Profit and Loss Basic Concepts Explained with Formulas, Tricks, and Examples for Government Exams:
What is Profit and Loss?
Profit and Loss is a topic from Arithmetic Section that deals with cost price (CP), selling price (SP), profit, and loss in the context of buying and selling goods.
Real-life connection: Whenever a shopkeeper sells something, he either makes a profit or incurs a loss, depending on how the selling price compares to the cost price.
Basic Terms and Definitions:
| Term | Meaning |
|---|---|
| Cost Price (CP) | The price at which an item is purchased. |
| Selling Price (SP) | The price at which the item is sold. |
| Profit or Gain | If SP > CP, the seller earns a profit = SP – CP |
| Loss | If CP > SP, the seller incurs a loss = CP – SP |
| Marked Price (MP) | The price tag (MRP) on a product before any discount. |
| Discount | Reduction given on MP; usually a % off. |
Important Formulas:
| Concept | Formula |
|---|---|
| Profit | SP – CP |
| Loss | CP – SP |
| Profit % | (Profit / CP) × 100 |
| Loss % | (Loss / CP) × 100 |
| SP (for profit %) | CP × (1 + Profit% / 100) |
| SP (for loss %) | CP × (1 – Loss% / 100) |
| CP (when profit %) | SP / (1 + Profit% / 100) |
| CP (when loss %) | SP / (1 – Loss% / 100) |
| Marked Price (MP) | SP / (1 – Discount% / 100) |
Examples with Solutions:
Let’s go through a few exam-style examples:
Example 1: Basic Profit Calculation
Question: A shopkeeper buys a pen for ₹40 and sells it for ₹50. What is the profit and profit %?
Solution:
- CP = ₹40
- SP = ₹50
- Profit = SP – CP = 50 – 40 = ₹10
- Profit % = (10 / 40) × 100 = 25%
✅ Answer: Profit = ₹10, Profit % = 25%
Example 2: Loss Percentage
Question: A book is bought for ₹200 and sold for ₹160. Find the loss and loss %.
Solution:
- CP = ₹200
- SP = ₹160
- Loss = CP – SP = 200 – 160 = ₹40
- Loss % = (40 / 200) × 100 = 20%
✅ Answer: Loss = ₹40, Loss % = 20%
Example 3: Finding SP for Given Profit %
Question: A product is bought at ₹120. At what price should it be sold to gain 15%?
Solution:
SP = CP × (1 + Profit% / 100)
SP = 120 × (1 + 15/100) = 120 × 1.15 = ₹138
✅ Answer: ₹138
Example 4: Discount and Profit
Question: An article is marked at ₹500. A discount of 20% is given, but the seller still makes a 10% profit. What is the cost price?
Solution:
- MP = ₹500
- SP after discount = 500 × (1 – 20/100) = ₹400
- CP = SP / (1 + Profit% / 100) = 400 / 1.10 = ₹363.64
✅ Answer: Cost Price ≈ ₹363.64
Shortcut Tricks and Tips
Here are a few tricks that can help you solve questions faster in exams:
1. Successive Profit/Loss
If there are two successive profit/loss % (say, x% and y%), then:
Net % = x + y + (x × y) / 100
👉 If both are profits, use +
👉 If one is profit, one is loss, use negative accordingly
2. Selling Two Articles at Same Price:
If two items are sold at the same SP, one at x% gain, one at x% loss, then overall loss % is:
(x² / 100)%
✅ Always a loss!
| CP (₹) | Profit % | SP (₹) | Loss % | SP (₹) |
|---|---|---|---|---|
| 100 | 10% | 110 | 10% | 90 |
| 120 | 25% | 150 | 25% | 90 |
| 200 | 20% | 240 | 20% | 160 |
| 80 | 15% | 92 | 15% | 68 |
Exam-Level Practice Questions
Try solving these on your own:
- A trader sells a watch at a profit of 20%. If the cost price is ₹250, find the selling price.
- A man buys 3 shirts for ₹900 and sells them at ₹350 each. What is his gain or loss %?
- An article is sold for ₹600 at a 25% loss. What is the cost price?
- A dealer marked a TV at ₹15,000 and allowed a 10% discount. Still, he made a 5% profit. Find the cost price.
- If CP is ₹800 and profit is ₹120, find SP and profit %.
📌 Answers are at the bottom of this page.
Real-Life Applications in Exams
- In SSC CGL Tier 1 & Tier 2, you’ll often get direct formula-based MCQs.
- Bank exams (IBPS, SBI) test your ability to handle word problems with discounts and markups.
- Railway NTPC & Group D asks logic-based cost/selling combos.
Learning the Profit and Loss Basic Concepts is essential to get good understanding of the topic and solving questions easily in exams.
Final Tips
- Understand the base: Profit/loss % is always calculated on Cost Price, not SP(unless mentioned in questions).
- Memorize key formulas.
- Practice with mock tests, and analyze mistakes.
- Always double-check % increase/decrease logic.
📥 Want More Practice?
👉 Now you understand the Profit and Loss Basic Concepts its very much needed that you practice so many questions to make your understanding more deeper and to increase you speed in solving problems ?
1. To practice questions of Profit & Loss- Visit Here( Link To be updated)
2. To Learn more Profit & Loss Related Concepts – Visit Here ( Link To be updated)
Conclusion
Profit and Loss is not just a math topic — it’s a scoring opportunity in almost every govt job exam. With the right formulas, examples, and shortcuts, you can solve questions in under a minute. So, make it a stronghold in your preparation.
Remember — Practice + Concept = Confidence!
Answers to Practice Questions
- ₹300
- CP = ₹900, SP = ₹1050, Profit = ₹150 → Profit% = 16.67%
- CP = SP / (1 – Loss%) = 600 / 0.75 = ₹800
- SP = 15,000 × 0.9 = ₹13,500 → CP = SP / 1.05 = ₹12,857
- SP = 800 + 120 = ₹920, Profit% = (120 / 800) × 100 = 15%
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