📊 Profit & Loss – Quick & Easy Study Notes
(For Dadra & Nagar Haveli & Daman & Diu Forest Guard Quantitative Aptitude)
1️⃣ Simple Explanation
- Profit = Selling Price – Cost Price
- Loss = Cost Price – Selling Price
- Profit % = (\dfrac{\text{Profit}}{\text{Cost Price}}\times 100)
- Loss % = (\dfrac{\text{Loss}}{\text{Cost Price}}\times 100)
Remember:
- If Selling Price > Cost Price → Profit
- If Selling Price < Cost Price → Loss
2️⃣ Key Points & Formulas
| Concept | Symbol | Formula | Interpretation |
|---|---|---|---|
| Cost Price | CP | – | Price at which item was bought |
| Selling Price | SP | – | Price at which item was sold |
| Profit | P | SP – CP | Positive amount earned |
| Loss | L | CP – SP | Positive amount lost |
| Profit % | %P | (P / CP) × 100 | % of CP earned |
| Loss % | %L | (L / CP) × 100 | % of CP lost |
| Markup | – | (SP – CP) / CP | % added to CP to set SP |
| Margin | – | (SP – CP) / SP | % of SP that is profit |
Special Cases
| Situation | Formula | Note |
|---|---|---|
| Multiple purchases at different CPs | Average CP = (\dfrac{\sum \text{CP}_i}{n}) | Use to find CP before computing P or L |
| Selling at a discount | Discount % = (Discount amount / SP) × 100 | SP after discount = SP - Discount |
| Selling at a markup | Markup % = (Markup amount / CP) × 100 | SP after markup = CP + Markup |
| Two items sold at same price | If (SP_1 = SP_2) but CP differ, compare CPs for profit/loss |
3️⃣ Worked Example
Problem
A shopkeeper bought 10 pens at ₹50 each. He sold them at a 20 % profit on the cost price.
Then he bought 5 more pens at ₹60 each and sold them at a 15 % loss on the cost price.
What was the overall profit or loss percentage for the whole transaction?
Step‑by‑Step Solution
| Stage | Quantity | CP per unit | Total CP | SP per unit | Total SP | Profit / Loss |
|---|---|---|---|---|---|---|
| First batch | 10 | ₹50 | ₹500 | ₹50 × 1.20 = ₹60 | ₹600 | Profit ₹100 |
| Second batch | 5 | ₹60 | ₹300 | ₹60 × 0.85 = ₹51 | ₹255 | Loss ₹45 |
| Totals | 15 | – | ₹800 | – | ₹855 | Profit ₹55 |
- Total Cost Price (CP) = ₹500 + ₹300 = ₹800
- Total Selling Price (SP) = ₹600 + ₹255 = ₹855
- Overall Profit = ₹855 – ₹800 = ₹55
Overall Profit %
[
\text{% Profit} = \frac{55}{800} \times 100 = 6.875% \approx 6.88%
]
Answer: The shopkeeper made an overall profit of ≈ 6.88 %.
4️⃣ Quick Revision Summary
| Topic | What to Remember |
|---|---|
| Profit / Loss | SP – CP; Profit if SP > CP, Loss if SP < CP |
| Percent | (Profit or Loss / CP) × 100 |
| Markup vs Margin | Markup = (SP – CP)/CP; Margin = (SP – CP)/SP |
| Multiple Purchases | Compute average CP before overall P/L |
| Discount / Markup | Adjust SP accordingly before P/L |
| Quick Check | If CP × (1 ± %)/= SP → compute % directly |
Quick Practice Question
A trader bought 8 units for ₹120 each and sold them for ₹150 each.
Another 12 units were bought for ₹90 each and sold for ₹85 each.
What is the overall profit or loss percentage?
(Try solving before checking the answer below.)
Answer
- CP₁ = 8 × 120 = ₹960
- SP₁ = 8 × 150 = ₹1,200 → Profit ₹240
- CP₂ = 12 × 90 = ₹1,080
- SP₂ = 12 × 85 = ₹1,020 → Loss ₹60
- Total CP = ₹2,040; Total SP = ₹2,220 → Profit ₹180
- Profit % = (180 ÷ 2,040) × 100 ≈ 8.82 %
Final Tip
Always write down CP, SP, and profit/loss for each part before adding them.
This prevents mistakes and keeps calculations clear—especially under exam time pressure.
Good luck with your preparation! 🚀