A dishonest shopkeeper uses two different scales while buying and selling the goods. Both the scales are faulty. While buying he uses a scale that shows 900 gm per kg of the goods bought. Similarly while selling, he uses a scale that shows 1100 gm per kg of the goods sold. What is his profit percent, if he claims to sell the goods at cost price?

Let's break down the problem to calculate the shopkeeper's profit percentage.

### Step 1: Understand the weights used in buying and selling
- **Buying:** The shopkeeper uses a scale that shows 900 grams when he actually receives 1000 grams (1 kg).
- **Selling:** The shopkeeper uses a scale that shows 1100 grams when he actually gives away 1000 grams (1 kg).

### Step 2: Determine the effective cost price and selling price
1. **Cost Price (CP):**
   - The shopkeeper buys 1000 grams (1 kg) but only pays for 900 grams.
   - Let the cost of 1 gram be \( C \).
   - The cost for 1000 grams (which he actually receives) would be \( 900C \).

2. **Selling Price (SP):**
   - The shopkeeper sells 1000 grams (1 kg) but charges for 1100 grams.
   - Using the same cost per gram \( C \), the selling price he charges for 1000 grams would be \( 1100C \).

### Step 3: Calculate the profit
- The profit amount = Selling Price - Cost Price
  \[
  \text{Profit} = 1100C - 900C = 200C
  \]

### Step 4: Calculate the profit percentage
The profit percentage is given by:
\[
\text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}}\right) \times 100
\]
\[
\text{Profit Percentage} = \left(\frac{200C}{900C}\right) \times 100 = \left(\frac{200}{900}\right) \times 100
\]
\[
\text{Profit Percentage} = \frac{200}{9} \approx 22.22\%
\]

### Conclusion:
The shopkeeper's profit percentage is **22.22%**.

---

Do you want details or have any questions?

Here are five related questions:
1. What would be the profit percentage if the shopkeeper used a scale showing 800 grams for buying and 1200 grams for selling?
2. How would the profit percentage change if the shopkeeper sold the goods at 10% above the cost price?
3. What is the formula to calculate profit percentage when weights are different for buying and selling?
4. Can this method of cheating be detected if a customer uses their own scale for weighing?
5. How does this scenario illustrate the importance of accurate measurements in commerce?

**Tip:** Always double-check the accuracy of scales to ensure fair trade practices.

Learn how to calculate the profit percentage of a shopkeeper using faulty scales during buying and selling. Understand the concept of profit percentage, formulas involved, and step-by-step calculation. Suitable for Grades 7-9 students learning about fractions, percentages, and profit calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation