📚 Profit & Loss – Study Notes
(Andaman & Nicobar Islands PSC – Quantitative Aptitude)
1. Simple Explanation
| Term | Definition | Formula |
|---|---|---|
| Profit | Amount earned when selling price (SP) > cost price (CP) | Profit = SP – CP |
| Loss | Amount lost when SP < CP | 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 |
| Selling Price | Price at which the item is sold | SP = CP + Profit (if profit) or SP = CP – Loss (if loss) |
| Cost Price | Original price paid for the item | CP = SP – Profit or CP = SP + Loss |
Tip: Always keep CP as the base for percentages.
2. Key Points & Formulae
| Scenario | Formula | Notes |
|---|---|---|
| Profit % | P% = (SP – CP) / CP × 100 |
Use CP in denominator. |
| Loss % | L% = (CP – SP) / CP × 100 |
Same denominator. |
| Selling Price from % | SP = CP × (1 + P/100) |
For profit. |
| Selling Price from % | SP = CP × (1 – L/100) |
For loss. |
| Cost Price from % | CP = SP / (1 + P/100) |
Reverse of above. |
| Cost Price from % | CP = SP / (1 – L/100) |
Reverse of loss. |
| Profit or Loss in ₹ | ₹ = SP – CP (positive → profit, negative → loss) |
Straight difference. |
Quick Check:
- Profit % > 0 → Profit
- Loss % > 0 → Loss
3. Worked Example
Problem:
A shopkeeper bought an item for ₹ 8,000. He sold it at a 25 % profit. What is the selling price? Also, if he sold another item for ₹ 9,000 and made a 10 % loss, what was its cost price?
Step‑by‑step
Part 1 – Selling Price (Profit)
- Identify CP: ₹ 8,000
- Profit %: 25 % →
P/100 = 0.25 - Compute SP:
[ SP = CP \times (1 + P/100) = 8000 \times (1 + 0.25) = 8000 \times 1.25 = 10,000 ] - Result: SP = ₹ 10,000
Quick sanity check: 25 % of 8,000 is 2,000; add to 8,000 → 10,000 ✔️
Part 2 – Cost Price (Loss)
- Identify SP: ₹ 9,000
- Loss %: 10 % →
L/100 = 0.10 - Compute CP:
[ CP = \frac{SP}{1 - L/100} = \frac{9000}{1 - 0.10} = \frac{9000}{0.90} = 10,000 ] - Result: CP = ₹ 10,000
Quick sanity check: 10 % loss on 10,000 is 1,000; 10,000 – 1,000 = 9,000 ✔️
4. Quick Revision Summary
| What to remember | Formula | Example |
|---|---|---|
| Profit / Loss amount | Profit = SP – CP / Loss = CP – SP |
10,000 – 8,000 = 2,000 profit |
| Profit % | P% = (SP – CP) / CP × 100 |
(10,000 – 8,000)/8,000 ×100 = 25 % |
| Loss % | L% = (CP – SP) / CP × 100 |
(10,000 – 9,000)/10,000 ×100 = 10 % |
| SP from CP & % | SP = CP × (1 ± %/100) |
8,000 × 1.25 = 10,000 |
| CP from SP & % | CP = SP / (1 ± %/100) |
9,000 / 0.90 = 10,000 |
Tips for PSC Exam
- Read carefully – check whether the percentage is on CP or SP.
- Work with fractions – converting percentages to decimals (e.g., 25 % → 0.25) reduces error.
- Use a calculator – always double‑check arithmetic.
- Quick mental math –
- 25 % of a number = ¼ of the number.
- 10 % loss = reduce by 10 % of CP.
- Common mistakes –
- Mixing up CP and SP in denominator.
- Forgetting the sign (profit positive, loss negative).
Practice Problem
A trader bought goods for ₹ 15,000 and sold them for ₹ 18,000.
- Find the profit in ₹ and %
- If he had sold them for ₹ 13,500, what would be the loss %?
(Try solving before checking the answer below)
Answer
- Profit ₹ 3,000 ⇒
Profit% = 3,000/15,000 ×100 = 20 % - Loss ₹ 1,500 ⇒
Loss% = 1,500/15,000 ×100 = 10 %
Happy studying! 🚀