Profit & Loss – Quick Study Notes
(For Tripura Police Constable – Quantitative Aptitude)
1. Simple Explanation
| Term | What it Means |
|---|---|
| Cost Price (CP) | Price paid for an item. |
| Selling Price (SP) | Price at which the item is sold. |
| Profit | Money earned = SP – CP. |
| Loss | Money lost = CP – SP. |
| Profit % | (Profit / CP) × 100% |
| Loss % | (Loss / CP) × 100% |
Rule of Thumb
If SP > CP → Profit;
If SP < CP → Loss.
2. Key Points (Quick Reference)
| Concept | Formula | Notes |
|---|---|---|
| Profit / Loss | P/L = SP – CP |
Positive → Profit, Negative → Loss |
| Profit % | P% = (SP – CP) / CP × 100 |
Often required in questions. |
| Loss % | L% = (CP – SP) / CP × 100 |
Same as above. |
| Selling Price from CP & % | SP = CP × (1 ± P%/100) |
+ for profit, – for loss. |
| Cost Price from SP & % | CP = SP / (1 ± P%/100) |
+ for profit, – for loss. |
| Profit/Loss on a Batch | Total Profit/Loss = Σ (SPi – CPi) |
Add up individual profit/loss. |
| Average Cost Price | Avg CP = Total CP / Total Quantity |
Useful when items bought at different prices. |
| Break‑Even Point | Total Revenue = Total Cost |
No profit, no loss. |
| Profit on Sale of a Batch | Profit% = (Total Profit / Total CP) × 100 |
Good for bulk calculations. |
3. Worked Example
Problem
A shopkeeper bought 10 shirts at ₹800 each and 5 jackets at ₹1500 each.
He sold all shirts for ₹1000 each and all jackets for ₹1800 each.
Find the overall profit percentage.
Step‑by‑Step
| Item | Quantity | CP per unit | Total CP | SP per unit | Total SP | Profit on Item |
|---|---|---|---|---|---|---|
| Shirts | 10 | ₹800 | ₹8,000 | ₹1000 | ₹10,000 | ₹2,000 |
| Jackets | 5 | ₹1,500 | ₹7,500 | ₹1,800 | ₹9,000 | ₹1,500 |
-
Total Cost Price
Total CP = ₹8,000 + ₹7,500 = ₹15,500 -
Total Selling Price
Total SP = ₹10,000 + ₹9,000 = ₹19,000 -
Total Profit
Total Profit = Total SP – Total CP = ₹19,000 – ₹15,500 = ₹3,500 -
Profit Percentage
Profit % = (Total Profit / Total CP) × 100
= (₹3,500 / ₹15,500) × 100 ≈ 22.58%
Answer: The shopkeeper made a profit of ≈ 22.6 % on the whole batch.
4. Quick Revision Summary
| What to Memorise | Key Formula |
|---|---|
| Profit / Loss | P/L = SP – CP |
| Profit % | P% = (SP – CP)/CP × 100 |
| Loss % | L% = (CP – SP)/CP × 100 |
| Calculate SP from CP & % | SP = CP × (1 + P%/100) |
| Calculate CP from SP & % | CP = SP / (1 + P%/100) |
| Overall % on batch | Overall % = (Total Profit / Total CP) × 100 |
- Always check the sign: positive → profit, negative → loss.
- For mixed transactions (buying and selling at different prices), compute totals first.
- Remember:
Profit %is always relative to Cost Price, not Selling Price.
Use these quick points to solve any profit‑loss problem quickly during exams. Happy studying!