A merchant earns `25%` profit in general. Once his `25%` consignment 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 analyze the situation involving the merchant's profit and loss due to the consignment being abducted.

### Step 1: Understand the Initial Situation
The merchant earns a profit of 25%. This means that if the cost price (CP) of an item is \( x \), the selling price (SP) can be calculated as follows:
\[ SP = CP + (25\% \text{ of } CP) = CP + 0.25 \times CP = 1.25 \times CP \]

### Step 2: Determine the Cost Price
Let's assume the cost price of the entire consignment is \( 100 \) (for simplicity). Therefore, the selling price would be:
\[ SP = 1.25 \times 100 = 125 \]

### Step 3: Calculate the Loss Due to Abduction
Since 25% of the consignment was abducted, the merchant loses:
\[ \text{Lost CP} = 25\% \text{ of } 100 = 25 \]
Thus, the remaining cost price of the consignment is:
\[ \text{Remaining CP} = 100 - 25 = 75 \]

### Step 4: Calculate the New Selling Price After Increase
The merchant decides to sell the remaining consignment at an increased selling price of 20%. The original selling price for the remaining consignment (which is 75) would have been:
\[ SP_{\text{original}} = 1.25 \times 75 = 93.75 \]
Now, increasing this selling price by 20%:
\[ \text{Increase} = 20\% \text{ of } 93.75 = 0.20 \times 93.75 = 18.75 \]
Thus, the new selling price (SP) becomes:
\[ SP_{\text{new}} = 93.75 + 18.75 = 112.5 \]

### Step 5: Calculate the New Profit or Loss
Now, we need to determine the profit or loss based on the new selling price:
\[ \text{Profit} = SP_{\text{new}} - \text{Remaining CP} = 112.5 - 75 = 37.5 \]

### Step 6: Calculate the New Percentage Profit
To find the new percentage profit:
\[ \text{Percentage Profit} = \left(\frac{\text{Profit}}{\text{Remaining CP}}\right) \times 100 = \left(\frac{37.5}{75}\right) \times 100 = 50\% \]

### Final Answer
The new percentage profit is **50%**.

---