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I know this may be a bit of a 'go back to school' question but today I had an issue with one of my clients regarding a 20% deposit.

The total that was due for the services was £1350. I normally take a 20% deposit for all services.

I usually work out 20% like this: 0.2 * 1350 = 270

I told the customer he owed me £270 as that is 20% of £1350

My customer argued that I am working out the 20% wrong and that the deposit is in fact £225

He explained that he worked it out like this:

1350 / 1.20 = 1125

1350 - 1125 = 225

I'm pretty sure we are both working it out right here but in slightly different ways, so am I doing anything wrong with my way here?

I have always used my method, I have a feeling he is using a method that usually involves VAT calculations.

What is the essential difference between these two methods?

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    I have no guess as to what the customer is computing, your computation is plainly correct. – 2017-02-14

2 Answers 2

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You know that 20% is equivalent to $\frac{1}{5}$, so if you add the result of your 20% calculation to itself 5 times, you should get the original amount.

270 + 270 + 270 + 270 + 270 = 1350

225 + 225 + 225 + 225 + 225 = 1125

So you see that your calculation is correct. Why does your customer's calculation seem correct? He is finding the original amount after a 20% markup. For example, let's say I sell widgets at retail. I add 20% to the price I pay for the widgets (in order to pay my overhead, make a profit, etc.). The amount I sell a widget for is 1.2 times the amount I pay wholesale. So if my customer wants to know how much I paid for the widget, they divide the cost by 1.2 (as your customer did). The quotient is the original price; the difference is the total amount of markup. Does that make sense?

Your customer was actually calculating $\frac{1}{6}$ of the cost of services and telling you it was $\frac{1}{5}$. If your customer should know better, then I would avoid doing business with them in the future.

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    Thanks for clarifying. So my customer is effectively finding the 20% on the quotient (£1125) like @Cole Merkosky said? – 2017-02-15
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Your way calculates 20% of the £1350 (alternatively you could go £1350 x 1.2, which is the same as adding 0.2 on)

His way is calculating 20% on the £1125, like if he wanted to know the price of the service before VAT (he's effectively saying 1.2 x £1125 = £1350)

I'd venture to say your way is correct, as I assume you are charging on the total (including VAT)