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ELI5 Yahaaa

Taking a slice off the top

How Do Shops Work Out a Sale Price?

A discount is a percentage of the old price, so the same '30% off' saves different amounts.

Before £4030% off £12 off, so £28
The percentage is fixed. The saving is not.

  1. Step 1 of 5

    The percentage is of the old price.

    30% of £10£3 off30% of £40£12 off30% of £4£1.20 off

    Thirty per cent off means thirty out of every hundred pence of the original. Change the original and you change the saving.

  2. Step 2 of 5

    There is a shortcut: pay the rest.

    Two steps Find 30%, then subtractOne step Find 70% and you aredone

    Instead of finding thirty per cent and taking it away, find seventy per cent and stop. One step instead of two.

  3. Step 3 of 5

    Two discounts do not add up.

    1 £1002 −20% → £803 −10% of £80 →£72, not £70

    Twenty per cent off, then a further ten per cent, is not thirty per cent off. The second cut is taken from the already-reduced price.

  4. Step 4 of 5

    Buy one get one free is thinking in units.

    You wanted two A real 50% savingYou wanted one You spent more, notless

    Two items for the price of one is fifty per cent off — but only if you wanted two. Otherwise it is no discount at all.

  5. Step 5 of 5

    The honest comparison is always the unit price.

    1 Any offer2 Divide by howmany you get3 Compare thatone number

    The only number that survives every offer is what one of the thing costs. Everything else is arithmetic dressed up.

    Shops know that '£12 off' and '30% off' feel different even when they are the same, and choose whichever sounds bigger.

The short version

A discount is a percentage of the old price, two discounts never add up, and only the unit price compares offers honestly.

Try it yourself

Find a '3 for 2' shelf and work out the price of one item. Compare it with the single-item price nearby.

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