AFCAT – Quantitative Aptitude
Topic: Profit & Loss
AFCAT (Air Force Common Admission Test) frequently tests basic profit & loss concepts. Mastery of these formulas will help you solve many questions quickly.
1. Simple Explanation
| Term | What it Means | Formula |
|---|---|---|
| Cost Price (CP) | The price at which an item is bought. | — |
| Selling Price (SP) | The price at which an item is sold. | — |
| Profit | Money earned, i.e., SP – CP. | Profit = SP – CP |
| Loss | Money lost, i.e., CP – SP. | Loss = CP – SP |
| Profit % | Profit expressed as a percentage of CP. | Profit % = (Profit / CP) × 100 |
| Loss % | Loss expressed as a percentage of CP. | Loss % = (Loss / CP) × 100 |
Key Idea:
– If SP > CP → Profit.
– If SP < CP → Loss.
– The percentage depends only on CP, not on SP.
2. Key Points to Remember
| Concept | Note |
|---|---|
| Profit & Loss are linear | The profit or loss per unit is the same for all units bought at the same CP. |
| Percentage calculations use CP | Even if the SP changes, the percent is always based on CP. |
| Combined profit/loss | Add individual profits and losses before computing total percent. |
| Profit after discount | First find the discounted price, then apply profit formula. |
| Profit on sale after price increase | Treat the new price as SP; use CP of original purchase. |
| Break‑even point | SP = CP → 0% profit/loss. |
| Margin of safety | Difference between actual sales and break‑even sales. |
3. Worked Example
Problem
A shopkeeper buys 15 identical items at ₹120 each.
He sells 5 items at a 10% profit, 5 items at a 5% loss, and 5 items at the break‑even price.
What is the overall profit or loss percentage?
Step‑by‑Step
| Item | CP (₹) | SP (₹) | Profit/Loss | % Profit/Loss |
|---|---|---|---|---|
| 1 | 120 | 120 × 1.10 = 132 | +12 | +10% |
| 2 | 120 | 120 × 1.05 = 126 | +6 | +5% |
| 3 | 120 | 120 | 0 | 0% |
-
Total CP = 15 × 120 = ₹1,800
-
Total SP = (5×132) + (5×126) + (5×120)
= 660 + 630 + 600 = ₹1,890 -
Overall Profit = 1,890 – 1,800 = ₹90
-
Profit % = (90 ÷ 1,800) × 100 = 5%
Answer: The shopkeeper makes an overall profit of 5 %.
4. Quick Revision Summary
- Profit = SP – CP Loss = CP – SP
- Profit % = (Profit ÷ CP) × 100
- Loss % = (Loss ÷ CP) × 100
- For combined scenarios:
- Compute individual profits/losses.
- Sum them.
- Divide by total CP to get overall %.
- Remember: Percentage is always relative to the Cost Price.
- Quick checks:
- If SP = CP → 0% (break‑even).
- If SP = CP × (1 + profit %) → Profit.
- If SP = CP × (1 – loss %) → Loss.
- Practice conversions:
- 10% profit → SP = 1.10 × CP
- 5% loss → SP = 0.95 × CP
Tip for AFCAT – Write down the formulas first, plug in numbers, and avoid rounding until the final step.
With these notes, you should be able to tackle any profit‑and‑loss question in the AFCAT Quantitative Aptitude section. Happy studying!