# What happened to the missing £10? [duplicate]

I have come across a puzzle, which makes no sense. Does anyone know the answer to the below?

You and two friends go on holiday. When checking out, the total bill comes to £300. You pay the bill and begin to walk out. The clerk realises that he’s made an error and hands the bellhop a £50 note to return to you. He realises that he cannot split the £50 equally, so he decides to give each guest £10 and keep £20 as a tip for himself. Hence, each guest received £10 back, meaning they only paid £90 each. This means the total paid by the three people was £270 (£90 x 3). Add in the £20 the bellhop kept and the total comes to £290. What happened to the missing £10?

• Not only is it a duplicate, there's even another question about where it came from. This version is closer to the original but it's still a duplicate on Puzzling. Jun 24 '15 at 12:22

You should be deducting the Bellhop's £20 from the £270, not adding it.

Edited with more details: The question is deliberately misleading you into thinking there's a paradox, and some money has gone missing.

The total amount paid initially was £300, £100 each.

The total amount paid after the partial refund was £270, £90 each.

The sly bellhop kept the final £20 for himself - had he split this evenly, the total amount paid would have been £250 - £83.333... each.

The question is misleading in the way it deducts the refund received by the customers, but then attempts to add the refund stolen by the bellhop.

• Welcome to Puzzling! The idea looks correct, could you please add more details to your answer? Solutions with scarce explanation are likely to be deleted, even if upvoted. Jun 24 '15 at 11:54

Let's consider the total amounts of money.

BEFORE PAYING:

Guests: 300 (3x100)
Clerk: 0
Shop: 0

The clerk gets a 20 tip, while each man pays 90 (gives 100 but is returned 10).

AFTER PAYING:

Guests: 30 (3x10)
Clerk: 20
Shop: 250

As you can see there is no paradox, the only mistake was trying to sum 20 to 270 which absolutely makes no sense!

You pay £300.
The clerk returns £50.
The bellhop returns £30 of the £50 and keeps £20.
You and your friends have paid £270.
The clerk intended for you to have paid £250.

£300 = £250 + £50(change)
£50 = £10 + £10 + £10 (returned to you) + £20 (kept by bellhop)

I'm not sure where you see a missing £10, so I can't tell you what happened to it.