A person purchaed a saree for Rs. 7710 after availing a net discount of Rs. 1285. The percentage of discount, the saree shop offers, is

Options

A. `14(1)/(7)%`
B. `14(2)/(7)%`
C. `14(3)/(7)%`
D. `14(4)/(7)%`

Answer

To solve the problem of finding the percentage of discount offered by the saree shop, we can follow these steps:

### Step 1: Identify the given values
- The final price after discount (Selling Price, SP) = Rs. 7710
- The discount amount = Rs. 1285

### Step 2: Calculate the Market Price (MP)
To find the Market Price (MP), we need to add the discount amount to the Selling Price:
\[ \text{Market Price (MP)} = \text{Selling Price (SP)} + \text{Discount} \]
Substituting the values:
\[ \text{MP} = 7710 + 1285 = 8995 \]

### Step 3: Set up the formula for discount percentage
Let the percentage of discount be \( X\% \). The discount amount can also be expressed as:
\[ \text{Discount} = \frac{X}{100} \times \text{Market Price (MP)} \]
Substituting the known values:
\[ 1285 = \frac{X}{100} \times 8995 \]

### Step 4: Solve for \( X \)
To find \( X \), we can rearrange the equation:
\[ X = \frac{1285 \times 100}{8995} \]
Calculating this gives:
\[ X = \frac{128500}{8995} \approx 14.27 \]

### Step 5: Round to the nearest whole number
Since discount percentages are typically rounded to the nearest whole number, we can round 14.27 to 14%.

### Final Answer
The percentage of discount offered by the saree shop is approximately **14%**.

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