📚 Profit & Loss – Quick Study Notes
(State TET | Quantitative Aptitude)
1️⃣ Simple Explanation
| Term | Definition | How It’s Calculated |
|---|---|---|
| Cost Price (CP) | Price at which an item is bought | Given or found |
| Selling Price (SP) | Price at which an item is sold | Given or found |
| Profit | Gain = SP – CP | If SP > CP |
| Loss | Loss = CP – SP | If SP < CP |
| Profit % | [(SP – CP) / CP] × 100 |
Percentage of CP |
| Loss % | [(CP – SP) / CP] × 100 |
Percentage of CP |
| Break‑Even | SP = CP | No profit, no loss |
Quick rule of thumb –
- Profit % = (SP – CP) ÷ CP × 100
- Loss % = (CP – SP) ÷ CP × 100
2️⃣ Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Use CP as the base when calculating percentage of profit or loss. | Because profit/loss is a fraction of what the seller paid. |
| 2 | Profit % ≠ Loss % even if the amounts of profit & loss are equal. | Example: CP = ₹100, SP = ₹150 → 50% profit; CP = ₹100, SP = ₹50 → 50% loss. |
| 3 | To find CP when given SP & profit %: | |
CP = SP ÷ (1 + Profit %) |
Allows reverse calculations. | |
| 4 | To find SP when given CP & loss %: | |
SP = CP × (1 – Loss %) |
Useful in discount problems. | |
| 5 | Multiple items – Add individual profits/losses before dividing by total CP. | Helps in batch problem solving. |
| 6 | Unit profit/loss – When quantities vary, compute per unit first. | Simplifies large‑scale calculations. |
| 7 | Break‑Even Point (BEP) – BEP = CP |
Key for business decisions. |
3️⃣ Worked Example
Problem
A shopkeeper buys 50 shirts at ₹200 each.
He sells them at a 20 % profit on the selling price.
What is the selling price of each shirt and the total profit?
Step‑by‑Step Solution
| Step | Calculation | Result |
|---|---|---|
| 1. Total Cost Price | 50 shirts × ₹200 = ₹10,000 | CP = ₹10,000 |
| 2. Let SP of each shirt = x | 20 % profit on SP → Profit = 0.20 x |
|
| 3. Profit in rupees per shirt | Profit = SP – CP_per_shirt → 0.20 x = x – 200 |
|
| 4. Solve for x | 0.20 x = x – 200 → x – 0.20x = 200 → 0.80x = 200 → x = 200 ÷ 0.80 = ₹250 |
|
| 5. Selling price per shirt | ₹250 | |
| 6. Total SP | 50 × ₹250 = ₹12,500 | |
| 7. Total profit | ₹12,500 – ₹10,000 = ₹2,500 |
Answer
- Selling price of each shirt = ₹250
- Total profit = ₹2,500
4️⃣ Quick Revision Summary
- Profit/Loss =
SP – CP - Profit % =
(SP – CP) ÷ CP × 100 - Loss % =
(CP – SP) ÷ CP × 100 - Reverse formulas
- CP =
SP ÷ (1 + Profit %) - SP =
CP × (1 – Loss %)
- CP =
- Break‑Even: SP = CP (no profit, no loss)
- Always use CP as the base for percentage calculations.
- Equal profit & loss amounts → different percentages
- For multiple items: sum CP, sum SP, then compute overall profit/loss.
Tip: When solving, write down the variables, set up the equation, and solve step‑by‑step. This keeps the process clear and reduces errors.
Practice Problems
- A book costs ₹120 and is sold at a 15 % profit on the selling price. Find its selling price.
- If a trader buys 200 units at ₹80 each and sells them at a 25 % loss, what’s the total loss?
- Find the break‑even price if a machine costs ₹50,000 and a maintenance fee of ₹2,000 must be covered.
Use the formulas above to solve these quickly!