By selling oranges at the rate of Rs `6 3/4` — per orange, a man gets Rs 378. How many oranges does he sell?

Answer

To find out how many oranges the man sells, we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The cost of one orange is given as Rs \(6 \frac{3}{4}\). We need to convert this mixed number into an improper fraction.

\[ 6 \frac{3}{4} = \frac{(6 \times 4) + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4} \]

### Step 2: Set up the equation
We know that the total amount received from selling the oranges is Rs 378. Let \(x\) be the number of oranges sold. The total cost can be expressed as:

\[ \text{Total Cost} = \text{Number of oranges} \times \text{Cost per orange} \]

This gives us the equation:

\[ 378 = x \times \frac{27}{4} \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:

\[ x = \frac{378}{\frac{27}{4}} = 378 \times \frac{4}{27} \]

### Step 4: Simplify the calculation
Now, we can simplify the multiplication:

\[ x = \frac{378 \times 4}{27} \]

### Step 5: Calculate \(378 \div 27\)
First, we divide 378 by 27:

\[ 378 \div 27 = 14 \]

### Step 6: Multiply by 4
Now, we multiply the result by 4:

\[ x = 14 \times 4 = 56 \]

### Conclusion
The man sells **56 oranges**.

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