Mathematics and Statistics · Ch 9 — Commission, Brokerage and Discount

Successive Discounts

Sometimes two (or more) discounts are offered one after another on the same article — for example "20% off, and a further 10% off". These are successive discounts. The second discount is applied not to the list price but to the amount left after the first discount has been deducted, so successive discounts can never simply be added.

Note

Selling price after successive discounts

For a list price $L$ and successive discounts of $d_1\%$ and $d_2\%$ ,

$\text{Selling price} = L\times\Big(1-\tfrac{d_1}{100}\Big)\times\Big(1-\tfrac{d_2}{100}\Big).$

More discounts simply add more factors of the same form.

Note

Single equivalent discount

The single discount that would give the same selling price is

$D = \left[\,1-\Big(1-\tfrac{d_1}{100}\Big)\Big(1-\tfrac{d_2}{100}\Big)\right]\times 100\ \%.$

For two discounts this can also be written directly as $D = d_1 + d_2 - \dfrac{d_1 d_2}{100}$ . …

Definition 13Successive discounts

Two or more discounts applied one after another, each on the amount remaining after the previous discount; they cann …

Definition 14Single equivalent discount

$D=\left[1-\left(1-\tfrac{d_1}{100}\right)\left(1-\tfrac{d_2}{100}\right)\right]\times100\%$ , the one discount giving the same net price as successive discounts $d_1\%$ and $d_2\%$ ; for two discount …

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