A dishonest shopkeeper makes a cheating at 20% at the time of bying the goods and 40% cheating at the time of selling the goods. He promise to sell his goods at 10% loss. Find the profit %.

Options

A. 0.9
B. 0.8
C. 1.1
D. 0.5

Answer

To solve the problem step by step, let's break down the situation involving the dishonest shopkeeper:

### Step 1: Understand the Cost Price (CP) and Selling Price (SP)
Assume the cost price of 1000 grams of goods is ₹1000.

### Step 2: Calculate the Effective Quantity Bought
The shopkeeper cheats by 20% while buying. This means he actually receives more goods than he pays for.

- **Actual quantity received** = 1000 grams + 20% of 1000 grams
- **Actual quantity received** = 1000 grams + 200 grams = 1200 grams

So, he effectively buys 1200 grams for ₹1000.

### Step 3: Calculate the Effective Quantity Sold
When selling, he cheats by 40%. This means he sells less than what he claims.

- **Claimed quantity sold** = 1000 grams
- **Actual quantity sold** = 1000 grams - 40% of 1000 grams
- **Actual quantity sold** = 1000 grams - 400 grams = 600 grams

### Step 4: Determine the Selling Price with a 10% Loss
The shopkeeper claims to sell at a 10% loss.

- **Loss on CP** = 10% of ₹1000 = ₹100
- **Selling Price (SP)** = CP - Loss = ₹1000 - ₹100 = ₹900

### Step 5: Calculate the Effective Selling Price per Gram
Since he is selling 600 grams for ₹900, we can find the effective selling price per gram.

- **Effective SP per gram** = Selling Price / Actual quantity sold
- **Effective SP per gram** = ₹900 / 600 grams = ₹1.5 per gram

### Step 6: Calculate the Cost Price per Gram
Now, we need to find the cost price per gram based on the effective quantity he bought.

- **Effective CP per gram** = Cost Price / Actual quantity received
- **Effective CP per gram** = ₹1000 / 1200 grams = ₹0.8333 per gram

### Step 7: Calculate the Profit
Now we can find the profit made by the shopkeeper.

- **Profit per gram** = Effective SP per gram - Effective CP per gram
- **Profit per gram** = ₹1.5 - ₹0.8333 = ₹0.6667

### Step 8: Calculate Total Profit
Now, we can calculate the total profit for the entire quantity sold.

- **Total Profit** = Profit per gram × Actual quantity sold
- **Total Profit** = ₹0.6667 × 600 grams = ₹400

### Step 9: Calculate Profit Percentage
Finally, we can calculate the profit percentage.

- **Profit Percentage** = (Total Profit / Cost Price) × 100
- **Profit Percentage** = (₹400 / ₹1000) × 100 = 40%

### Final Answer
The profit percentage of the dishonest shopkeeper is **40%**.

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