A man bought 18 oranges for a rupee and sold them at 12 oranges for a rupee. What is the profit percentage?

Options

A. `33.33%`
B. `50%`
C. `66.66%`
D. none of these

Answer

To find the profit percentage from the given problem, we will follow these steps:

### Step 1: Calculate the Cost Price (CP) of One Orange
The man bought 18 oranges for 1 rupee. Therefore, the cost price (CP) of one orange can be calculated as:
\[ \text{CP of 1 orange} = \frac{1 \text{ rupee}}{18 \text{ oranges}} = \frac{1}{18} \text{ rupee} \]

### Step 2: Calculate the Selling Price (SP) of One Orange
The man sold 12 oranges for 1 rupee. Therefore, the selling price (SP) of one orange can be calculated as:
\[ \text{SP of 1 orange} = \frac{1 \text{ rupee}}{12 \text{ oranges}} = \frac{1}{12} \text{ rupee} \]

### Step 3: Calculate the Profit
Profit can be calculated using the formula:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we found:
\[ \text{Profit} = \frac{1}{12} - \frac{1}{18} \]

To subtract these fractions, we need a common denominator. The least common multiple of 12 and 18 is 36. Therefore:
\[ \frac{1}{12} = \frac{3}{36} \quad \text{and} \quad \frac{1}{18} = \frac{2}{36} \]
Now, substituting back:
\[ \text{Profit} = \frac{3}{36} - \frac{2}{36} = \frac{1}{36} \text{ rupee} \]

### Step 4: Calculate the Profit Percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Profit Percentage} = \left( \frac{\frac{1}{36}}{\frac{1}{18}} \right) \times 100 \]
Calculating the fraction:
\[ \frac{\frac{1}{36}}{\frac{1}{18}} = \frac{1}{36} \times \frac{18}{1} = \frac{18}{36} = \frac{1}{2} \]
Now, substituting back into the profit percentage formula:
\[ \text{Profit Percentage} = \left( \frac{1}{2} \right) \times 100 = 50\% \]

### Final Answer
The profit percentage is **50%**.

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