A shopkeeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pay Rs 3402 as the price including the sales tax. Then the marked price is

Options

A. Rs 3400
B. Rs 3450
C. Rs 3200
D. Rs 3500

Answer

To find the marked price of the item, we can follow these steps:

### Step 1: Define the Variables
Let the marked price be \( X \).

### Step 2: Calculate the Selling Price after Discount
The shopkeeper allows a discount of 10% on the marked price. Therefore, the selling price after the discount is:
\[ \text{Selling Price} = X - 0.10X = 0.90X \]

### Step 3: Calculate the Price after Sales Tax
The shopkeeper charges a sales tax of 8% on the discounted price. Therefore, the price after adding the sales tax is:
\[ \text{Price after Sales Tax} = \text{Selling Price} + 0.08 \times \text{Selling Price} = 1.08 \times \text{Selling Price} \]
Substituting the selling price we found in Step 2:
\[ \text{Price after Sales Tax} = 1.08 \times 0.90X = 0.972X \]

### Step 4: Set Up the Equation
According to the problem, the customer pays Rs 3402, which is equal to the price after sales tax:
\[ 0.972X = 3402 \]

### Step 5: Solve for \( X \)
To find \( X \), we divide both sides of the equation by 0.972:
\[ X = \frac{3402}{0.972} \]
Calculating this gives:
\[ X \approx 3500 \]

### Conclusion
The marked price of the item is Rs 3500.

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