Discount & Successive Discount
Discount is always a percentage of the MARKED price, not the cost or selling price. SP = MP × (1 − d/100). When a shop offers two discounts back to back, you cannot add them — the second discount applies to the already-reduced price. Apply them as a multiplier chain: SP = MP × (1 − d1/100) × (1 − d2/100). The net single discount equivalent to d1 then d2 is d1 + d2 − d1·d2/100 (note the MINUS, since both reduce). Because profit is on CP and discount is on MP, CAT mixes the two freely: a shopkeeper can mark up 50%, give 20% off, and still profit 20% — the trick is to track MP and CP separately and only compare SP to CP at the end. Assuming CP = 100 keeps every number clean.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
Auto-graded with full solutions; saved to your dashboard. Use the calculator and formula sheet (top-right) any time.
Formula Reference Sheet
Price, profit and loss
| Profit | SP − CP (when SP > CP) |
|---|---|
| Loss | CP − SP (when CP > SP) |
| Profit % | (SP − CP)/CP × 100 |
| Loss % | (CP − SP)/CP × 100 |
| SP from CP | SP = CP × (1 + profit%/100) |
| CP from SP | CP = SP ÷ (1 ± profit/loss%/100) |
Marked price and discount
| Discount | MP − SP |
|---|---|
| Discount % | (MP − SP)/MP × 100 |
| SP from MP | SP = MP × (1 − discount%/100) |
| Successive discounts d1, d2 | net = d1 + d2 − d1·d2/100 (%) |
| False-weight gain % | error/(true − error) × 100 |
| Partnership profit split | ratio of (capital × time) |