Dissapearing cash

Logic Level 2

Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later the clerk realizes the bill should only be $25. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself. Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1? This is where the flaw is. There cannot be two answers to the math problem. It is true that the 25 in the register the 3 back to the guest and 2 for a tip = 30. However, anyway you look at it, 9×3=27 +2= 29!

the dollar was never there they are demented irrelevent this twists space and time immature this is wrong rielly lied innapropraite

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Krishna Karthik
Nov 14, 2018

Using the process of elimination, we can find out that since all answers except the right one can't be true, the answer is 'the dollar was never there'.

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The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25). This is instead a sum of a smaller amount the people could have paid ($9 * 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). Another way to say this is, the $27 already includes the bellhop's tip. To add the $2 to the $27 would be to double-count it. So, the three guests' cost of the room, including the bellhop's tip, is $27. Each of the 3 guests has $1 in his pocket, totalling $3. When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30.

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