Successive Discounts and the Single Equivalent Discount

Sometimes a shopkeeper offers more than one discount, one after another, on the same article — for instance '20% off, and a further 10% off on the reduced price.' These are successive discounts. The crucial point is that the second discount is taken on the already-reduced price, not on the original marked price — so two successive discounts are not the same as adding the two rates.

For successive discounts of $d_1\%$ and $d_2\%$ on a marked price $MP$:

This extends naturally to three or more discounts by multiplying one more factor for each:

Single equivalent discount. The one discount that would produce the same final selling price as the whole series is called the single equivalent discount. For two discounts it can be found directly: