A vendor buys oragnes @ Rs. 2 for 3 oranges and sells them at a rupee each. To make a profit of Rs.10, he must sell :

Options

A. 10 oranges
B. 20 oranges
C. 30 oranges
D. 40 oranges

Answer

To solve the problem step by step, we need to find out how many oranges the vendor must sell to achieve a profit of Rs. 10.

### Step 1: Determine the Cost Price (CP) of Oranges
The vendor buys oranges at Rs. 2 for 3 oranges.
- Therefore, the cost price (CP) of 1 orange = Rs. 2 / 3 = Rs. 2/3.

### Step 2: Determine the Selling Price (SP) of Oranges
The vendor sells each orange for Rs. 1.
- Therefore, the selling price (SP) of 1 orange = Rs. 1.

### Step 3: Set Up the Profit Equation
Let the number of oranges sold be \( x \).
- The total cost price (CP) for \( x \) oranges = \( \text{CP of } x \text{ oranges} = x \times \frac{2}{3} = \frac{2x}{3} \).
- The total selling price (SP) for \( x \) oranges = \( \text{SP of } x \text{ oranges} = x \times 1 = x \).

### Step 4: Calculate the Profit
Profit is given by the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we have:
\[ \text{Profit} = x - \frac{2x}{3} \]

### Step 5: Simplify the Profit Equation
To simplify \( x - \frac{2x}{3} \):
- Find a common denominator (which is 3):
\[ \text{Profit} = \frac{3x}{3} - \frac{2x}{3} = \frac{3x - 2x}{3} = \frac{x}{3} \]

### Step 6: Set the Profit Equal to Rs. 10
We want the profit to be Rs. 10:
\[ \frac{x}{3} = 10 \]

### Step 7: Solve for \( x \)
To find \( x \), multiply both sides by 3:
\[ x = 10 \times 3 = 30 \]

### Conclusion
The vendor must sell **30 oranges** to make a profit of Rs. 10.