A fruit-seller buys oranges at 4 for Rs 3 and sells them at 3 for Rs 4. Find his profit percent.

Answer

To find the profit percent of the fruit-seller who buys and sells oranges, we can follow these steps:

### Step 1: Determine the Cost Price (CP) of one orange.
The fruit seller buys 4 oranges for Rs 3.

\[ \text{Cost Price of 4 oranges} = \text{Rs } 3 \]

To find the cost price of one orange, we divide the total cost by the number of oranges:

\[ \text{CP of 1 orange} = \frac{3}{4} \text{ Rs} \]

### Step 2: Determine the Selling Price (SP) of one orange.
The fruit seller sells 3 oranges for Rs 4.

\[ \text{Selling Price of 3 oranges} = \text{Rs } 4 \]

To find the selling price of one orange, we divide the total selling price by the number of oranges:

\[ \text{SP of 1 orange} = \frac{4}{3} \text{ Rs} \]

### Step 3: Calculate the Profit.
Profit is calculated as the difference between the selling price and the cost price.

\[ \text{Profit} = \text{SP} - \text{CP} = \frac{4}{3} - \frac{3}{4} \]

To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12.

\[ \frac{4}{3} = \frac{16}{12} \quad \text{and} \quad \frac{3}{4} = \frac{9}{12} \]

Now, substituting back into the profit equation:

\[ \text{Profit} = \frac{16}{12} - \frac{9}{12} = \frac{7}{12} \text{ Rs} \]

### Step 4: Calculate the Profit Percent.
Profit percent is calculated using the formula:

\[ \text{Profit Percent} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]

Substituting the values we have:

\[ \text{Profit Percent} = \left( \frac{\frac{7}{12}}{\frac{3}{4}} \right) \times 100 \]

To divide these fractions, we multiply by the reciprocal:

\[ \text{Profit Percent} = \left( \frac{7}{12} \times \frac{4}{3} \right) \times 100 \]

Calculating this gives:

\[ \text{Profit Percent} = \left( \frac{28}{36} \right) \times 100 = \frac{700}{9} \approx 77.78\% \]

Thus, the profit percent of the fruit seller is:

\[ \text{Profit Percent} \approx 77 \frac{7}{9} \% \]

### Summary of Steps:
1. Calculate the cost price of one orange.
2. Calculate the selling price of one orange.
3. Find the profit by subtracting the cost price from the selling price.
4. Calculate the profit percent using the profit and cost price.