A dishonest shopkeeper takes 25% more than the indicated weight when he purchases the items from the dealer. He gives 25% less than the indicated weight to his customer at the cost price, then find the profit percentage of the shopkeeper.

Options

A. A)`44.44%`
B. B)`66.67%`
C. C)`50.55%`
D. D)`37.75%`

Answer

To solve the problem step by step, we will analyze the situation involving the dishonest shopkeeper's purchasing and selling practices.

### Step 1: Understand the purchasing scenario
The shopkeeper takes 25% more than the indicated weight when purchasing from the dealer.

- If the indicated weight is considered as 4 units, the weight he actually takes from the dealer is:
\[ \text{Weight taken} = 4 + 25\% \text{ of } 4 = 4 + 1 = 5 \text{ units} \]

**Hint:** Remember that taking 25% more means you add 25% of the original amount to itself.

### Step 2: Understand the selling scenario
When selling, the shopkeeper gives 25% less than the indicated weight to the customer at the cost price.

- If the indicated weight is 4 units, the weight he actually sells to the customer is:
\[ \text{Weight sold} = 4 - 25\% \text{ of } 4 = 4 - 1 = 3 \text{ units} \]

**Hint:** When giving less weight, subtract 25% of the original amount from itself.

### Step 3: Determine the cost price and selling price
- The cost price (CP) for the shopkeeper for 5 units (the weight he bought) is based on the price for 4 units. Let's assume the cost price for 4 units is 4 currency units. Therefore, the cost price for 5 units is:
\[ \text{Cost Price} = 4 \text{ currency units} \]

- The selling price (SP) for the customer for 3 units (the weight he sold) is also based on the cost price for 4 units. The selling price for 3 units is:
\[ \text{Selling Price} = 4 \text{ currency units} \]

**Hint:** The cost price and selling price are based on the indicated weights, so adjust them according to the actual weights involved.

### Step 4: Calculate the profit
Now, we can calculate the profit made by the shopkeeper:
- Profit = Selling Price - Cost Price
\[ \text{Profit} = 4 - 3 = 1 \text{ currency unit} \]

**Hint:** Profit is simply the difference between what you sell for and what you paid.

### Step 5: Calculate the profit percentage
To find the profit percentage, we use the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{1}{3} \right) \times 100 = 33.33\% \]

**Hint:** Profit percentage is calculated based on the cost price, so ensure you divide the profit by the cost price before multiplying by 100.

### Final Answer
The profit percentage of the shopkeeper is **33.33%**.