The Mystery of the Missing Paisa

         Two women were selling marbles in the market place – one at three for a paisa and other at two for a paisa. One day both of them were obliged to return home when each had thirty marbles unsold. They put together the two lots of marbles and handing them over to a friend asked her to sell them at five for 2 paise. According to their calculation, after all, 3 for one paisa and 2 for one paisa was exactly the same as 5 for 2 paise.

        Now they were expecting to get 25 paise for the marbles, as they would have got, if sold separately. But much to their surprise they got only 24 paise for the entire lot.

       Now where did the one paisa go? Can you explain the mystery?

Answer:   There isn’t really any mystery because the explanation is simple. While the two ways of selling are only identical. When the number of marbles sold at three for a paisa and two for a paisa is in the proportion of three to two. Therefore, if the first woman 24, they would have fetched 24 paise, immaterial of, whether sold separately or at five for 2 paise. But if they had the same number of marbles which led to loss of 1 paisa when sold together, in every 60 marbles. So, if they had 60 each, there would be a loss of 2 paise and if there were 90 each (180 altogether) they would lose 3 paise and so on.

              In the case of 60, the missing 1 paisa arises from the fact that the 3 marbles per paisa woman gains 2 paise and the 2 marbles per paisa woman lose 3 paise. 

             The first woman receives 9½ paise and the second woman 14½, so that each loses ½ paise in the transaction.