If books bought at price from Rs. 150 to Rs. 300 are sold at prices ranging from Rs. 250 to Rs. 350. What is the greatest possible profit that might be made in selling 15 books?

Answer

To find the greatest possible profit from selling 15 books, we need to analyze the cost price (CP) and selling price (SP) ranges provided in the question.

### Step 1: Identify the Cost Price Range
The cost price of one book ranges from Rs. 150 to Rs. 300.
- Minimum CP = Rs. 150
- Maximum CP = Rs. 300

### Step 2: Identify the Selling Price Range
The selling price of one book ranges from Rs. 250 to Rs. 350.
- Minimum SP = Rs. 250
- Maximum SP = Rs. 350

### Step 3: Calculate the Profit for Each Scenario
Profit can be calculated using the formula:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]

#### Case 1: Maximum Profit Scenario
To achieve the greatest profit, we should sell the book at the maximum selling price and buy it at the minimum cost price.
- Maximum SP = Rs. 350
- Minimum CP = Rs. 150

Calculating the profit for one book:
\[ \text{Profit per book} = 350 - 150 = Rs. 200 \]

### Step 4: Calculate Total Profit for 15 Books
Now, we multiply the profit per book by the number of books sold (15):
\[ \text{Total Profit} = \text{Profit per book} \times \text{Number of books} \]
\[ \text{Total Profit} = 200 \times 15 = Rs. 3000 \]

### Conclusion
The greatest possible profit that might be made in selling 15 books is Rs. 3000.

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