# Puzzle

Two women were selling marbles in the market place — one at three for a Rupee and other at two for a Rupee. One day both of then 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 then at five for 2 Rupees. According to their calculation, after all, 3 for one Rupee and 2 for one Rupee was exactly same as 5 for two Rupees.
Now they were expecting to get 25 Rupees for the marbles, (10 Rupees to first and 15 Rupees to second), as they would have got, if sold separately. But much to their surprise they got only 24 Rupees ( $60 \times \frac {2} {5}$ ) for the entire lot.

Now where did the one Rupee go? CAN YOU EXPLAIN THE MYSTERY?

# Solution

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 role at three for a Rupee and two for a Rupee is in the proportion of three by two. Therefore, if the first woman had handed over 36 marbles and the second woman 24, they would have fetched 24 Rupee, immaterial of, whether they sold separately or at five for 2 Rupee. But if they had the same number of marbles which led to loss of 1 Rupee when role together, in every 60 marbles. So, if they had 60 each, there would be a loss of 2 Rupee and if there were 90 each (180 altogether) they would lose 3 Rupees and so on.
In the case of 60, the missing 1 Rupee arises from the fact that the 3 marbles per Rupee woman gains 2 Rupees and the 2 marbles per Rupee woman loses 3 Rupees.
The first woman receives 9½ Rupees and the second woman 14½ , so that each loses ½ Rupees in the transaction.

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