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      Question

      Akash has a few pencils with him. By distributing it

      equally to the children he is left with 3 pencils. If there were 2 students lesser, he would have been left with only 1 pencil on distributing it equally by giving 2 additional pencils to each child. Had there been 4 children less than the original number, each child would have got 5 additional pencils and Akash would have been left with 3 pencils. How many pencils does Akash have?
      A 31 Correct Answer Incorrect Answer
      B 33 Correct Answer Incorrect Answer
      C 23 Correct Answer Incorrect Answer
      D 26 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let original number of children = x, and pencils per child = y
      We have xy + 3 = (x-2)(y+2) + 1
      or xy + 3 = xy + 2x - 2y - 4 + 1
      or x - y = 3 or x = y + 3
      Next we have:
      xy + 3 = (x-4)(y+5) + 3
      xy + 3 = xy +5x - 4y -20 + 3
      5x - 4y = 20
      Since x = y + 3, 5y + 15 - 4y = y + 15 = 20
      y = 5, x = 8
      Total pencils = xy + 3 = 43

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