A plate was sold for Rs. 6,300 after giving two successive discounts of `12 1/2% and 10%`. Find the marked price.

Options

A. Rs. 7,300
B. Rs. 7,700
C. Rs. 8,000
D. Rs. 7,250

Answer

To find the marked price of the plate after applying two successive discounts of 12.5% and 10%, we can follow these steps:

### Step 1: Understand the Discounts
The first discount is 12.5%, which can be expressed as a fraction:
\[ 12.5\% = \frac{12.5}{100} = \frac{1}{8} \]
The second discount is 10%, which can be expressed as:
\[ 10\% = \frac{10}{100} = \frac{1}{10} \]

### Step 2: Set Up the Problem
Let the marked price (MP) of the plate be represented as \( x \).

### Step 3: Calculate the Selling Price After the First Discount
After applying the first discount of 12.5%, the selling price (SP1) can be calculated as:
\[ SP1 = x - \left(\frac{1}{8} \times x\right) = x \left(1 - \frac{1}{8}\right) = x \left(\frac{7}{8}\right) \]

### Step 4: Calculate the Selling Price After the Second Discount
Now, apply the second discount of 10% on SP1:
\[ SP2 = SP1 - \left(\frac{1}{10} \times SP1\right) = SP1 \left(1 - \frac{1}{10}\right) = SP1 \left(\frac{9}{10}\right) \]
Substituting SP1:
\[ SP2 = \left(\frac{7}{8} x\right) \left(\frac{9}{10}\right) = \frac{63}{80} x \]

### Step 5: Set the Selling Price Equal to the Given Value
We know that the final selling price (SP2) is Rs. 6,300. Therefore, we can set up the equation:
\[ \frac{63}{80} x = 6300 \]

### Step 6: Solve for the Marked Price
To find \( x \), we can rearrange the equation:
\[ x = 6300 \times \frac{80}{63} \]
Calculating this gives:
\[ x = 6300 \times \frac{80}{63} = 8000 \]

### Conclusion
The marked price of the plate is Rs. 8,000.

---