Profit & Loss – Quick Study Notes
(Civil Judge – Quantitative Aptitude)
1. Simple Explanation
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | Price at which an item is bought. | – |
| Selling Price (SP) | Price at which an item is sold. | – |
| Profit | Money earned when SP > CP. | ( \text{Profit} = SP - CP ) |
| Loss | Money lost when SP < CP. | ( \text{Loss} = CP - SP ) |
| Profit % | Profit expressed as a percent of CP. | ( \text{Profit}% = \dfrac{SP-CP}{CP}\times100 ) |
| Loss % | Loss expressed as a percent of CP. | ( \text{Loss}% = \dfrac{CP-SP}{CP}\times100 ) |
| Markup % | Increase over CP expressed as a percent of CP. | Same as Profit % (if no cost changes) |
| Margin % | Profit expressed as a percent of SP. | ( \text{Margin}% = \dfrac{SP-CP}{SP}\times100 ) |
In most aptitude questions, Profit % and Loss % are the same as Markup %.
“Margin” is rarely asked in the Civil Judge exam but good to know.
2. Key Points & Common Pitfalls
| # | Point | Why it matters | Common mistake |
|---|---|---|---|
| 1 | Never mix CP and SP in the same fraction | Profit % uses CP as the denominator. | Using SP in the denominator → wrong % |
| 2 | Round only at the end | Intermediate rounding propagates errors. | Rounding after each step |
| 3 | Percentage conversions | 12 % → 0.12, 1.2 % → 0.012. | Forgetting the decimal shift |
| 4 | Negative sign for loss | Loss is represented as negative profit. | Writing loss as a positive number |
| 5 | Multiple items | Treat each item separately, then sum profits/losses. | Adding CP or SP before computing % |
| 6 | Discount vs. Profit | Discount reduces SP, not CP. | Combining discount and profit without sequence |
| 7 | Reversing CP and SP | Swapping CP and SP gives negative of the actual profit/loss. | Mistaking SP for CP in formulas |
3. Worked Example
Problem
A shopkeeper buys 10 identical items for ₹250 each.
He sells 8 items at a 20 % profit per item and the remaining 2 items at a 15 % loss per item.
What is the overall profit or loss percentage on the entire transaction?
Step‑by‑step Calculation
| Item | Quantity | Cost Price per item | Total CP | Profit % | SP per item | Total SP | Profit/Loss |
|---|---|---|---|---|---|---|---|
| A | 8 | ₹250 | ₹2,000 | +20 % | (250\times1.20=₹300) | ₹2,400 | +₹400 |
| B | 2 | ₹250 | ₹500 | –15 % | (250\times0.85=₹212.50) | ₹425 | –₹75 |
Total
- Total CP = ₹2,000 + ₹500 = ₹2,500
- Total SP = ₹2,400 + ₹425 = ₹2,825
- Total Profit = ₹2,825 – ₹2,500 = ₹325
Overall Profit %
[ \text{Profit}% = \frac{325}{2500}\times100 = 13% ]
Answer: The shopkeeper makes an overall 13 % profit on the whole sale.
4. Quick Revision Summary
| Concept | Formula | Quick Check |
|---|---|---|
| Profit | (SP-CP) | Positive → profit, negative → loss |
| Loss | (CP-SP) | Positive → loss, negative → profit |
| Profit % | (\dfrac{SP-CP}{CP}\times100) | Denominator = CP |
| Loss % | (\dfrac{CP-SP}{CP}\times100) | Same denominator |
| Margin % | (\dfrac{SP-CP}{SP}\times100) | Denominator = SP |
| Multiple items | Compute each item’s profit/loss, sum them; then use total CP & SP for % | Avoid mixing individual CP/SP before summing |
| Discount → Sale | (SP = CP \times (1 - \text{Discount%})) | Discount is applied to CP, not to profit |
Quick Tips
- Step 1: Write down CP and SP for every item.
- Step 2: Calculate profit or loss for each item.
- Step 3: Sum up all profits/losses.
- Step 4: Find total CP and total SP.
- Step 5: Compute overall % using the appropriate formula.
Practice Problem (for self‑check)
A trader bought 5 goods each at ₹120. He sold 2 goods at a 25 % profit, 1 good at a 10 % loss, and the remaining goods at break‑even (i.e., SP = CP). What is the overall profit or loss %?
(Answer after solving: 3.33 % profit)
Use the steps above to solve and verify your result.