Profit and Loss
Delhi Police Exam
1. What is Profit & Loss?
Profit & Loss is a key topic in arithmetic that deals with buying and selling of goods. It measures gain or loss based on the difference between Cost Price (C.P.) and Selling Price (S.P.).
Cost Price (C.P.): Price at which item is bought
Selling Price (S.P.): Price at which item is sold
Profit: When S.P. > C.P.
Loss: When C.P. > S.P.
Examples:
Example 1: Bought an item for ₹500, sold for ₹600 → Profit = ₹100
Example 2: Bought an item for ₹800, sold for ₹700 → Loss = ₹100
2. Basic Formulas
| Concept | Formula | Example |
|---|---|---|
| Profit | Profit = S.P. – C.P. | 600 – 500 = 100 |
| Loss | Loss = C.P. – S.P. | 800 – 700 = 100 |
| Profit % | Profit % = (Profit / C.P.) × 100 | 100/500 × 100 = 20% |
| Loss % | Loss % = (Loss / C.P.) × 100 | 100/800 × 100 = 12.5% |
| S.P. from C.P. and Profit % | S.P. = C.P. + Profit | 500 + 20% of 500 = 600 |
| S.P. from C.P. and Loss % | S.P. = C.P. – Loss | 800 – 12.5% of 800 = 700 |
| C.P. from S.P. and Profit % | C.P. = S.P. / (1 + Profit%) | 600 / 1.2 = 500 |
| C.P. from S.P. and Loss % | C.P. = S.P. / (1 – Loss%) | 700 / 0.875 = 800 |
3. Shortcut Tricks
| Scenario | Trick |
|---|---|
| Profit % = x% | S.P. = C.P. × (1 + x/100) |
| Loss % = x% | S.P. = C.P. × (1 – x/100) |
| Profit & Loss on multiple items | Find total C.P. and total S.P., then calculate overall % |
| Successive Profit | Net Profit % = P1 + P2 + (P1×P2)/100 |
| Successive Loss | Net Loss % = L1 + L2 + (L1×L2)/100 |
4. Combined Profit & Loss
If multiple items are sold with different profits/losses:
Overall Profit/Loss % = (Total Profit or Loss / Total C.P.) × 100
Example:
Item 1: C.P. = 200, S.P. = 220 → Profit = 20
Item 2: C.P. = 300, S.P. = 270 → Loss = 30
Net = –10 → Overall Loss % = 10/500 × 100 = 2%
5. Marked Price & Discount
Marked Price (M.P.)
Price marked by the seller
Discount
Reduction from M.P.
S.P. = M.P. – Discount
Discount % = (Discount / M.P.) × 100
Example:
M.P. = ₹500, Discount = ₹50 → S.P. = ₹450
Discount % = 50/500 × 100 = 10%
6. Cost Price after Successive Discounts
If an item is sold with multiple successive discounts:
Net S.P. = C.P. × (1 – d₁/100) × (1 – d₂/100)...
Example:
C.P. = 1000, Discount = 10% and 20%
S.P. = 1000 × 0.9 × 0.8 = ₹720
7. Real-Life Analogy
Think of Profit & Loss like buying fruits from a market
Profit Scenario
Buy apples for ₹500 → sell for ₹600
you profit ₹100
Loss Scenario
Buy apples for ₹500 → sell for ₹400
you lose ₹100
Profit & Loss tells you how much money you gained or lost in your buying and selling transactions.
8. Common Delhi Police / SSC Exam Facts
Formula: Profit = S.P. – C.P., Loss = C.P. – S.P.
Discount reduces S.P.
Successive Profit/Loss problems are frequent
Always convert % to decimal when multiplying (20% → 0.2)
Net profit/loss on multiple items = Total Profit/Loss ÷ Total C.P. ×100
Marked price and discount questions are common
9. Practice Questions (Exam-Type)
| No. | Question | Solution | Answer |
|---|---|---|---|
| 1 | C.P. = 500, S.P. = 600. Find Profit % | (100/500)×100 | 20% |
| 2 | C.P. = 800, S.P. = 700. Find Loss % | (100/800)×100 | 12.5% |
| 3 | Profit 20% on ₹400, find S.P. | 400 + 20% of 400 = 480 | ₹480 |
| 4 | Loss 15% on ₹600, find S.P. | 600 – 15% of 600 = 510 | ₹510 |
| 5 | Successive Profit 10% & 20% on ₹1000 | Net = 10 + 20 + (10×20)/100 = 32% | 32% Profit |
10. Quick Recap
| Concept | Summary |
|---|---|
| C.P. | Original buying price |
| S.P. | Selling price |
| Profit | S.P. – C.P. (if S.P. > C.P.) |
| Loss | C.P. – S.P. (if C.P. > S.P.) |
| Profit % | (Profit ÷ C.P.) × 100 |
| Loss % | (Loss ÷ C.P.) × 100 |
| Discount | Reduces M.P. → S.P. = M.P. – Discount |
| Successive Profit/Loss | Net % = P1 + P2 + (P1×P2)/100 |
You've completed Profit and Loss Concepts!
Courage Tip: Practice profit and loss problems regularly, focusing on different types like percentage calculations, successive transactions, and discount problems. Remember the key formulas and relationships between cost price, selling price, and profit/loss percentages to solve problems quickly in exams.
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