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      Question

      With P starting the work, working on alternate days, P

      and Q can finish a work in 17 days. If Q works on the first day and Q and P work alternately, the work is finished in 53/3 days. How many days will each take individually to execute the work?
      A P = 35 days; Q = 35 days Correct Answer Incorrect Answer
      B P = 35/3 days; Q = 35 days Correct Answer Incorrect Answer
      C P = 12 days; Q = 35 days Correct Answer Incorrect Answer
      D P = 35 days; Q = 35/3 days Correct Answer Incorrect Answer

      Solution

      ˆLet P's 1 day work = x and Q's 1 day work = y If P start the work, working on alternate days, P and Q can finish a work in 17 days. P works for = 9 days Q works for = 8 days Total work = 9x + 8y If Q works on the first day and P and Q work alternately, the work is finished in 53/3 days =53/3 = 17+(2/3) Days Q works for = 9 days P work for = 8 + (2/3) = 26/3 days Total work = 9y + 26x/3 According to the question 9x + 8y = 9y + 26x/3 9x-26x/3 = 9y-8y  x/3 = y x: y =3:1 Total work = 9x + 8y = 9×3+8×1 = 35 Q alone can finish the whole work in = 35/1 = 35 P alone can finish the whole work in = 35/3 days.

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