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.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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