A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?

Answer

To find the gain percentage for the trader, we will follow these steps:

### Step 1: Determine 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 40% above the cost price. Therefore, the marked price (MP) can be calculated as:
\[ MP = CP + 40\% \text{ of } CP = x + 0.4x = 1.4x \]

### Step 3: Calculate the Selling Price (SP)
The trader allows a discount of 25% on the marked price. The selling price (SP) can be calculated as:
\[ SP = MP - 25\% \text{ of } MP = MP - 0.25 \times MP = 1.4x - 0.25 \times 1.4x \]
Calculating \( 0.25 \times 1.4x \):
\[ 0.25 \times 1.4x = 0.35x \]
Now substituting back:
\[ SP = 1.4x - 0.35x = 1.05x \]

### Step 4: Calculate the Gain
Gain can be calculated as:
\[ \text{Gain} = SP - CP = 1.05x - x = 0.05x \]

### Step 5: Calculate the Gain Percentage
Gain percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Gain Percentage} = \left( \frac{0.05x}{x} \right) \times 100 = 5\% \]

### Final Answer
The gain percentage for the trader is **5%**.

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