Profit and loss shortcuts
Profit and loss questions are really just percentage questions wearing a costume — cost price, selling price, and discount are the same fraction-of-a-number arithmetic from the percentage shortcuts, applied to a specific story.
The core relationship
Selling Price = Cost Price × (1 + Profit% / 100)
Selling Price = Cost Price × (1 − Loss% / 100)
The shortcut isn't a different formula — it's using the percentage building-block method (10% and 1%) from the percentage shortcuts post to compute the multiplier fast instead of doing long multiplication.
Worked example: 15% profit on cost price 240
10% of 240 = 24. 5% = 12. 15% = 24 + 12 = 36. Selling price = 240 + 36 = 276.
Discount stacking
Two successive discounts (like "30% off, then an extra 10% off") don't add to 40% — this is the exact same successive-percentage- change trap from the percentage shortcuts post:
For 30% then 10%: 30 + 10 − (30×10)/100 = 40 − 3 = 37% net discount, not 40%.
Working backward from selling price
A common exam twist gives you the selling price and profit percentage, and asks for the cost price:
Cost Price = Selling Price × 100 / (100 + Profit%)
Example: sold at 276 with 15% profit. Cost price = 276 × 100 / 115 = 240. This is just running the first example in reverse.