Marked price of a bat is Rs 350.A shopkeeper gives a discount of Rs x and makes a profit of `12(1)/(2)%`. If manufacturing cost of bat is Rs 280, then find the discount percent given by shopkeeper on bat?

Options

A. `10%`
B. `6%`
C. `4%`
D. `3%`

Answer

To find the discount percent given by the shopkeeper on the bat, we can follow these steps:

### Step 1: Understand the given information
- Marked Price (MP) of the bat = Rs 350
- Cost Price (CP) of the bat = Rs 280
- Profit Percentage = 12.5% (which is equivalent to \( \frac{25}{2}\% \))

### Step 2: Calculate the Selling Price (SP)
To find the Selling Price (SP), we can use the profit percentage formula:
\[ \text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} \]
Substituting the values:
\[ \text{Profit} = 280 \times \frac{12.5}{100} = 280 \times 0.125 = 35 \]
Now, we can find the Selling Price:
\[ \text{SP} = \text{CP} + \text{Profit} = 280 + 35 = 315 \]

### Step 3: Relate Selling Price to Marked Price and Discount
The Selling Price can also be expressed in terms of the Marked Price and the discount:
\[ \text{SP} = \text{MP} - \text{Discount} \]
Let the discount be \( x \):
\[ 315 = 350 - x \]
Rearranging gives:
\[ x = 350 - 315 = 35 \]

### Step 4: Calculate the Discount Percentage
Now, we can calculate the discount percentage using the formula:
\[ \text{Discount Percentage} = \left( \frac{\text{Discount}}{\text{Marked Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Discount Percentage} = \left( \frac{35}{350} \right) \times 100 = 10\% \]

### Conclusion
The discount percent given by the shopkeeper on the bat is **10%**.

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