📚 Profit & Loss – Quantitative Aptitude
Mizoram PSC – Study Notes
1. Simple Explanation
- Cost Price (CP) – The price at which an item is bought.
- Selling Price (SP) – The price at which the same item is sold.
- Profit –
SP – CP(when SP > CP). - Loss –
CP – SP(when SP < CP).
Profit/Loss Percentage
[
\text{Profit %} = \frac{\text{Profit}}{\text{CP}} \times 100
]
[
\text{Loss %} = \frac{\text{Loss}}{\text{CP}} \times 100
]
2. Key Points
| Item | Symbol | Formula | Interpretation |
|---|---|---|---|
| Cost Price | CP | – | Price paid to acquire the item |
| Selling Price | SP | – | Price at which it is sold |
| Profit | P | (SP - CP) | Positive when SP > CP |
| Loss | L | (CP - SP) | Positive when CP > SP |
| Profit % | ( %P ) | ( \frac{P}{CP} \times 100) | How much profit relative to cost |
| Loss % | ( %L ) | ( \frac{L}{CP} \times 100) | How much loss relative to cost |
| Relation | – | (SP = CP \pm \text{Profit/Loss}) | Add profit to CP to get SP; subtract loss from CP to get SP |
Common Pitfalls
- Using SP as denominator – always use CP for % calculations.
- Sign errors – Remember profit is positive; loss is negative for calculations.
- Mixing “profit” and “gain” – In most contexts they’re the same, but always follow the given definitions.
3. Worked Example
Problem
A shopkeeper bought a set of lamps for ₹3,600. He sold them for ₹4,500.
- Find the profit earned.
- Calculate the profit percentage.
Step‑by‑Step
| Step | Calculation | Result |
|---|---|---|
| 1. Profit (P) | (SP - CP = 4500 - 3600) | ₹900 |
| 2. Profit % | (\frac{P}{CP}\times 100 = \frac{900}{3600}\times 100) | 25% |
Answer
- Profit = ₹900
- Profit percentage = 25 %
4. Quick Revision Summary
| Concept | Formula | Example |
|---|---|---|
| Profit | (P = SP - CP) | If SP = ₹800, CP = ₹600 → P = ₹200 |
| Loss | (L = CP - SP) | If SP = ₹500, CP = ₹700 → L = ₹200 |
| Profit % | (\displaystyle \frac{P}{CP}\times100) | ₹200 profit on ₹800 CP → 25 % |
| Loss % | (\displaystyle \frac{L}{CP}\times100) | ₹200 loss on ₹800 CP → 25 % |
| SP from CP & % | (SP = CP \times (1 \pm \frac{%}{100})) | CP ₹1,000 + 20 % profit → SP = ₹1,200 |
| CP from SP & % | (CP = \frac{SP}{1 \pm \frac{%}{100}}) | SP ₹1,200 with 20 % loss → CP = ₹1,500 |
Quick Practice Question
A trader bought an item for ₹2,400 and sold it at a 12 % loss.
a) What was the selling price?
b) What would be the selling price if the trader wanted a 10 % profit instead?
Solve:
a) (SP = CP \times (1 - 0.12) = 2400 \times 0.88 = ₹2,112)
b) (SP = 2400 \times (1 + 0.10) = 2400 \times 1.10 = ₹2,640)
Tip: Always write the given values first, then substitute into the appropriate formula. Keep the signs straight: add profit, subtract loss. Good luck!