61. The Missing Two Rupees
Three friends walk into a shop to buy a wall-clock. The assistant quotes the price as Rs. 60, so each friend hands over Rs. 20, making Rs. 60 in total.
Later the shop owner discovers that the correct price of the clock should have been only Rs. 50. He gives the assistant Rs. 10 to return to the customers.
On the way back, however, the assistant decides to keep Rs. 4 for himself and hands back just Rs. 2 to each friend (a total of Rs. 6).
Now think about the money:
- Each friend originally paid Rs. 20 and got Rs. 2 back, so each ultimately paid Rs. 18. Altogether they paid 3 × 18 = Rs. 54.
- The assistant kept Rs. 4.
If we add these together we seem to get Rs. 54 + Rs. 4 = Rs. 58 – but Rs. 60 was originally handed over. Where are the missing two rupees?
Added 1 September 2012
Hint: Do you really need to add the assistant’s Rs. 4 to the Rs. 54 paid for the clock, or should you be matching amounts that belong on opposite sides of the ledger?
Solution:
The apparent paradox comes from mixing two different kinds of numbers: the amount paid for the clock and the amount taken by the assistant. They should not be added; they should be separated into where the money ended up.
Here is the correct accounting:
- Shop owner receives the proper price of the clock: Rs. 50.
- Assistant keeps: Rs. 4.
- Money returned to the friends: Rs. 6 (three lots of Rs. 2).
Total: 50 + 4 + 6 = Rs. 60, exactly the amount originally given.
When we say each friend ended up paying Rs. 18, the Rs. 54 thus obtained already includes the Rs. 4 kept by the assistant (50 + 4 = 54). Therefore adding the Rs. 4 again double-counts it and produces the false total of Rs. 58. There is no missing money; it is simply a bookkeeping misdirection.
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