Hiten marks his pen at Rs 9800 and after allowing discount of 20%, he still earns 12% profit. What is the cost price (in Rs) of the pen?

Options

A. 7600
B. 7200
C. 6500
D. 7000

Answer

To find the cost price of the pen, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price of the pen is Rs 9800, and Hiten allows a discount of 20%.

To calculate the discount:
\[ \text{Discount} = \text{Marked Price} \times \frac{\text{Discount Percentage}}{100} = 9800 \times \frac{20}{100} = 1960 \]

Now, subtract the discount from the marked price to find the selling price:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 9800 - 1960 = 7840 \]

### Step 2: Relate Selling Price to Cost Price
Hiten earns a profit of 12% on the cost price (CP). Therefore, the selling price can also be expressed in terms of the cost price:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} = \text{Cost Price} + 0.12 \times \text{Cost Price} = 1.12 \times \text{Cost Price} \]

### Step 3: Set Up the Equation
We can set up the equation using the selling price we calculated:
\[ 7840 = 1.12 \times \text{Cost Price} \]

### Step 4: Solve for Cost Price
To find the cost price, rearrange the equation:
\[ \text{Cost Price} = \frac{7840}{1.12} \]

Calculating this gives:
\[ \text{Cost Price} = \frac{7840}{1.12} = 7000 \]

### Final Answer
The cost price of the pen is Rs 7000.

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