Question

A shopkeeper proposes to sell his goods at cost price but uses a weight of 850gms instead of a kilogram weight. What is his profit percentage?

• A. \(17^{\frac{14}{17} } \)%
• B. \(17^{\frac{11}{17} } \)%
• C. \(17^{\frac{16}{17} } \)%
• D. \(17^{\frac{12}{17} } \)%
• E. None of these

Answer 1

Answer: (E)

Step 1: Understand the problem.
The shopkeeper sells goods at the cost price but uses a weight of 850 grams instead of 1 kilogram (1000 grams). This means that for every 1 kg of goods, the customer receives only 850 grams, but they pay for 1000 grams (the cost price). We need to find the profit percentage.

Step 2: Calculate the cost and selling prices.
Let the cost price of 1 kg of goods be \( C \). This means the cost for 1 kg is \( C \) rupees.
The shopkeeper, however, gives only 850 grams, but charges the customer for 1000 grams at the cost price, so the selling price for 850 grams is \( C \) rupees.

Step 3: Calculate the effective cost for 850 grams.
The cost price for 850 grams is:
Cost for 850 grams = \( \frac{850}{1000} \times C = 0.85 \times C \)

Step 4: Find the profit.
The profit is the difference between the selling price (which is \( C \) rupees) and the cost price for 850 grams (which is \( 0.85 \times C \)):
Profit = Selling price - Cost price for 850 grams
Profit = \( C - 0.85 \times C = 0.15 \times C \)

Step 5: Calculate the profit percentage.
Profit percentage is given by the formula:
Profit percentage = \( \frac{{\text{Profit}}}{{\text{Cost Price for 850 grams}}} \times 100 \)
Profit percentage = \( \frac{{0.15 \times C}}{{0.85 \times C}} \times 100 \)
Profit percentage = \( \frac{{0.15}}{{0.85}} \times 100 = 17.65\% \)

Step 6: Conclusion.
The profit percentage of the shopkeeper is 17.65%.

Final Answer:
The profit percentage is 17.65%.

The correct option is (E): None of these.