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Business Mathematics and Statistics · Ch 1 — Profit and Loss

Profit and Loss Percentage

2

Profit and Loss Percentage

The single most important convention in this chapter is that profit percentage and loss percentage are always calculated on the cost price, unless a problem explicitly states otherwise. The cost price is the reference (the base = 100%) against which the gain or shortfall is measured.

Profit%=ProfitCP×100=SP−CPCP×100\text{Profit}\% = \frac{\text{Profit}}{CP}\times 100 = \frac{SP - CP}{CP}\times 100

Loss%=LossCP×100=CP−SPCP×100\text{Loss}\% = \frac{\text{Loss}}{CP}\times 100 = \frac{CP - SP}{CP}\times 100

Finding SP when CP and the percentage are known. Rearranging the definitions gives two direct formulas:

SP=CP(1+Profit%100)(on a profit)SP = CP\left(1 + \frac{\text{Profit}\%}{100}\right) \qquad\text{(on a profit)}

SP=CP(1−Loss%100)(on a loss)SP = CP\left(1 - \frac{\text{Loss}\%}{100}\right) \qquad\text{(on a loss)}

Finding CP when SP and the percentage are known. Inverting the same relations:

CP=SP1+Profit%100orCP=SP1−Loss%100CP = \frac{SP}{1 + \dfrac{\text{Profit}\%}{100}} \qquad\text{or}\qquad CP = \frac{SP}{1 - \dfrac{\text{Loss}\%}{100}}

Note

The base is always the cost price

A gain of 20% means the profit equals 20% of the cost price, so the selling price is 120% of the cost price. Treating the selling price or the marked price as the base is the single most common error in this chapter — the whole percentage always sits on top of the CP. …

Definition 1Profit Percentage

Profit expressed as a percentage of the cost price: Profit%=SP−CPCP×100\text{Profit}\% = \dfrac{SP-CP}{CP}\times 100. The cost pric …

Definition 2Loss Percentage

Loss expressed as a percentage of the cost price: $\text{Loss}% = \dfrac{CP-SP}{ …

Definition 3Selling Price from Percentage

SP=CP(1±Profit or Loss%100)SP = CP\left(1 \pm \dfrac{\text{Profit or Loss}\%}{100}\right) — add for a profit, subt …

Definition 4Cost Price from Percentage

CP=SP1±(Profit or Loss)%/100CP = \dfrac{SP}{1 \pm \text{(Profit or Loss)}\%/100} — obtained by inverting the selling …

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