Profit & Loss – Quick & Clear Study Notes
(Tripura Police Sub‑Inspector – Quantitative Aptitude)
1. Simple Explanation
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | Price at which an item is bought or produced. | – |
| Selling Price (SP) | Price at which an item is sold. | – |
| Profit | The amount by which SP exceeds CP. | ( \text{Profit} = SP - CP ) |
| Loss | The amount by which CP exceeds SP. | ( \text{Loss} = CP - SP ) |
| Profit % | Profit expressed as a percentage of CP. | ( \text{Profit%} = \dfrac{SP-CP}{CP} \times 100 ) |
| Loss % | Loss expressed as a percentage of CP. | ( \text{Loss%} = \dfrac{CP-SP}{CP} \times 100 ) |
| Discount % | Reduction in price given on a product. | ( \text{Discount%} = \dfrac{Original,Price-Discounted,Price}{Original,Price} \times 100 ) |
Key Idea – Profit or loss is always measured against the Cost Price.
2. Key Points to Remember
| # | Concept | Quick Tip |
|---|---|---|
| 1 | Profit / Loss is a difference (SP – CP). | If SP > CP → profit; if SP < CP → loss. |
| 2 | Percentage is always relative to CP. | Use CP as the denominator. |
| 3 | Profit % + Loss % ≠ 100%. | They are independent; their sum can be any value. |
| 4 | If CP and SP are fractions of a whole price, convert them to the same base before calculating. | |
| 5 | Compound Profit/Loss (multiple stages) – multiply the factors: | |
| ( (1+\frac{Profit_1}{100}) \times (1+\frac{Profit_2}{100}) \times \dots ). | Works the same for losses (use negative percentages). | |
| 6 | Break‑even point – SP = CP (Profit = Loss = 0). | Useful in business problems. |
| 7 | Margin vs. Mark‑up – | |
| Margin = (SP – CP)/SP | ||
| Mark‑up = (SP – CP)/CP | Often confused; remember margin uses SP as denominator. | |
| 8 | Rounding – In exam, round only at the final step. | Avoid intermediate rounding errors. |
| 9 | Unit conversions – 1 % = 0.01, 10 % = 0.10, etc. | Keep decimals handy. |
| 10 | Cross‑checking – After finding SP or CP, re‑calculate profit/loss to verify. | Ensures no calculation slip. |
3. Worked Example
Problem
Bikash bought 20 identical items for ₹120 each. He sold them at a profit of 25 %. What is the selling price of each item?
Steps
-
Find Cost Price (CP) of one item.
( CP = ₹120 ) -
Determine Profit %
( Profit% = 25% = 0.25 ) -
Compute Profit per item
( Profit = CP \times Profit% = 120 \times 0.25 = ₹30 ) -
Add Profit to CP to get SP
( SP = CP + Profit = 120 + 30 = ₹150 )
Answer: Each item was sold at ₹150.
Cross‑Check
( \dfrac{SP-CP}{CP} \times 100 = \dfrac{150-120}{120} \times 100 = \dfrac{30}{120}\times100 = 25% ) ✓
4. Quick Revision Summary
| Topic | Formula | Quick Check |
|---|---|---|
| Profit | (P = SP - CP) | (P>0) → profit |
| Loss | (L = CP - SP) | (L>0) → loss |
| Profit % | ( \dfrac{SP-CP}{CP}\times100 ) | Use CP as base |
| Loss % | ( \dfrac{CP-SP}{CP}\times100 ) | Same base |
| SP from CP & Profit % | ( SP = CP \times (1 + \dfrac{Profit%}{100}) ) | Quick multiplication |
| CP from SP & Loss % | ( CP = SP \times (1 + \dfrac{Loss%}{100}) ) | Same idea |
| Compound Profit | Multiply factors ( (1+P_1/100)(1+P_2/100)\ldots ) | Handles multiple stages |
| Break‑even | ( SP = CP ) | Profit = Loss = 0 |
Practice Tip – Always write down CP, SP, Profit, and Loss in a small table before performing calculations. It keeps the logic clear and reduces mistakes.
Quick Self‑Quiz
- A shopkeeper buys an item for ₹200 and sells it at a loss of 15 %. What is the selling price?
- If an item is sold at ₹360 and the profit is 20 %, what was the cost price?
- Two stages of trade: first, a 10 % profit; second, a 5 % loss on the new price. What is the overall profit/loss percent?
(Try solving before checking the solutions in your study book.)
Good luck with your preparation!