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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 \(\dfrac{3}{4}\). Find the original fraction?

  • A.\(\dfrac{2}{5}\)
  • B.\(\dfrac{7}{9}\)
  • C.\(\dfrac{3}{11}\)
  • D.\(\dfrac{8}{5}\)

Answer: C

The denominator be \(P\), the numerator will be \((P - 8)\)
The fraction will be \(\dfrac{(P - 8)}{P}\)
Adding 3 to the numerator and subtracting 3 from the denominator,
\(\dfrac{(P - 8 + 3)}{P - 3}= \dfrac{3}{4}\)
\(\dfrac{(P - 5)}{P - 3}= \dfrac{3}{4}\)
\(P = 20 - 9 \Rightarrow P = 11\)
The fraction is: \(\dfrac{3}{11}\)

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