A person sells a pen at 15% profit. If he had bought it at 7% less price and sold it for Rs 250 more, then he would have gained 25%. What is the cost price (in Rs) of the pen?

Options

A. 20000
B. 18000
C. 25000
D. 23000

Answer

To find the cost price of the pen, let's break down the problem step by step.

### Step 1: Define the Variables
Let the cost price (CP) of the pen be \( x \) rupees.

### Step 2: Calculate Selling Price with 15% Profit
If the pen is sold at a 15% profit, the selling price (SP) can be calculated as:
\[ SP = CP + 15\% \text{ of } CP = x + 0.15x = 1.15x \]

### Step 3: Calculate New Cost Price with 7% Less Price
If the pen was bought at 7% less, the new cost price (CP2) would be:
\[ CP2 = CP - 7\% \text{ of } CP = x - 0.07x = 0.93x \]

### Step 4: Calculate Selling Price with 25% Profit
If he sells it for Rs 250 more than the previous selling price and gains 25%, the new selling price (SP2) can be calculated as:
\[ SP2 = CP2 + 25\% \text{ of } CP2 = 0.93x + 0.25 \times 0.93x = 0.93x + 0.2325x = 1.1625x \]

### Step 5: Set Up the Equation
According to the problem, the new selling price is Rs 250 more than the original selling price:
\[ SP2 = SP + 250 \]
Substituting the values we have:
\[ 1.1625x = 1.15x + 250 \]

### Step 6: Simplify the Equation
Now, let's simplify the equation:
\[ 1.1625x - 1.15x = 250 \]
\[ 0.0125x = 250 \]

### Step 7: Solve for x
Now, solve for \( x \):
\[ x = \frac{250}{0.0125} \]
\[ x = 20000 \]

### Conclusion
The cost price of the pen is \( \text{Rs } 20000 \).

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