Math CentralQuandaries & Queries


Question from Tom:

I work in a clothes shop which can also do mail-orders. My Head Office has sent a report with which we can check the records we keep in store tally with those at HO.

According to that report we have taken £2578.25 in orders, excluding VAT (20%),which would therefore be £3093.91 including VAT (2578.25+20%=3093.91).

According to my records, we have taken £3179.32 including VAT, which would be £2543.45 excluding VAT (3179.32-20%=2543.45).

Why is it that the difference between the VAT inclusive figures (3179.32-3093.91) is +£85.41, but the difference between the VAT exclusive figures (2543.45-2578.26) is -£34.81?

Now, I can see from the report that 1 order has not been recorded by HO, and I know that our average order value is around £30, so the -£34.81 makes sense. But surely both figures should be a minus, regardless of whether they include VAT?

I'm sure there is an obvious answer, but I just cannot see it! Any help would be gratefully received.

Hi Tom,

I can show you one place where there is an error in your reasoning but I'm not sure that fixing it completely solves the problem. When you say "we have taken £3179.32 including VAT, which would be £2543.45 excluding VAT (3179.32-20%=2543.45." you are subtracting 20% of £3179.32 which is the orders including the VAT but the 20% should should be on the before VAT orders. You know that

\[\mbox{(the before VAT orders + 20%) }= £3179.32\]


\[\mbox{(the before VAT orders)} \times 1.20 = £3179.32\]

which means that

\[\mbox{(the before VAT orders}) = \frac{ £3179.32}{1.20} = £2649.43.\]

But £2649.43 - £2578.25 = £71.18. Is it possible that the missing order has a value of £71.18?


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