator, the fraction is equal to 2/3

⚘ To Find :

• To find the original fraction 3

⚘ Solution :

Let, The denominator be = x

Thus, numerator = x – 6

Therefore,

➩ x – 6 + 3 / x = 2/3

➩ 3 (x – 3) = 2x

➩ 3x – 9 = 2x

➩ x = 9

• So denominator : x = 9
• Therefore, Numerator = x – 6 = 9 – 6 = 3

Original fraction = 3/9

Answer 2

$\frak{Given}\begin{cases}{\;\;\;\bf{\dfrac{Numerator+3}{Denominator}=\dfrac{2}{3}}}\end{cases}$

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$\frak{To\;Find:\;}$ The Original fraction?

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❍ Let the Denominator of the fraction be x and according to the question, Numerator be (x – 6) respectively.

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• If 3 is added to the numerator, the fraction is equal to ⅔.

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$:\implies\begin{gathered}\\\end{gathered}{\sf{\dfrac{x-6+3}{x}=\dfrac{2}{3}}}$

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$~~~~~:\implies\begin{gathered}\\\end{gathered}{\sf{\dfrac{x-3}{x}=\dfrac{2}{3}}}$

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$~~~~~~~~~~:\implies\begin{gathered}\\\end{gathered}{\sf{3x-9=2x}}$

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$~~~~~~~~~~~~~~~:\implies\begin{gathered}\\\end{gathered}{\sf{3x-2x=9}}$

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$~~~~~~~~~~~~~~~~~~~~:\implies\begin{gathered}\\\end{gathered}{\underline{\boxed{\pink{\frak{x=9}}}}}\:\bigstar$

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Hence,

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• Numerator = (x – 6) = (9 – 6) = 3
• Denominator = x = 9

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$\therefore\;{\underline{\sf{Hence,\;the\;original\;fraction\;is\;\bf{\dfrac{3}{9}}}.}}$⠀