Discount
What you must know
Marked price (MP) is the list price; discount is a reduction on MP, so discount% = (MP − SP)/MP × 100. This is the key structural distinction from profit and loss: discount lives on MP, profit lives on CP. The bridge formula is SP = MP(1 − d/100) = CP(1 + p/100).
Successive discounts of a% and b% give a single equivalent discount of a + b − ab/100 percent, because they multiply: (1 − a/100)(1 − b/100). Three successive discounts extend the same way. A common exam twist gives MP, discount% and profit% and asks for CP; solve in two steps: find SP from MP and discount, then CP from SP and profit.
Traps
- Adding successive discounts (10% + 20% is 28%, not 30%).
- Computing discount on CP instead of MP.
- Confusing "marked up by x% then discounted by x%" - this always produces a loss of x²/100 percent relative to CP, since MP = CP(1+x/100) and SP = MP(1−x/100).
- Forgetting that discount is allowed only on MP; if an item is sold at CP with a discount, the discount equals the mark-up.
Rule of thumb and example
Chain the multipliers left to right: SP = MP × (discount factor) × (any further factor).
Worked example: MP = ₹800, two successive discounts of 25% and 10%. SP = 800 × 0.75 × 0.90 = ₹540. Equivalent single discount = 25 + 10 − 250/100 = 32.5%, and indeed 800 × 0.675 = 540. If CP was ₹500, profit = 40/500 = 8%.