Profit & Loss – Study Notes
(Quantitative Aptitude – SET)
1. Simple Explanation
- Profit is the amount earned over the cost of an item.
- Loss is the amount lost when the selling price is less than the cost.
- They are measured as a percentage of the cost price (CP) or the selling price (SP).
| Situation | Formula | Interpretation |
|---|---|---|
| Profit | (P = SP - CP) | Positive number → profit |
| Loss | (L = CP - SP) | Positive number → loss |
| Profit % | (\displaystyle \frac{SP-CP}{CP}\times100) | Percentage of CP |
| Loss % | (\displaystyle \frac{CP-SP}{CP}\times100) | Percentage of CP |
2. Key Points
| Concept | Detail |
|---|---|
| Cost Price (CP) | Amount paid to acquire goods. |
| Selling Price (SP) | Amount received from sale. |
| Profit | (SP > CP) |
| Loss | (SP < CP) |
| Profit / Loss % | Expressed relative to CP (most common). |
| Mark-up | ( \displaystyle \frac{SP-CP}{CP}\times100) – same as profit % when selling a single item. |
| Margin | ( \displaystyle \frac{SP-CP}{SP}\times100) – profit relative to selling price. |
| Buy & Sell at Different Rates | Use Average Cost formula for multiple purchases. |
| Combined Profit/Loss | When two purchases are sold at a common SP, compute total CP and total SP. |
| Trade & Profit | In trade, profit is often expressed as a margin on cost or a markup on cost. |
| Ratio of Sales & Cost | Useful when an item is sold in two parts or at different rates. |
3. Profit & Loss Calculations
3.1 Single Transaction
| Given | Formula | Result |
|---|---|---|
| CP = ₹200, SP = ₹240 | (Profit = 240-200 = ₹40) | Profit ₹40 |
| Profit % | (\displaystyle \frac{40}{200}\times100 = 20%) | 20 % profit |
3.2 Multiple Purchases (Average Cost)
| Step | Formula | Explanation |
|---|---|---|
| 1. Buy 10 units @ ₹50 each → Total CP = 10×50 = ₹500 | ||
| 2. Buy 15 units @ ₹70 each → Total CP = 15×70 = ₹1,050 | ||
| Total CP = 500 + 1,050 = ₹1,550 | ||
| Total Quantity = 10 + 15 = 25 units | ||
| Average Cost per Unit = ( \frac{1550}{25} = ₹62) | ||
| Sell all 25 units @ ₹80 each → Total SP = 25×80 = ₹2,000 | ||
| Profit = 2,000 – 1,550 = ₹450 | ||
| Profit % = ( \frac{450}{1550}\times100 ≈ 29.03%) |
3.3 Combined Profit & Loss (Different CP, Same SP)
| Item | CP | Quantity | SP per unit (common) | Total CP | Total SP | Net |
|---|---|---|---|---|---|---|
| A | ₹100 | 10 | ₹150 | ₹1,000 | ₹1,500 | +₹500 |
| B | ₹120 | 15 | ₹150 | ₹1,800 | ₹2,250 | +₹450 |
| Total | — | 25 | — | ₹2,800 | ₹3,750 | +₹950 |
| Profit % | — | — | — | — | — | ( \frac{950}{2800}\times100 ≈ 33.93%) |
4. Rate of Profit & Loss
- Profit Rate = (\displaystyle \frac{Profit}{CP}\times100)
- Loss Rate = (\displaystyle \frac{Loss}{CP}\times100)
Example
Purchase price = ₹1,200; selling price = ₹1,080.
Loss = 1,200 – 1,080 = ₹120.
Loss % = (\frac{120}{1200}\times100 = 10%)
5. Trade, Mark-up & Margin
| Term | Formula | Notes |
|---|---|---|
| Mark‑up | (\displaystyle \frac{SP-CP}{CP}\times100) | Same as profit % if selling one item. |
| Margin | (\displaystyle \frac{SP-CP}{SP}\times100) | Profit relative to selling price. |
| Retail Mark‑up | Often given in % (e.g., 30 % markup on cost). | |
| Example | CP = ₹200, markup = 25 % → SP = ₹200 × (1 + 0.25) = ₹250. |
6. Ratio of Sales & Cost (Useful in Mixed Transactions)
If an item is sold at two different prices, the profit/loss ratio can be found using the sales ratio.
Formula
[
\text{Profit %} = \frac{1}{\left(\frac{SP_1}{CP}\right) \times \frac{Q_1}{Q_1+