To determine the percentage profit of the shopkeeper, we need to analyze both the pricing strategy and the weight discrepancy. Let's break this down step by step.

Step 1: Understanding the Markup and Discount

1. Cost Price (CP): Let the cost price be $x$.
2. Marked Price (MP): The goods are marked 40% above the cost price. $\text{MP} = x + 0.4x = 1.4x$
3. Selling Price (SP): A discount of 15% is offered on the marked price. $\text{SP} = \text{MP} - 0.15 \times \text{MP} = 1.4x - 0.15 \times 1.4x = 1.4x \times 0.85 = 1.19x$

Step 2: Adjusting for Weight Discrepancy

The shopkeeper uses a weight of 1100 grams instead of 1000 grams (1 kg).

Since 1100 grams is being sold as 1000 grams, the customer is actually getting 10% more goods than they think they are getting. This means the effective cost price for the shopkeeper is not just $x$, but $x$ for what should have been 1000 grams but is instead 1100 grams. Therefore, the effective cost price per 1000 grams (1 kg) becomes: $\text{Effective CP per 1000 grams} = \frac{x}{1.1} = \frac{x}{1.1}$

Step 3: Calculating the Profit

Profit is the difference between the selling price and the effective cost price.

$\text{Profit} = \text{SP} - \text{Effective CP}$ $\text{Effective CP} = \frac{x}{1.1}$ $\text{SP} = 1.19x$

$\text{Profit} = 1.19x - \frac{x}{1.1} = 1.19x - \frac{1.1x}{1.1^2} = 1.19x - \frac{1.1x}{1.21} = 1.19x - \frac{1.1x}{1.21}$

To simplify: $\text{Profit} = 1.19x - 0.9091x = 0.2809x$

Step 4: Calculating Percentage Profit

Percentage profit is given by: $\text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Effective CP}} \right) \times 100$ $\text{Effective CP} = \frac{x}{1.1} = 0.9091x$

$\text{Percentage Profit} = \left( \frac{0.2809x}{0.9091x} \right) \times 100 = \left( \frac{0.2809}{0.9091} \right) \times 100 \approx 30.88\%$

Thus, the percentage profit of the shopkeeper is approximately 30.88%.

Would you like more details on any part of this solution or have any other questions?

Here are some questions you might be interested in:

1. How to calculate profit margin in different scenarios?
2. What are some common pricing strategies and their impacts?
3. How to handle discounts and markups in retail math?
4. What are the impacts of measurement discrepancies in business?
5. How to calculate the breakeven point in a business?

Tip: Always double-check your weight measurements and price calculations to ensure accurate profit and avoid any potential discrepancies.