A little bit tough that can come in UGC NET

### Question 3: Compound Transactions

**Question:** A shopkeeper buys 100 identical items at ₹50 each. He sells 60 of them at a 20% profit and the remaining 40 at a 10% loss. Calculate the overall profit or loss and the percentage profit or loss.

**Solution:**
1. **Cost Price Calculation:**
   \[
   \text{Total Cost Price} = 100 \times 50 = ₹5000
   \]

2. **Selling Price for the 60 items (at 20% profit):**
   \[
   \text{Cost Price of 60 items} = 60 \times 50 = ₹3000
   \]
   \[
   \text{Profit on 60 items} = 20\% \text{ of } ₹3000 = 0.20 \times 3000 = ₹600
   \]
   \[
   \text{Selling Price of 60 items} = ₹3000 + ₹600 = ₹3600
   \]

3. **Selling Price for the 40 items (at 10% loss):**
   \[
   \text{Cost Price of 40 items} = 40 \times 50 = ₹2000
   \]
   \[
   \text{Loss on 40 items} = 10\% \text{ of } ₹2000 = 0.10 \times 2000 = ₹200
   \]
   \[
   \text{Selling Price of 40 items} = ₹2000 - ₹200 = ₹1800
   \]

4. **Total Selling Price:**
   \[
   \text{Total Selling Price} = ₹3600 + ₹1800 = ₹5400
   \]

5. **Overall Profit or Loss:**
   \[
   \text{Overall Profit} = \text{Total Selling Price} - \text{Total Cost Price}
   \]
   \[
   \text{Overall Profit} = ₹5400 - ₹5000 = ₹400
   \]

6. **Percentage Profit Calculation:**
   \[
   \text{Percentage Profit} = \left(\frac{\text{Overall Profit}}{\text{Total Cost Price}}\right) \times 100
   \]
   \[
   \text{Percentage Profit} = \left(\frac{400}{5000}\right) \times 100 = 8\%
   \]

Thus, the overall profit is ₹400, and the percentage profit is 8%.

Would you like more details or have any questions on this? Here are five more questions you can ask next:

1. How to determine the selling price to achieve a desired overall profit percentage?
2. How to calculate the breakeven point in terms of sales needed to cover the cost?
3. What is the effect of discounting on profit and loss?
4. How to calculate the selling price per item to achieve a specific profit margin?
5. How to handle profit and loss calculations with varying cost prices for bulk purchases?

**Tip:** When dealing with compound transactions, it's crucial to separate the calculations for different portions of the goods and then combine the results for the final overall calculation.

Learn how to calculate overall profit and percentage profit from compound transactions involving sales of goods at different prices. This problem involves understanding profit margins, cost prices, selling prices, and percentage profit calculations. Suitable for advanced high school students and those preparing for competitive exams.

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