Profit & Loss

Mathematics · 6 min read · Sunitha Rao

Cost price, selling price, marked price and discount chains.

Profit and loss is percentage applied to trade. Everything is measured on the cost price unless the question says otherwise, and this single habit prevents most errors. Profit = SP - CP, and profit percent = profit / CP x 100.

Discount, by contrast, is always calculated on the marked price. A shopkeeper who marks goods 40% above cost and then offers a 20% discount still earns a profit: SP = 1.40 x 0.80 x CP = 1.12 CP, which is a 12% gain.

The classic trap is the false-weight question. A trader who sells at cost price but uses a 900 g weight for a kilogram earns 100/9 = 11.11% profit, because the effective cost is lower than claimed.

Important points

  • Profit % and loss % are calculated on cost price.
  • Discount % is calculated on marked price.
  • Selling at the same percentage above and below cost always gives a net loss.
  • If two articles sell at the same price with +x% and -x%, net loss = x^2/100 percent.

Key formulas

Profit % = (SP - CP) / CP x 100

SP = CP x (100 + profit%) / 100

Net loss on equal +x% / -x% deals = x^2 / 100 percent

Examples

  1. CP = 400, SP = 500. Profit = 100, profit % = 100/400 x 100 = 25%.
  2. Marked price 1,000 with 20% discount gives SP = 800.

Practise Profit & Loss questions →