A man purchases a certain number of Banana at 25 a rupee and the same number at 20 a rupee. He mixes them together and sells them at 45 for two rupees. How much percent does he gain or loss in the transaction

Answer

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

### Step 1: Determine the Cost Price of Bananas
The man purchases bananas in two batches:
1. **First Batch**: He buys bananas at the rate of Rs 25 per rupee. This means he gets 25 bananas for Rs 1. If he buys 100 bananas, the cost will be:
\[ \text{Cost Price of 100 Bananas} = \frac{100}{25} = 4 \text{ rupees} \]

2. **Second Batch**: He buys bananas at the rate of Rs 20 per rupee. This means he gets 20 bananas for Rs 1. If he buys 100 bananas, the cost will be:
\[ \text{Cost Price of 100 Bananas} = \frac{100}{20} = 5 \text{ rupees} \]

### Step 2: Calculate the Total Cost Price
Now, we combine the cost prices of both batches:
\[ \text{Total Cost Price} = 4 + 5 = 9 \text{ rupees} \]
This is the cost price for 200 bananas (100 from each batch).

### Step 3: Determine the Selling Price
The man sells the bananas at the rate of Rs 45 for 2 rupees. This means he sells:
\[ \text{Selling Price for 2 Rupees} = 45 \text{ bananas} \]
Thus, the selling price for 1 banana is:
\[ \text{Selling Price per Banana} = \frac{2}{45} \text{ rupees} \]
For 200 bananas, the selling price will be:
\[ \text{Selling Price for 200 Bananas} = 2 \times \frac{200}{45} = \frac{400}{45} = 8.888 \text{ rupees} \]

### Step 4: Calculate Gain or Loss
Now, we can calculate the gain or loss:
\[ \text{Gain or Loss} = \text{Selling Price} - \text{Cost Price} = 8.888 - 9 = -0.112 \text{ rupees} \]
Since the result is negative, it indicates a loss.

### Step 5: Calculate the Percentage of Loss
To find the percentage of loss, we use the formula:
\[ \text{Percentage Loss} = \left(\frac{\text{Loss}}{\text{Cost Price}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Loss} = \left(\frac{0.112}{9}\right) \times 100 \approx 1.244\% \]

### Final Answer
The man incurs a loss of approximately **1.24%** in the transaction.

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