📚 Profit & Loss – Quick & Easy Study Notes
(For Rajasthan Police Constable – Quantitative Aptitude)
1. Simple Explanation
Profit or loss is the difference between the selling price (SP) and the cost price (CP) of an item.
- Profit = SP – CP (when SP > CP)
- Loss = CP – SP (when CP > SP)
Percentage profit or loss is calculated with respect to the cost price.
Quick rule of thumb
- If you can increase the price by 10% and the cost decreases by 10%, you’ll break even!
- For every 1% that price goes up and cost goes down, you gain 2% in profit.
2. Key Points & Formulas
| Concept | Formula | Example |
|---|---|---|
| Profit | ( \text{Profit} = SP - CP ) | Selling 150, cost 100 → Profit = 50 |
| Loss | ( \text{Loss} = CP - SP ) | Cost 200, selling 150 → Loss = 50 |
| Profit/Loss % | ( % \text{Profit/Loss} = \frac{\text{Profit or Loss}}{CP} \times 100 ) | Profit 50 on cost 100 → 50 % |
| Selling Price from Profit % | ( SP = CP \times \left(1 + \frac{P%}{100}\right) ) | CP 200, 25 % profit → SP = 200 × 1.25 = 250 |
| Cost Price from Loss % | ( CP = SP \times \left(1 + \frac{L%}{100}\right) ) | SP 180, 10 % loss → CP = 180 × 1.10 = 198 |
| Break‑Even Point | ( SP = CP ) | When price equals cost. |
| Profit or Loss on a Batch | ( \text{Total Profit} = \text{Total SP} - \text{Total CP} ) | Sum all items. |
| Profit or Loss on a Sale of Multiple Items | ( \text{Percentage} = \frac{(SP_{\text{total}}-CP_{\text{total}})}{CP_{\text{total}}}\times100 ) | Combine all. |
| Profit after Discount | ( SP = \text{Discounted Price} = \text{MSRP} \times \left(1 - \frac{D%}{100}\right) ) | 200 ₹, 20 % discount → 160 ₹. |
| Profit after Tax | ( SP = \text{Pre‑Tax SP} \times \left(1 + \frac{T%}{100}\right) ) | 100 ₹, 10 % tax → 110 ₹. |
3. Worked Example
Problem
A shopkeeper buys 50 kg of rice at ₹12 per kg.
He sells the rice at a 20 % profit on the cost price.
What is the final selling price per kg and the total profit?
Step‑by‑step solution
| Step | Calculation | Result |
|---|---|---|
| 1. Find CP per kg | ₹12 | ₹12 |
| 2. Compute profit rate | 20 % of ₹12 = 0.20 × 12 = ₹2.40 | ₹2.40 |
| 3. Determine SP per kg | CP + profit = 12 + 2.40 = ₹14.40 | ₹14.40 |
| 4. Total CP for 50 kg | 12 × 50 = ₹600 | ₹600 |
| 5. Total SP for 50 kg | 14.40 × 50 = ₹720 | ₹720 |
| 6. Total profit | 720 – 600 = ₹120 | ₹120 |
Answer
- Selling price per kg: ₹14.40
- Total profit on 50 kg: ₹120
4. Quick Revision Summary
- Profit = SP – CP → positive → profit, negative → loss.
- Profit % = (Profit ÷ CP) × 100.
- SP from profit %:
SP = CP × (1 + profit%/100). - CP from loss %:
CP = SP × (1 + loss%/100). - Break‑even: SP = CP.
- For multiple items, add up total CP and SP, then apply percentage formula.
- Discounts reduce SP; taxes increase SP.
- Quick mental trick: For a 10 % price rise and 10 % cost fall → 20 % profit.
Use these formulas and steps to solve any profit & loss question swiftly—exactly what you need for the Rajasthan Police Constable exam!