A shopkeeper gives an initial discount of 15% on the marked price of the sewing machine. He then gives 8% additional discount on the discounted price. If the final sale price of the machine is Rs.1,564, find the marked price.

Options

A. A)3000
B. B)2500
C. C)2000
D. D)2400

Answer

To find the marked price of the sewing machine, we will follow these steps:

### Step 1: Define the Marked Price
Let the marked price of the sewing machine be denoted as \( M \).

### Step 2: Calculate the Price After the Initial Discount
The shopkeeper gives an initial discount of 15% on the marked price. Therefore, the selling price after the initial discount can be calculated as:
\[ \text{Selling Price after 15% discount} = M - 0.15M = 0.85M \]

### Step 3: Calculate the Price After the Additional Discount
Next, the shopkeeper gives an additional discount of 8% on the already discounted price. The selling price after this additional discount can be calculated as:
\[ \text{Final Selling Price} = 0.85M - 0.08(0.85M) = 0.85M \times (1 - 0.08) = 0.85M \times 0.92 = 0.782M \]

### Step 4: Set Up the Equation
According to the problem, the final selling price of the machine is Rs. 1,564. Therefore, we can set up the equation:
\[ 0.782M = 1564 \]

### Step 5: Solve for the Marked Price
To find \( M \), we divide both sides of the equation by 0.782:
\[ M = \frac{1564}{0.782} \]

Calculating this gives:
\[ M \approx 2000 \]

### Conclusion
Thus, the marked price of the sewing machine is Rs. 2000.

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