Profit & Loss – Quick Study Guide
(For Andaman & Nicobar Islands Forest Guard – Quantitative Aptitude)
1. Simple Explanation
- Profit is the amount by which the selling price (SP) exceeds the cost price (CP).
- Loss is the amount by which the SP is less than the CP.
- The percentage of profit or loss is expressed as a fraction of the CP.
Formulae
| Concept | Formula | Example |
|---|---|---|
| Profit | ( \text{Profit} = \text{SP} - \text{CP} ) | If CP = 200, SP = 260 → Profit = 60 |
| Loss | ( \text{Loss} = \text{CP} - \text{SP} ) | If CP = 500, SP = 450 → Loss = 50 |
| Profit % | ( % \text{Profit} = \dfrac{\text{Profit}}{\text{CP}}\times 100 ) | (60/200\times100 = 30%) |
| Loss % | ( % \text{Loss} = \dfrac{\text{Loss}}{\text{CP}}\times 100 ) | (50/500\times100 = 10%) |
| Selling Price (SP) | ( \text{SP} = \text{CP} \pm \text{Profit/Loss} ) | (200 + 60 = 260) |
| Cost Price (CP) | ( \text{CP} = \text{SP} \mp \text{Profit/Loss} ) | (260 - 60 = 200) |
Tip: Always keep the sign in mind: “+” for profit, “−” for loss.
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Profit = SP – CP | Basic building block for all problems. |
| 2 | Loss = CP – SP | Same as above, just reversed. |
| 3 | Profit % / Loss % | Often the required answer; use CP as denominator. |
| 4 | SP = CP (1 ± %/100) | Quick way to find SP when only the percentage is known. |
| 5 | CP = SP / (1 ± %/100) | Useful when SP and % are given, need CP. |
| 6 | Multiple items | Treat each item separately, then add profits/losses. |
| 7 | Combined percentages | Cannot average percentages; convert to amounts first. |
| 8 | Break-even | SP = CP → 0% profit/loss. |
| 9 | Margin vs. Markup | Slight difference: Markup = (SP–CP)/CP; Margin = (SP–CP)/SP. |
| 10 | Check units | Prices in rupees, percentages in %; avoid mixing. |
3. Worked Example (Typical Forest Guard Question)
Question
A forest guard buys 10 bundles of timber at ₹150 each.
He sells them for ₹180 each.
Additionally, he sells 5 bundles at a 10 % discount on ₹180 each.
What is the overall profit percentage?
Step‑by‑Step Solution
| Step | Calculation | Result |
|---|---|---|
| 1 | Total Cost Price (CP) | (10 \times 150 = ₹1{,}500) |
| 2 | Full‑price Sale (10 bundles) | (10 \times 180 = ₹1{,}800) |
| 3 | Discount on 5 bundles | 10 % of ₹180 = ₹18 → Sale price per bundle = ₹180 – 18 = ₹162 |
| 4 | Sale of discounted bundles | (5 \times 162 = ₹810) |
| 5 | Total Selling Price (SP) | (1{,}800 + 810 = ₹2{,}610) |
| 6 | Total Profit | (2{,}610 – 1{,}500 = ₹1{,}110) |
| 7 | Profit % | (\frac{1{,}110}{1{,}500}\times100 = 74%) |
Answer: The overall profit percentage is 74 %.
4. Quick Revision Summary
| Topic | Formula | Quick Check |
|---|---|---|
| Profit | (P = SP - CP) | SP > CP → Profit |
| Loss | (L = CP - SP) | SP < CP → Loss |
| Profit % | (%P = \frac{P}{CP}\times100) | Convert to % |
| Loss % | (%L = \frac{L}{CP}\times100) | Convert to % |
| SP from CP & % | (SP = CP \times (1 \pm \frac{%}{100})) | Add for profit, subtract for loss |
| CP from SP & % | (CP = \frac{SP}{1 \pm \frac{%}{100}}) | Reverse of above |
| Combining items | Sum all CPs → Total CP; sum all SPs → Total SP | Then use profit/loss formula |
| Important Note | Always use CP in denominator for % calculations. | Avoid errors with incorrect base |
Practice Tip:
Convert every problem into amounts (rupees) first, then compute percentages. It eliminates confusion about “percentage of” versus “percentage of the selling price.”
Final Thought
Mastering profit & loss is all about consistent application of the basic formulas and careful attention to the direction of the inequality (profit vs. loss). With the above cheat‑sheet, you’ll handle any Forest Guard aptitude problem in no time!