A trader gets 25% profit by selling an article. If he buys at half the rate and sells at the same selling price as before, then what will be his percentage profit?

Options

A. 50
B. 100
C. 125
D. 150

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Initial Cost Price (CP) and Selling Price (SP)
Let's assume the initial Cost Price (CP) of the article is ₹100.

### Step 2: Calculate the Selling Price (SP) with 25% Profit
Given that the trader makes a 25% profit, we can calculate the Selling Price (SP) using the formula:
\[ SP = CP + (Profit \% \times CP) \]
Substituting the values:
\[ SP = 100 + (25\% \times 100) \]
\[ SP = 100 + 25 = ₹125 \]

### Step 3: Determine the New Cost Price (CP) when Halved
If the trader buys the article at half the original cost, the new Cost Price (CP) will be:
\[ New \, CP = \frac{100}{2} = ₹50 \]

### Step 4: Calculate the Profit with the New Cost Price
The Selling Price remains the same at ₹125. Now we can calculate the profit using the formula:
\[ Profit = SP - New \, CP \]
Substituting the values:
\[ Profit = 125 - 50 = ₹75 \]

### Step 5: Calculate the Percentage Profit
To find the percentage profit, we use the formula:
\[ Percentage \, Profit = \left( \frac{Profit}{New \, CP} \times 100 \right) \]
Substituting the values:
\[ Percentage \, Profit = \left( \frac{75}{50} \times 100 \right) \]
\[ Percentage \, Profit = 1.5 \times 100 = 150\% \]

### Final Answer
The percentage profit when the trader buys at half the rate and sells at the same selling price is **150%**.

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