Profit & Loss – Quick Study Notes
For the Haryana Police Constable Exam – Quantitative Aptitude
1. Simple Explanation
| Term | Meaning |
|---|---|
| Profit | Gain obtained when the selling price (SP) exceeds the cost price (CP). |
| Loss | Decrease obtained when SP is less than CP. |
| Profit/Loss Percentage | (Profit or Loss ÷ CP) × 100 % |
Formula
Profit = SP – CP
Loss = CP – SP
Profit % = (Profit ÷ CP) × 100
Loss % = (Loss ÷ CP) × 100
2. Key Points to Remember
| # | Concept | Quick Tip |
|---|---|---|
| 1 | Profit and Loss are opposite | If you increase SP, profit grows; if you decrease SP, loss grows. |
| 2 | Percentage always uses CP as the base | Even if the amount of profit or loss is known, the percentage must be calculated against the original cost. |
| 3 | Profit % = (SP – CP) ÷ CP × 100 | Simplify: (SP ÷ CP – 1) × 100 |
| 4 | Loss % = (CP – SP) ÷ CP × 100 | Equivalent to (1 – SP ÷ CP) × 100 |
| 5 | Composite transactions | For multiple items, compute total CP and total SP first, then use the formula. |
| 6 | Discounts and Markups | Discount reduces SP, markup increases SP. |
| 7 | Break‑even point | SP = CP ⇒ 0 % profit/loss. |
| 8 | Profit–Loss relationship | Profit % = 100 × (SP/CP – 1) ; Loss % = 100 × (1 – SP/CP). |
| 9 | Reverse problems | Convert percentages to fractions (e.g., 20 % profit ⇒ factor 1.20). |
| 10 | Rounding | Usually round to nearest whole number unless specified. |
3. Worked Example
Problem
A shopkeeper buys a set of 10 watches for ₹3,000. He sells them at a 15 % profit.
What is the selling price of each watch?
Also, if he later sells them at a 10 % loss, what would be the new selling price per watch?
Solution
-
Compute total CP per watch
- Total CP = ₹3,000
- CP per watch = ₹3,000 ÷ 10 = ₹300
-
Profit of 15 %
- Profit factor = 1 + 15 % = 1.15
- SP per watch = CP × 1.15 = ₹300 × 1.15 = ₹345
-
Loss of 10 %
- Loss factor = 1 – 10 % = 0.90
- New SP per watch = CP × 0.90 = ₹300 × 0.90 = ₹270
Answers
- Selling price with 15 % profit: ₹345 per watch.
- Selling price with 10 % loss: ₹270 per watch.
4. Quick Revision Summary
| Concept | Formula | Example |
|---|---|---|
| Profit | SP – CP | ₹400 – ₹300 = ₹100 |
| Loss | CP – SP | ₹300 – ₹250 = ₹50 |
| Profit % | (SP ÷ CP – 1) × 100 | (1.15 – 1) × 100 = 15 % |
| Loss % | (1 – SP ÷ CP) × 100 | (1 – 0.90) × 100 = 10 % |
| Total CP & SP | Sum of individual CP / SP | Add all items before applying % |
| Break‑even | SP = CP | No profit, no loss |
| Discount | New SP = SP × (1 – Discount %) | 20 % discount: 0.80 × SP |
| Markup | New SP = CP × (1 + Markup %) | 25 % markup: 1.25 × CP |
Remember: Always use the cost price as the base for percentage calculations.
Good luck with your preparation! Feel free to revisit these notes whenever you need a quick refresh.