📘 Maharashtra TET – Quantitative Aptitude
Topic: Profit & Loss
Goal: Understand how to find profit, loss, and their percentages using the simplest language and everyday examples.
1. Basic Ideas
| Term | Everyday Meaning | How to Remember |
|---|---|---|
| Cost Price (CP) | The price you pay to buy something. | Think of “cost” as the money you spend. |
| Selling Price (SP) | The price at which you sell it. | Think of “sell” as the money you receive. |
| Profit | You earn more money than you paid. | SP > CP → Profit = SP – CP |
| Loss | You earn less money than you paid. | SP < CP → Loss = CP – SP |
| Profit / Loss Percentage | How big the profit or loss is compared with what you paid. | (Profit or Loss ÷ CP) × 100 |
Quick rule:
Profit or loss is always measured against the Cost Price.
2. Simple Calculations
2.1 Profit / Loss (in rupees)
| Situation | Formula | Example |
|---|---|---|
| Profit (₹) | Profit = SP – CP |
Bought ₹100, sold ₹150 → Profit = 150 – 100 = ₹50 |
| Loss (₹) | Loss = CP – SP |
Bought ₹100, sold ₹80 → Loss = 100 – 80 = ₹20 |
2.2 Profit / Loss Percentage
| Situation | Formula | Example |
|---|---|---|
| Profit % | (Profit ÷ CP) × 100 |
Profit ₹50 on CP ₹100 → (50 ÷ 100) × 100 = 50 % |
| Loss % | (Loss ÷ CP) × 100 |
Loss ₹20 on CP ₹100 → (20 ÷ 100) × 100 = 20 % |
3. Finding Unknowns
3.1 You know SP and profit/loss %, find CP
| When | Formula | Example |
|---|---|---|
| Profit % known | CP = SP ÷ (1 + Profit% ÷ 100) |
SP ₹150, profit 20 % → CP = 150 ÷ 1.20 = ₹125 |
| Loss % known | CP = SP ÷ (1 – Loss% ÷ 100) |
SP ₹80, loss 20 % → CP = 80 ÷ 0.80 = ₹100 |
3.2 You know CP and profit/loss %, find SP
| When | Formula | Example |
|---|---|---|
| Profit % known | SP = CP × (1 + Profit% ÷ 100) |
CP ₹100, profit 20 % → SP = 100 × 1.20 = ₹120 |
| Loss % known | SP = CP × (1 – Loss% ÷ 100) |
CP ₹100, loss 20 % → SP = 100 × 0.80 = ₹80 |
4. Ratio of Profit to Loss
If the profit and loss are in a ratio, you can find CP and SP.
- Let Profit : Loss = a : b
- Let CP = x
- Then Profit = (a/(a+b)) × SP
- And Loss = (b/(a+b)) × SP
A simpler way:
| Step | Action |
|---|---|
| 1 | Add the ratio parts: total = a + b |
| 2 | Cost Price = SP × (b ÷ total) or CP = SP × (b ÷ total) |
| 3 | Selling Price = CP × (a ÷ b) (or just add Profit to CP) |
Tiny Example
Profit : Loss = 3 : 2, SP = ₹500
total = 3 + 2 = 5- `CP = 500 ×