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Where is the missing amount??

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Two women were selling marbles in the market place —one at three for a paise and other at two for a paise. 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 paise and 2 for one paise was exactly the same as 5 for 2 paise.
But when the takings were handed over to them, they were both most surprised, because the entire lot together had fetched only 24 paisel If however, they had sold their marbles separately they would have fetched 25 paise.
Now where did the one paise go? Can you explain the mystery?

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JamesBond Pundit Asked on 26th July 2015 in Microsoft Interview Puzzles.
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    There isn’t really any mystery, because the ex-planation is simple. While the two ways of selling are only identical, when the number of marbles sold at three for a paise and two for a paise is in the proportion of three to two. There-fore when the first woman handed over 36 marbles and the second woman 24, they would have fetched 24 paise, immaterial of sold separately or at five for 2 paise. But if they each held the same number of marbles there would be a loss when sold together of 1 paise 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 paise arises from the fact that the 3 a paise woman gains 2 paise and the 2 a paise woman loses 3 paise. The first woman receives 9.5 paise and the second woman 14.5, so that each loses 0.5 paise in the transaction.

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    John123 Expert Answered on 26th July 2015.
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    When they sell separately the ratio they get is 25/60 or 5/12 = 4.16666… , but when selling together the ration the made is only 2/5 (24/60) = 0.4. That’s why after selling 60 marbles there is a difference of one paise.

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    Moshe Expert Answered on 12th March 2023.
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