# Bicycle Thieves – A puzzle

One day a man, who looked like a tourist, came to a bicycle shop and bought a bicycle from a shop for $70. The cost price of the bicycle was$60. So the shopkeeper was happy that he had made a profit of $10 on the sale. However, at the time of setting the bill, the tourist offered to pay in travellers cheques as he had no cash money with him. The shopkeeper hesitated. He had no arrangement with the banks to encash travellers cheques. But he remembered that his friend, the shopkeeper next door, has such a provision, and so he took the cheques to his friend next door and got cash from him. The travellers cheques were all of$20 each and so he had taken four cheques from the tourist totalling to $80. On encashing them the shopkeeper paid back the tourist the balance of$10.
The tourist happily climbed the bicycle and pedaled away whistling a tune.
However, the next morning shopkeeper’s friend who had taken the travellers cheques to the bank called on him and returned the cheques which had proved valueless and demanded the refund of his money. The shopkeeper quietly refunded the money to his friend and tried to trace the tourist who had given him the worthless cheques and taken away his bicycle. But the tourist could not be found.

How much did the shopkeeper lose altogether in this unfortunate transaction?

One can think of different answers for this question, but yet the correct answer is very simple. All we have to consider is that the shop owner could not have possibly lost more than the tourist actually stole.
The tourist got away with the bicycle which cost the shop owner $60 and the$10 ‘change’ , and therefore, he made off with \$70. And this is the exact amount of the shopkeeper’s loss.

Source of The Puzzle:

Puzzle 7, Puzzles to Puzzle You

This puzzle is l’ll modified than the original.

# The Mystery of the Missing Money – A classical puzzle by Human Computer Shakuntala Devi With Solution

### 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 ( $60 \times \frac {2} {5}$ ) times 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 recieves 9½ Rupees and the second woman 14½ , so that each loses ½ Rupees in the transaction.