The Missing Money - Answer

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THE MISSING MONEY 

- ANSWER

Age group: All

The question was:

"Three friends check into a motel for the night and the clerk tells them the bill is Rs. 3000, payable in advance. So, they each pay the clerk Rs. 1000 and go to their room. A few minutes later, the clerk realises he has made an error and overcharged the trio by Rs. 500. He asks the Assistant to return Rs. 500 to the 3 friends who had just checked in.

The Assistant sees this as an opportunity to make Rs. 200 as he reasons that the three friends would have a tough time dividing Rs. 500 evenly among them; so he decides to tell them that the clerk made a mistake of only Rs. 300, giving a hundred rupee note back to each of the friends. He pockets the leftover Rs. 200 and goes home for the day! N

ow, each of the three friends gets a hundred rupee back. thus they each paid Rs. 900 for the room, which is a total of Rs. 2700 for the night. We know the Assistant pocketed Rs. 200 and adding that to the 2,700, you get Rs. 2,900, not Rs. 3,000 which was originally spent.

Where did the other hundred rupees go?"


You can also view the question here:

Now coming to the Answer!

Let us think about this clearly. The three friends paid Rs. 3000. However, they should have paid only Rs. 2500. The clerk sends back Rs. 500. Rs. 300 is returned to the friends while Rs. 200 remains with the assistant i.e. the total of Rs. 500 is still there.

The trick is that addition and subtraction have been done at wrong times to misdirect our thinking such that often, it becomes impossible to think about it in any other way. 

Another way of looking at this question is, that even after getting back 100 rupees each, they didnt pay 900 rupees each, rather they paid 2500/3 = 833.33 rupees each.

Now, 

833.33*3 = 2500 (since 833.33 is actually 2500/3) and
2500 + 300 (Given back) + 200 (Taken by Assistant) = 3000.

The below solution was given by Shirin Sitara which I would definitely like to share with you all:

The idea of "3000" must be dissolved. The original price of the room is Rs. 2500, and the group totally paid Rs. 2700, thus the remaining money (i.e. Rs. 200) went to the assistant.

***

If you have got the same answer in any other way, then do let me know in the comments section!

If you have interpreted this question in another suitable way, then do let me know in the comments section again!

If I have made any significant errors, do let me know about that too, and I will be sure to make the necessary changes!
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I hope you enjoyed this :)


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With Warm Wishes,
Lavanya


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