Understanding the Dishonest Shopkeeper Problem

This problem involves a scenario where a shopkeeper attempts to profit by selling goods at a price lower than his cost price per unit weight, while also deceiving customers about the quantity they receive using faulty weights.

Extracting Key Information

• Cost Price (CP) rate: ₹25 per kilogram (or per 1000 grams).
• Claimed Selling Price (SP) rate: ₹23 per kilogram (or per 1000 grams).
• Actual quantity of goods given to the customer: 600 grams.
• Intended quantity of goods (implied by the rate): 1000 grams.

Calculating Profit or Loss Percentage

To determine the overall profit or loss, we need to calculate the total cost incurred by the shopkeeper for the goods he actually sold and compare it with the total revenue he received.

Step 1: Calculate the Cost Price (CP) for the actual quantity sold

The shopkeeper actually sold 600 grams of the item. We first find the cost price for this specific quantity.

Given that the Cost Price for 1000 grams = ₹25.

Therefore, the Cost Price for 600 grams is calculated as:

CP for 600 grams = \( \left( \frac{600 \text{ grams}}{1000 \text{ grams}} \right) \times ₹25 \)

CP for 600 grams = \( 0.6 \times ₹25 \)

CP for 600 grams = \( ₹15 \)

Step 2: Calculate the Selling Price (SP) for the actual quantity sold

The shopkeeper claims to sell the item at ₹23 per kg. However, he uses faulty weights and provides only 600 grams. In problems involving dishonest traders and faulty weights, the stated selling price is typically considered the total revenue received for the quantity actually handed over to the customer.

Thus, the total amount the shopkeeper receives for the 600 grams is ₹23.

SP for 600 grams = \( ₹23 \)

Step 3: Determine Profit or Loss

Now, we compare the Selling Price (SP) with the Cost Price (CP) for the 600 grams sold:

• Cost Price (CP) = ₹15
• Selling Price (SP) = ₹23

Since the Selling Price (\(₹23\)) is greater than the Cost Price (\(₹15\)), the shopkeeper makes a profit.

Step 4: Calculate the Profit Amount

The profit is the difference between the selling price and the cost price.

Profit = SP - CP

Profit = \( ₹23 - ₹15 \)

Profit = \( ₹8 \)

Step 5: Calculate the Profit Percentage

The profit percentage is calculated with respect to the Cost Price.

Profit Percentage = \( \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\% \)

Profit Percentage = \( \left( \frac{₹8}{₹15} \right) \times 100\% \)

To simplify the calculation:

Profit Percentage = \( \left( \frac{800}{15} \right) \% \)

Dividing both the numerator and the denominator by 5:

Profit Percentage = \( \left( \frac{160}{3} \right) \% \)

Converting this improper fraction into a mixed number:

Profit Percentage = \( 53\frac{1}{3}\% \)

Final Conclusion

The shopkeeper makes a total profit of \( 53\frac{1}{3}\% \). This profit is achieved because the shopkeeper buys the goods at ₹25 per kg but effectively charges ₹23 for only 600 grams, resulting in a gain on the actual quantity dispensed.