The most likely maths behind the alleged petrol-pump price scam being reported on Facebook.

I don’t normally share this kinda thing …

Unless there’s bad maths involved!?

On Facebook usually if a post starts “Ok so I’m not normally one to share things like this but…” then it’s down to some marketing genius trying to dole out product links cloaked as hot tips. So, when I saw this post I assumed that it was something along those lines. Instead (at first look at least) it appears to be a report of over-charging for petrol:

“Now I heard about garages starting to clock the pumps to charge you more than advertised so I started putting the test to the theory and low and behold…they were right! Charging me more for my fuel…Bast**ds! Now I can’t belive I never actually checked this before!
As you can see, 1 Litre should cost 123.9 pence, when I put exactly 1 Litre in it came to 125pence!”
(Attila ッ Boros, unedited, via Facebook)

So, is this for real. And if it is why would the company advertise the “scam” right there on the pump for everyone to see?!?

If it’s not a scam …?

This has to be a scam right, the pump says £1.25 for 123.9p worth of petrol, doesn’t it?

What you see is not what you get!

What we’re not seeing here is the actual amount of petrol. Mr Boros says: “I put exactly 1 Litre in it came to 125pence!“. But how do we know how much fuel he put in – the dial reads 1.00, but that doesn’t mean exactly 1.00 litres, it means that the truncated or rounded amount is 1.00 litres.

What range of figures could we have here?

“[…] I put exactly 1 Litre in it came to 125pence!”

(4 decimal places shown, the last decimal place is rounded where necessary in all calculation results)

Truncated:

If the values shown are truncated – which seems right as these displays normally flip over (like a car mileage readout) as the 9 passes by in the hidden next place.

£1.2500 – £1.2599  will display as £1.25 when truncated.

1.0000L – 1.0099L will display as 1.00 L when truncated.

1.2390 £/L – 1.2399 £/L will display as £1.239 (ie 123.9p) when truncated.

Taking the extremes here 1.0099L * 1.2399 £/L gives us £1.2522 which is £1.25 when truncated.

If the price given is exact at 1.2390 £/L * 1.0099L gives us £1.2512 which is £1.25 when truncated.

FWIW the lowest volume that would display at a total cost of £1.25 would be 1.0088L.

Rounded:

If the values were rounded (probably not but worth considering, if it were a digital display this is more likely but still not as likely IMO as simple truncation).

£1.2450 – £1.2549 will all display as £1.25 when rounded.

0.9950L – 1.0049L will all display as 1.00L when rounded.

1.2385 £/L – 1.2394 £/L will all display as 1.239 £/L (ie 123.9p/L) when rounded.

Taking the extremes here 1.2394  £/L * 1.0049L gives us £1.2454 which is £1.25 rounded.

If the price given is exact at 1.2390 * 1.0049 gives us 1.2451 which is also 1.25 when rounded up.

Rounded or truncated, even requiring the price to be exactly the 123.9 p/L that is displayed allows for the calculations to be honest and completely above board.

So BP are totally legit then?

Well I didn’t say that … but at least this alleged scam appears to be a lot of fuss over everyday mathematics.

You may well be getting ripped off at the pumps but safe-to-say this Facebook posting doesn’t provide evidence for that. The only question left for me here is whether Mr Boros is an SEO genius sharing this to boost his likes and thus boost his Facebook link-graph and hence his ability to market to Facebook users in the future (accounts with lots of likes can be sold or used to sell advertising spots). But that sort of allegation is not for me to make.

[Image of full Facebook post in question, at the time of writing it had over 100,000 [one-hundred thousand] shares. The BP Garage in Cambridge that became the subject of the allegations. Related SNOPES post.]