Question

A shopkeeper claims to sell rice at cost price. He uses a false weight with the intention of selling rice at 25% profit. After selling Rice to a customer, he realizes that the customer has paid 10% less than what he should have paid. What is the actual profit percentage made by the shopkeeper?

• A. 6.25%
• B. 10%
• C. 12.5%
• D. 15%

Answer 1

The Correct Option is C

To solve this problem, we need to understand the scenario: The shopkeeper claims to sell rice at cost price but uses a false weight to gain profit. Furthermore, the customer accidentally pays 10% less than expected.

First, let's determine how the shopkeeper achieves a 25% profit through the use of a false weight.

1. Suppose the actual weight of rice he should give is 1000 grams (or 1 kg), and let the cost price of 1 kg be \(C\).
2. To aim for a 25% profit, the shopkeeper should sell less quantity while he still gets the money equivalent to 1 kg.
3. If he uses \(x\) grams as the weight, then he sets up his selling condition as: \(x = \frac{1000}{1 + \frac{25}{100}}\).
4. This simplifies to: \(x = \frac{1000}{1.25} = 800\) grams.
5. Thus, he uses a weight of 800 grams instead of 1000 grams while claiming to sell at cost price.

Now, to calculate the profit after the customer pays 10% less:

1. The customer should pay \(C\), but actually pays \(0.9C\).
2. Therefore, selling 800 grams for \(0.9C\) gives the actual selling price for 1000 grams as: \(\frac{0.9C}{800} \times 1000 = 1.125C\).
3. Thus, selling price per kg turns out to be 1.125 times the cost price which implies a profit percentage of: \(= 12.5\%\).

Hence, the actual profit percentage made by the shopkeeper is 12.5%, which corresponds to the correct option.