A trader marks his goods at 30% above cost price and allows a discount of 10%. What is his gain per cent?

Answer

To solve the problem step by step, let's break it down clearly.

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

### Step 2: Calculate the Marked Price (MP)
The trader marks his goods at 30% above the cost price. Therefore, the marked price (MP) can be calculated as:
\[ \text{MP} = \text{CP} + 30\% \text{ of CP} = x + 0.3x = 1.3x \]

### Step 3: Calculate the Discount
The trader allows a discount of 10% on the marked price. The discount amount can be calculated as:
\[ \text{Discount} = 10\% \text{ of MP} = 0.1 \times 1.3x = 0.13x \]

### Step 4: Calculate the Selling Price (SP)
The selling price (SP) after applying the discount can be calculated as:
\[ \text{SP} = \text{MP} - \text{Discount} = 1.3x - 0.13x = 1.17x \]

### Step 5: Calculate the Gain
To find the gain, we subtract the cost price from the selling price:
\[ \text{Gain} = \text{SP} - \text{CP} = 1.17x - x = 0.17x \]

### Step 6: Calculate the Gain Percentage
The gain percentage can be calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 = \left( \frac{0.17x}{x} \right) \times 100 = 17\% \]

### Final Answer
The gain percentage is **17%**.

---