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      Question

      A work can be completed by โ€˜Aโ€™ and โ€˜Bโ€™, alone in

      15 days and 10 days, respectively. Find the number of days taken by โ€˜Cโ€™ to complete the same work alone if โ€˜Aโ€™, โ€˜Bโ€™ and โ€˜Cโ€™ together can complete the whole work in 4 days.
      A 10 days Correct Answer Incorrect Answer
      B 10.5 days Correct Answer Incorrect Answer
      C 12.5 days Correct Answer Incorrect Answer
      D 12 days Correct Answer Incorrect Answer

      Solution

      Let total work = 30 units (LCM of 15 and 10) Efficiency of โ€˜Aโ€™ = (30/15) = 2 units/day Efficiency of โ€˜Bโ€™ = (30/10) = 3 units/day Combined efficiency of โ€˜Aโ€™, โ€˜Bโ€™ and โ€˜Cโ€™ = (30/4) = 7.5 units/day Efficiency of โ€˜Cโ€™ = 7.5 โ€“ (2 + 3) = 2.5 units/day Required time taken = (30/2.5) = 12 days

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