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      Question

      A and B are capable of completing a project individually

      in 40 days and 50 days, respectively. Initially, A and B collaborated on the project, and after 10 days, C joined them. With C's assistance, the total project was completed in 20 days. How long would it take for C to complete the project on their own?
      A 80 days Correct Answer Incorrect Answer
      B 90 days Correct Answer Incorrect Answer
      C 100 days Correct Answer Incorrect Answer
      D 75 days Correct Answer Incorrect Answer
      E 120 days Correct Answer Incorrect Answer

      Solution

      Part of the work done by A and B in one day = (1/40) + (1/50) = 9/200 Part of the work done by A and B in 10 days = 90/200 Remaining work = 1 – (90/200) = 110/200 Let the time taken by C alone to complete the work be ‘c’ days. So, (90/200) + (10/c) = 110/200 10/c = (110/200) – (90/200) c = 100 So, time taken by C alone to complete the work = 100 days

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