A fruit-seller bought bananas at the rate of 3 for Rs. 8 and sold them at the rate of 2 for Rs. 7. Find his gain or loss per cent.

Answer

To solve the problem step by step, we will first find the cost price and selling price of one banana, then calculate the gain, and finally determine the gain percentage.

### Step 1: Find the Cost Price (CP) of One Banana
The fruit seller bought 3 bananas for Rs. 8.
To find the cost price of one banana, we divide the total cost by the number of bananas.

\[ \text{Cost Price of 1 banana} = \frac{8}{3} \text{ Rs.} \]

### Step 2: Find the Selling Price (SP) of One Banana
The fruit seller sold 2 bananas for Rs. 7.
To find the selling price of one banana, we divide the total selling price by the number of bananas.

\[ \text{Selling Price of 1 banana} = \frac{7}{2} \text{ Rs.} \]

### Step 3: Compare Cost Price and Selling Price
Now we need to compare the cost price and selling price to determine if there is a gain or loss.

- Cost Price (CP) = \( \frac{8}{3} \)
- Selling Price (SP) = \( \frac{7}{2} \)

To compare, we can convert both to a common denominator or calculate their approximate values:
- \( \frac{8}{3} \approx 2.67 \)
- \( \frac{7}{2} = 3.5 \)

Since \( \frac{7}{2} > \frac{8}{3} \), the selling price is greater than the cost price, indicating a gain.

### Step 4: Calculate the Gain
Gain is calculated using the formula:

\[ \text{Gain} = \text{Selling Price} - \text{Cost Price} \]

Substituting the values:

\[ \text{Gain} = \frac{7}{2} - \frac{8}{3} \]

To perform this subtraction, we need a common denominator, which is 6:

\[ \text{Gain} = \left(\frac{7 \times 3}{2 \times 3}\right) - \left(\frac{8 \times 2}{3 \times 2}\right) = \frac{21}{6} - \frac{16}{6} = \frac{5}{6} \text{ Rs.} \]

### Step 5: Calculate the Gain Percentage
The gain percentage is calculated using the formula:

\[ \text{Gain Percentage} = \left(\frac{\text{Gain}}{\text{Cost Price}}\right) \times 100 \]

Substituting the values:

\[ \text{Gain Percentage} = \left(\frac{\frac{5}{6}}{\frac{8}{3}}\right) \times 100 \]

To simplify:

\[ \text{Gain Percentage} = \left(\frac{5}{6} \times \frac{3}{8}\right) \times 100 = \left(\frac{15}{48}\right) \times 100 = \frac{1500}{48} = 31.25\% \]

### Final Answer
The fruit seller has a gain of **31.25%**.

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