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      Question

      Three persons A, B and C can complete a piece of work

      alone in 12 days, 15 days and 20 days, respectively. I) A and B work together for x days. II) Then only C works for 3 days; after that, 2/5 of the work still remains to be done. III)  If instead only B had worked for 3 days (after A and B worked for x days), 7/20 of the work would have remained. What is the value of x?
      A 5 days Correct Answer Incorrect Answer
      B 3 days Correct Answer Incorrect Answer
      C 8 days Correct Answer Incorrect Answer
      D 10 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Work by A+B in x days = 3x/20 Case 1 (C): Remaining = 2/5 ⇒ done = 3/5 3x/20 + 3/20 = 3/5 (3x + 3)/20 = 3/5 3x + 3 = 12 3x = 9 x = 3 Check Case 2 (B): Work by B in 3 days = 1/5 Total done = 3x/20 + 1/5 = 9/20 + 1/5 = 9/20 + 4/20 = 13/20 Remaining = 1 − 13/20 = 7/20 (matches Condition 3). So x = 3 days. Hence the correct answer is (b) 3 days.

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