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      Question

      The time taken by P to complete a

      task is half of the time taken by Q. Q and R working together finish the task in 20 days, while P and R take 15 days. How long will P and Q together take to complete the task?
      A 20 days Correct Answer Incorrect Answer
      B 18 days Correct Answer Incorrect Answer
      C 12 days Correct Answer Incorrect Answer
      D 28 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let the total work be 60 units. {LCM (20 and 15)} Efficiency of Q + R = 60 ÷ 20 = 3 units/day Efficiency of P + R = 60 ÷ 15 = 4 units/day Let efficiencies be: Q = q, R = r P = 2q (because P works twice as fast) So, (q + r) = 3 ……… (i) (2q + r) = 4 ……… (ii) Subtracting (i) from (ii): q = 1 Efficiency of P = 2 × 1 = 2 units/day Required time = 60 ÷ (1 + 2) = 20 days

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