Equivalent Single Discount for Successive Discounts

Trick / Shortcut

Topic

Profit & Loss

How It Works

When two successive discounts of $a%$ and $b%$ are applied, the equivalent single discount is not simply $a+b%$. The formula for the equivalent single discount is:

Equivalent Single Discount ($D_{eq}$): $D_{eq} = \left(a + b - \frac{ab}{100}\right)%$

The equivalent single discount will always be less than the sum of the individual discounts ($a+b$).

Example

Calculate the equivalent single discount for successive discounts of $20%$ and $10%$.

Using the formula, $a=20$ and $b=10$: $D_{eq} = \left(20 + 10 - \frac{20 \times 10}{100}\right)%$ $D_{eq} = \left(30 - \frac{200}{100}\right)%$ $D_{eq} = (30 - 2)% = \textbf{28%}$

So, two successive discounts of $20%$ and $10%$ are equivalent to a single discount of $28%$ (not $30%$).

Verification (on NPR 1000):

$20%$ discount: $1000 - (0.20 \times 1000) = 1000 - 200 = 800$
$10%$ discount on remaining: $800 - (0.10 \times 800) = 800 - 80 = \textbf{720}$ Total discount $= 1000 - 720 = 280$, which is $28%$ of 1000.