Business arithmetic: buy at CP, sell at SP — the gap is profit or loss. Marked price (MP) is the tag; discount is the bridge from MP to SP. Every formula is a percentage on the correct baseline: profit/loss on CP, discount on MP.
| Term | Meaning | Baseline |
|---|---|---|
| Cost Price (CP) | Purchase price — your 100% baseline | Always denominator for profit/loss % |
| Selling Price (SP) | Sale price | — |
| Profit (Gain) | SP > CP → Profit = SP − CP |
|
| Loss | CP > SP → Loss = CP − SP |
|
| Marked Price (MP) | Tag / list price | Denominator for discount % |
| Discount | Reduction on MP: MP − SP |
Flow of price:
CP → (+ markup) → MP → (− discount) → SP. Markup is a choice; discount is a
promotion; profit/loss is the final result.
Critical rule: profit% and loss% are always on CP, unless the question explicitly says "on SP".
Profit % = (Profit / CP) × 100Loss % = (Loss / CP) × 100
Why CP? Profit is return on investment — investment is CP. Discount is
concession on the tag — so denominator is MP: Discount % = (Discount / MP) × 100.
P%: SP = CP × (1 + P/100) — e.g., 20% profit → SP is
120% of CP.
L%: SP = CP × (1 − L/100) — e.g., 10% loss → SP is 90% of
CP.
SP=500×1.20=600. If that 600 is
then discounted 10% → MP was 600? No — SP after discount is MP×0.90, so
MP=500×1.20 alone only if no discount. Chain them: CP 500 → markup 30% → MP 650 → discount 10%
→ SP 585. Profit% is still (585−500)/500=17%, not 20%.
Discount = MP − SPDiscount % = (Discount / MP) × 100 — always on MP.Markup vs profit: Markup% = (MP−CP)/CP (how much you inflate the tag). Discount% brings it back down. Net profit% = markup − discount effect (successive, not additive).
Two discounts x% and y% one after another (not added):
Net Discount % = x + y − (xy / 100)
Example: 10% and 10% is NOT 20% → 10+10−1=19%. For three discounts, apply
sequentially: first combine two, then combine result with third.
xy/100 is the double-count you remove. General form: net multiplier =
(1−x/100)(1−y/100).
Dealer claims to sell at CP but uses false weight (e.g., 900g instead of 1kg):
Profit % = [(True Weight − False Weight) / False Weight] × 100
Logic: dealer saves True−False grams, sells 900g but charges for 1000g —
investment is only for 900g. For 900g instead of 1000g → (100/900)×100 = 11.11%.
If he also claims a profit/loss on top, chain it: effective CP is for false weight, then apply that profit% on top.
Two items sold at same SP, one at x% profit, other at x% loss:
Always a net LOSS: Loss % = (x/10)²
Example: x=20% → loss = 4%. On SP=1200 each? Loss is on total CP, not SP. Total SP=2400, total CP = 1200/1.20 + 1200/0.80 =1000+1500=2500 → loss 100/2500=4% ✓. The loss% on CP equals (x/10)².
Intuition: The loss item needed more CP to produce same SP (because loss), so it weighs heavier in the average.
If cost price of x items equals selling price of y items:
Profit/Loss % = [(x − y) / y] × 100 — denominator is always items
sold (y). Positive → profit, negative → loss.
(5−4)/4×100=25% profit. Means 4 sold
give money for 5 bought — you got one free.(4−5)/5=−20% loss.
| What you know | Use |
|---|---|
| CP and profit/loss % → SP | CP×(1 ± P/100) |
| MP and discount % → SP | MP×(1 − D/100) |
| Two successive discounts | x+y−xy/100 |
| False weight | (True−False)/False×100 |
| Same SP, x% profit & x% loss | Loss (x/10)² |
| CP of x = SP of y | (x−y)/y×100 |
| Symbol | Meaning |
|---|---|
CP |
Cost price (baseline for profit/loss) |
SP |
Selling price |
MP |
Marked / list price (baseline for discount) |
P% / L% |
Profit / loss % |
D% |
Discount % |
Profit% and loss% are always on?
CP=400, 20% profit → SP?
Discount% is always on?
Two successive discounts 10% and 10% → net?
Dealer uses 900g for 1kg, claims at CP → profit%?
Two items same SP, one at 20% profit, one at 20% loss → net?
CP of 5 = SP of 4 → profit%?
Price flow: CP → ? → MP → ? → SP
CP ⇒ purchase (100% baseline) ; SP ⇒ sale ; MP ⇒ tag
Profit ⇒ SP−CP (SP>CP) ; Loss ⇒ CP−SP
Profit%/Loss% ⇒ on CP ; Discount% ⇒ on MP
Profit P% ⇒ SP=CP×(1+P/100) ; Loss L% ⇒ SP=CP×(1−L/100)
Flow ⇒ CP → +markup → MP → −discount → SP
a) Successive discounts ⇒ x+y−xy/100 (multiplier (1−x/100)(1−y/100))
(eg 10+10−1=19, not 20)
b) False weight ⇒ (True−False)/False×100 (eg 900 for 1000→11.11%)
c) Same SP ±x% ⇒ always loss (x/10)² (eg 20%→4% loss)
d) CP of x = SP of y ⇒ (x−y)/y×100 ; denom = items sold y
(eg 5=4 →25% profit)
CP ⇒ cost ; SP ⇒ selling ; MP ⇒ marked ; P%/L%/D% ⇒ percentages
Primary source: none pinned yet — drop your preferred video/book resource into RESOURCES.md and it will be linked here. Ask me anything that's unclear.
Questions? Ask your agent — you can follow up on any concept, quiz answer, or get extra practice problems tuned to this module.