A merchant earns 25% profit in general. Once his 25% consigment was abducted forever by some goondas. Trying to compensate his loss he sold the rest amount by increasing his selling price by 20%. What is the new percentage profit or loss?

Options

A. 10 % loss
B. 12.5% loss
C. 12.5% profit
D. 11.11% loss

Answer

To solve the problem step by step, we will break down the information provided and calculate the new percentage profit or loss after the merchant's consignment was partially lost.

### Step 1: Determine the Initial Cost Price and Selling Price
Let’s assume the total consignment of the merchant is 100 units, and the cost price (CP) of 1 unit is ₹1. Therefore, the total cost price (CP) of 100 units is:
\[ \text{Total CP} = 100 \text{ units} \times ₹1/\text{unit} = ₹100 \]

### Step 2: Calculate the Selling Price with 25% Profit
The merchant earns a profit of 25%. Therefore, the selling price (SP) of 100 units can be calculated as:
\[ \text{SP} = \text{CP} + 25\% \text{ of CP} = ₹100 + 0.25 \times ₹100 = ₹100 + ₹25 = ₹125 \]

### Step 3: Determine the Selling Price per Unit
The selling price per unit is:
\[ \text{SP per unit} = \frac{₹125}{100 \text{ units}} = ₹1.25 \]

### Step 4: Calculate the Remaining Consignment After Loss
Since 25% of the consignment was abducted, the remaining consignment is:
\[ \text{Remaining units} = 100 \text{ units} - 25\% \text{ of } 100 \text{ units} = 100 - 25 = 75 \text{ units} \]

### Step 5: Increase the Selling Price by 20%
The merchant increases the selling price by 20%. The new selling price per unit is calculated as follows:
\[ \text{New SP per unit} = \text{Old SP per unit} + 20\% \text{ of Old SP per unit} \]
Calculating 20% of ₹1.25:
\[ 20\% \text{ of } ₹1.25 = 0.20 \times ₹1.25 = ₹0.25 \]
Thus, the new selling price per unit becomes:
\[ \text{New SP per unit} = ₹1.25 + ₹0.25 = ₹1.50 \]

### Step 6: Calculate the Total New Selling Price for Remaining Units
The total new selling price for the remaining 75 units is:
\[ \text{Total New SP} = 75 \text{ units} \times ₹1.50/\text{unit} = ₹112.50 \]

### Step 7: Calculate the New Profit or Loss
Now, we compare the total new selling price with the total cost price:
\[ \text{Profit} = \text{Total New SP} - \text{Total CP} = ₹112.50 - ₹100 = ₹12.50 \]

### Step 8: Calculate the New Profit Percentage
The new profit percentage can be calculated as:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{Total CP}}\right) \times 100 = \left(\frac{₹12.50}{₹100}\right) \times 100 = 12.5\% \]

### Final Answer
The new percentage profit is **12.5%**.

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