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      Question

      The denominator of a fraction is 4 more than twice the

      numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.
      A 18/7 Correct Answer Incorrect Answer
      B 16/7 Correct Answer Incorrect Answer
      C 7/18 Correct Answer Incorrect Answer
      D 7/16 Correct Answer Incorrect Answer

      Solution

      Let the required fraction is p/q  According to the question,  q = 2p + 4       -----(1) When both the numerator and denominator are decreased by 6, New fraction = (p - 6)/(q - 6) Again, according to the question, (q - 6) = 12(p - 6) ⇒ q - 6 = 12p - 72 From equation (1) ⇒ (2p + 4) - 6 = 12p - 72     ⇒ 2p - 2 = 12p - 72 ⇒ 10p = 70 ⇒ p = 7 Again, from equation (1) q = 2 × 7 + 4 ⇒ q = 18 ∴ The required fraction is 7/18.

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