Introduction
Profit, Loss and Discount builds directly on the Percentage chapter — nearly every question here is a
percentage calculation dressed up in commercial language (cost price, selling price, marked price).
Basic Formulas
| Formula |
|---|
| Profit = SP − CP (when SP > CP) |
| Loss = CP − SP (when CP > SP) |
| Profit % = (Profit/CP) × 100 |
| Loss % = (Loss/CP) × 100 |
| SP = CP × (100 + Profit%)/100 |
| SP = CP × (100 − Loss%)/100 |
⚠️ Common Trap: Profit % and Loss % are always calculated on Cost Price, never on Selling Price — unless a question explicitly states otherwise.
Marked Price and Discount
| Formula |
|---|
| Discount = MP − SP |
| Discount % = (Discount/MP) × 100 |
| SP = MP × (100 − Discount%)/100 |
Successive Discount Formula
Same structure as successive percentage change (Chapter 6) — but discounts are always subtracted, so use negative values.
Flowchart — Two Successive Discounts
Net Discount % = a + b − (ab/100)
This is the successive-change formula with both a and b taken as positive discount values and the sign flipped to minus for the cross-term.
Q. A shop offers successive discounts of 20% and 10%. Find the net discount percentage.
Net discount = 20 + 10 − (20×10)/100 = 30 − 2 = 28%
Classic Pattern — "Marked Price Set Above Cost, Then Discounted"
Q. A shopkeeper marks his goods 40% above cost price and allows a discount of 25%. Find his profit or loss %.
Let CP = 100 → MP = 140
SP = 140 × (75/100) = 105
Profit = 105 − 100 = 5 → Profit % = 5%
Classic Pattern — "False Weight" Trick
Flowchart — Profit from Using a False Weight
Profit % = [Error / (True Value − Error)] × 100
Q. A dishonest dealer professes to sell his goods at cost price but uses a weight of 800 gm for a 1 kg weight. Find his profit %.
Error = 1000 − 800 = 200
Profit % = [200 / (1000 − 200)] × 100 = [200/800] × 100 = 25%
Classic Pattern — Selling Two Items at Same SP, One at Profit One at Loss
💡 Standard Result: If two items are sold at the same SP, one at x% profit and the other at x% loss, there is always a net loss — equal to (x/10)²%.
Q. A man sells two articles for ₹1000 each — one at 20% profit, the other at 20% loss. Find his overall gain/loss %.
Net loss % = (x/10)² = (20/10)² = 2² = 4% loss
✅ Practice Focus: CP/SP/Profit% formulas · Successive discount formula (a+b−ab/100) · Marked-price-above-cost-then-discount pattern · False weight profit shortcut · Equal-SP profit-loss standard result.