📊 Profit & Loss – Quick Study Notes
(For Puducherry Patwari / Lekhpal – Quantitative Aptitude)
1. Simple Explanation
| Term | Definition | Formula | Example |
|---|---|---|---|
| Profit | Gain obtained when selling price (SP) > cost price (CP) | Profit = SP – CP |
Selling a shirt for ₹120 when it cost ₹80 → Profit = ₹40 |
| Loss | Loss occurs when SP < CP | Loss = CP – SP |
Buying a watch for ₹500, selling for ₹400 → Loss = ₹100 |
| Profit % | % of CP that is gained | Profit % = (Profit / CP) × 100 |
40/80 × 100 = 50 % |
| Loss % | % of CP that is lost | Loss % = (Loss / CP) × 100 |
100/500 × 100 = 20 % |
| Selling Price (SP) | Price at which item is sold | SP = CP + Profit or SP = CP – Loss |
CP = ₹200, Profit = 25 % → SP = ₹250 |
| Cost Price (CP) | Price paid to acquire the item | CP = SP – Profit or CP = SP + Loss |
SP = ₹350, Profit = 20 % → CP = ₹291.67 |
| Profit–Loss Ratio | Ratio of profit to loss when both occur | Ratio = Profit : Loss |
Profit ₹80, Loss ₹20 → Ratio = 4 : 1 |
2. Key Points to Remember
| # | Concept | Why It Matters | Typical Question |
|---|---|---|---|
| 1 | Profit vs. Loss – Always check if SP > CP or vice versa | Determines which formula to use | “If a shop sells at ₹300 and bought at ₹250, what is the profit?” |
| 2 | Percentages – Profit % and Loss % are always relative to CP | Avoids mis‑calculations | “A ₹1200 item is sold at 20 % profit. Find SP.” |
| 3 | Reverse Calculations – Sometimes CP or SP is unknown | Use rearranged formulas | “If profit is 25 % and SP is ₹625, find CP.” |
| 4 | Profit–Loss Ratio – Useful when both profit and loss are given | Helps in compound‑ratio problems | “Profit 30 %, loss 10 %. Find total profit % on two items.” |
| 5 | Mixed Transactions – Multiple items bought at different prices | Add total CP and total SP | “Bought 3 items at ₹80 each and 2 items at ₹120 each. Sold all at ₹150 each.” |
| 6 | Percentage of SP – Not used for profit/loss calculations | Only CP matters for profit/loss % | “Don’t confuse 20 % profit with 20 % of SP.” |
| 7 | Rounding – Always compute the exact value before rounding | Avoids errors in final answer | “Profit % = 33.333…% → 33 % (round to nearest whole number).” |
3. Worked Example
Problem:
A shopkeeper buys a bundle of goods for ₹5 200. He sells them for ₹6 600.
- Find the profit and profit %
- If the shopkeeper had sold the goods at ₹5 980, what would have been the loss %?
Step‑by‑step Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Compute Profit | Profit = SP – CP = 6600 – 5200 = 1400 |
₹1 400 |
| 2. Profit % | Profit % = (Profit / CP) × 100 = (1400 / 5200) × 100 |
= 26.923…% ≈ 26.92 % |
| 3. Loss in second scenario | Loss = CP – SP = 5200 – 5980 = –780 (negative → Loss of ₹780) |
₹780 |
| 4. Loss % | Loss % = (Loss / CP) × 100 = (780 / 5200) × 100 |
= 15.000…% ≈ 15 % |
Answers
- Profit: ₹1 400 (≈ 26.92 %)
- Loss (if sold at ₹5 980): ₹780 (≈ 15 %)
4. Quick Revision Summary
| Concept | Formula | Quick Check |
|---|---|---|
| Profit | SP – CP |
>0 → Profit |
| Loss | CP – SP |
>0 → Loss |
| Profit % | (Profit / CP) × 100 |
Always relative to CP |
| Loss % | (Loss / CP) × 100 |
Same rule |
| Selling Price | CP + Profit or CP – Loss |
Plug‑in CP & % |
| Cost Price | SP – Profit or SP + Loss |
Reverse the above |
| Profit–Loss Ratio | Profit : Loss |
Useful for compound problems |
Tips
- Always start with CP when dealing with percentages.
- Check signs: If SP > CP → Profit; else → Loss.
- When dividing: Use
≈or “to nearest whole number” only after final step. - Practice: Mix single‑item and multiple‑item problems to build speed.
Happy studying! 🚀