Profit, Loss & Discount

Formula sheet

Everything for this chapter, in one place. CP is cost price, MP the marked or list price, SP the selling price.

The definitions, and what each percentage is of


Profit	$\text{SP} - \text{CP}$
Profit %	$\dfrac{\text{SP}-\text{CP}}{\text{CP}} \times 100$ — always on CP
Discount %	$\dfrac{\text{MP}-\text{SP}}{\text{MP}} \times 100$ — always on MP
Selling at $p\%$ profit	$\text{SP} = \text{CP}\left(1+\dfrac{p}{100}\right)$
Selling at $l\%$ loss	$\text{SP} = \text{CP}\left(1-\dfrac{l}{100}\right)$
After a discount $d\%$	$\text{SP} = \text{MP}\left(1-\dfrac{d}{100}\right)$

The chain — this is the chapter


Linking all three	$\text{MP}\left(1-\dfrac{d}{100}\right) = \text{CP}\left(1+\dfrac{p}{100}\right)$
So the markup over cost	$\dfrac{\text{MP}}{\text{CP}} = \dfrac{1+\frac{p}{100}}{1-\frac{d}{100}}$
Successive discounts	multiply: $(1-d_1)(1-d_2)$ , they never add

Two useful consequences


Two items at the same SP, one at $+x\%$ and one at $-x\%$	always a net loss of $\dfrac{x^2}{100}\%$
Equal numbers at $+x\%$ and $-x\%$ on the same CP	exactly break even

False weights and free goods


Gives $f$ while charging for $t$	profit $\% = \dfrac{t-f}{f}\times 100$
Gets $g$ free per $t$ bought	the effective cost per unit is $\dfrac{\text{paid}}{t+g}$
Both at once	work in cost per unit and revenue per unit, then compare

Several lots


Overall profit %	$\dfrac{\text{total SP} - \text{total CP}}{\text{total CP}} \times 100$
Never	the average of the individual profit percentages
Cost of a mixture	the weighted average of the component costs