A seller marks his goods 30% above their cost price but allows 15% discount for cash payment. His percentage of profit when sold in cash, is

Options

A. `10.5%`
B. 0.15
C. 0.09
D. `8.5%`

Answer

To solve the problem step by step, we will calculate the cost price, the marked price, the selling price after discount, and finally the percentage of profit.

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the goods be \(100\).

### Step 2: Calculate the Marked Price (MP)
The marked price is 30% above the cost price.
\[ \text{Marked Price (MP)} = \text{Cost Price} + 30\% \text{ of Cost Price} \]
\[ \text{MP} = 100 + \left( \frac{30}{100} \times 100 \right) = 100 + 30 = 130 \]

### Step 3: Calculate the Selling Price (SP) after Discount
The seller allows a 15% discount on the marked price.
\[ \text{Discount} = 15\% \text{ of Marked Price} \]
\[ \text{Discount} = \frac{15}{100} \times 130 = 19.5 \]
Now, we can find the selling price:
\[ \text{Selling Price (SP)} = \text{Marked Price} - \text{Discount} \]
\[ \text{SP} = 130 - 19.5 = 110.5 \]

### Step 4: Calculate the Profit
Profit is calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
\[ \text{Profit} = 110.5 - 100 = 10.5 \]

### Step 5: Calculate the Percentage of Profit
The percentage of profit is given by:
\[ \text{Percentage of Profit} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
\[ \text{Percentage of Profit} = \left( \frac{10.5}{100} \right) \times 100 = 10.5\% \]

Thus, the percentage of profit when sold in cash is **10.5%**.

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