Anil Kumar sold an article to Rajat for Rs15,000 by losing 25%, Rajat sells it to David at a price that would have given Anil Kumar a profit of 5%. The profit percentage earned by Rajat is:

Options

A. `25%`
B. `40%`
C. `42%`
D. `30%`

Answer

To solve the problem step by step, we will follow the given information about the transactions between Anil Kumar, Rajat, and David.

### Step 1: Determine Anil Kumar's Cost Price
Anil Kumar sold an article to Rajat for Rs. 15,000 at a loss of 25%.

Let the cost price (CP) for Anil Kumar be \( P \).

Since he sold it at a loss of 25%, we can express this as:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]
\[ 15,000 = P - 0.25P \]
\[ 15,000 = 0.75P \]

### Step 2: Calculate Anil Kumar's Cost Price
To find \( P \):
\[ P = \frac{15,000}{0.75} = 20,000 \]

### Step 3: Determine the Selling Price for Rajat
Rajat sells the article to David at a price that would have given Anil Kumar a profit of 5%.

To find this selling price, we calculate the selling price that would give Anil Kumar a 5% profit on his cost price:
\[ \text{Profit} = 5\% \text{ of } P = 0.05 \times 20,000 = 1,000 \]
\[ \text{Selling Price for Anil} = P + \text{Profit} = 20,000 + 1,000 = 21,000 \]

### Step 4: Calculate Rajat's Profit
Now, we know Rajat bought the article for Rs. 15,000 and sold it for Rs. 21,000.

To find Rajat's profit:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 21,000 - 15,000 = 6,000 \]

### Step 5: Calculate Rajat's Profit Percentage
The profit percentage is calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
\[ \text{Profit Percentage} = \left( \frac{6,000}{15,000} \right) \times 100 = 40\% \]

### Final Answer
The profit percentage earned by Rajat is **40%**.

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