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      Question

      A can complete a piece of work alone in 20 days, while B

      can do it alone in 30 days. They worked together for 5 days and left. The rest of the work is completed by C alone in 7 days. In what ratio should the payment be divided among them?
      A 4:5:6 Correct Answer Incorrect Answer
      B 3:2:7 Correct Answer Incorrect Answer
      C 1:8:9 Correct Answer Incorrect Answer
      D 2:6:9 Correct Answer Incorrect Answer

      Solution

      Let the total work be 60 units (LCM of 20 and 30) ⇒ Efficiency of A = 60/20 = 3 units/day ⇒ Efficiency of B = 60/30 = 2 units/day Combined efficiency of A and B = 3 + 2 = 5 units/day Work done by A and B in 5 days = 5 × 5 = 25 units Remaining work = 60 - 25 = 35 units Efficiency of C = 35/7 = 5 units/day Ratio of work done by A : B : C = Efficiency × time done by each Ratio of work done by A : B : C = 3×5 : 2×5 : 5×7 ⇒ Ratio of work done by A : B : C = 3 : 2 : 7 ∴ The payment is divided among A, B, and C in the ratio 3 : 2 : 7.

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