By selling 8 bananas, a fruit seller gains the selling price of 1 banana. Calculate his gain per cent.

Answer

To solve the problem step by step, we will first identify the key information provided and then calculate the gain percent.

### Step 1: Understand the given information
- The fruit seller sells 8 bananas.
- The gain from selling these 8 bananas is equal to the selling price of 1 banana.

### Step 2: Define variables
Let:
- SP = Selling Price of 1 banana
- CP = Cost Price of 1 banana
- Profit = Selling Price of 1 banana (since the gain is equal to the selling price of 1 banana)

### Step 3: Calculate the total selling price (SP) for 8 bananas
The total selling price for 8 bananas is:
\[ \text{Total SP} = 8 \times SP \]

### Step 4: Calculate the profit
According to the problem, the profit from selling 8 bananas is equal to the selling price of 1 banana:
\[ \text{Profit} = SP \]

### Step 5: Use the profit formula
The profit can also be calculated using the formula:
\[ \text{Profit} = \text{Total SP} - \text{Total CP} \]
Where:
- Total CP = Cost Price of 8 bananas = \( 8 \times CP \)

Thus, we can set up the equation:
\[ SP = (8 \times SP) - (8 \times CP) \]

### Step 6: Rearranging the equation
Rearranging gives:
\[ 8 \times CP = 8 \times SP - SP \]
\[ 8 \times CP = 7 \times SP \]

### Step 7: Calculate the cost price (CP)
From the equation above, we can find the cost price per banana:
\[ CP = \frac{7 \times SP}{8} \]

### Step 8: Calculate the profit percentage
The profit percentage is calculated using the formula:
\[ \text{Gain Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Gain Percentage} = \left( \frac{SP}{CP} \right) \times 100 \]

Substituting \( CP \):
\[ \text{Gain Percentage} = \left( \frac{SP}{\frac{7 \times SP}{8}} \right) \times 100 \]
This simplifies to:
\[ \text{Gain Percentage} = \left( \frac{8}{7} \right) \times 100 \]
\[ \text{Gain Percentage} = \frac{800}{7} \]
Calculating this gives approximately:
\[ \text{Gain Percentage} \approx 114.29\% \]

### Final Answer
The gain percentage of the fruit seller is approximately **114.29%**.

---