A tradesman marks his goods `30%` more than the cost price. If he allows a discount of `(6)1/4%` then his gain per cent is -

Options

A. `(23)3/4%`
B. `22%`
C. `(21)7/8%`
D. None of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the Cost Price (CP)
Let's assume the cost price (CP) of the goods is \(100\).

### Step 2: Calculate the Marked Price (MP)
The tradesman marks his goods at \(30\%\) more than the cost price. Therefore, we calculate the marked price (MP) as follows:
\[ \text{MP} = \text{CP} + 30\% \text{ of CP} = 100 + 30\% \text{ of } 100 = 100 + 30 = 130 \]

### Step 3: Calculate the Discount
The discount allowed is \(6 \frac{1}{4}\%\). We can convert this mixed fraction into an improper fraction:
\[ 6 \frac{1}{4}\% = \frac{25}{4}\% \]
Now, we calculate the discount amount on the marked price:
\[ \text{Discount} = \text{MP} \times \frac{25}{4} \% = 130 \times \frac{25}{4 \times 100} = 130 \times \frac{25}{400} \]
Calculating this gives:
\[ \text{Discount} = 130 \times \frac{25}{400} = \frac{130 \times 25}{400} = \frac{3250}{400} = 8.125 \]

### Step 4: Calculate the Selling Price (SP)
The selling price (SP) is calculated by subtracting the discount from the marked price:
\[ \text{SP} = \text{MP} - \text{Discount} = 130 - 8.125 = 121.875 \]

### Step 5: Calculate the Profit
Now, we calculate the profit made by the tradesman:
\[ \text{Profit} = \text{SP} - \text{CP} = 121.875 - 100 = 21.875 \]

### Step 6: Calculate the Gain Percentage
Finally, we calculate the gain percentage using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 = \left( \frac{21.875}{100} \right) \times 100 = 21.875\% \]

### Conclusion
The gain percentage is \(21.875\%\), which can also be expressed as \(21 \frac{7}{8}\%\).