Tricky percentages

Percentages describe proportions, not amounts, and forgetting that leads to some genuinely tricky situations.

Would you rather? You've won a contest with two options:

A looks four times better as a percentage. But if you can pick only once, B puts more money in your pocket, and the percentages, taken alone, pointed the other way.

A second case. A shop offers, on any purchase above ₹150, either 20% off or ₹50 off. Which is better?

It depends on the size of the purchase, because one option is a proportion and the other a fixed amount. On ₹180, 20% saves ₹36, so the ₹50 is better. On ₹225 the two are almost level. On ₹300, 20% saves ₹60, so the percentage wins. Find the crossing point for yourself.

Now the trickiest of all. Cakely offers '30% + 20% off'. Cakify offers '50% off'. Since 30 + 20 = 50, they should be identical. They aren't.

In shopping, '30% + 20%' means one discount after the other. On a ₹200 cake: 30% off takes away ₹60, leaving ₹140. Then 20% off is taken on the ₹140, not the ₹200, so it removes only ₹28, leaving ₹112.

Cakify's straight 50% takes ₹100 off, leaving ₹100. Cakify is cheaper by ₹12. The second discount in a stacked offer is always smaller than it looks, because it's measured against an already-reduced price. Percentages are always of something, and that something keeps moving.