Nisha bougth a number of organes at 2 for a rupess and an equal number at 3 for a rupee. To make a profit of 20% she should sell a dozen for

Options

A. Rs. 6
B. Rs. 8
C. Rs. 10
D. Rs. 12

Answer

To solve the problem, let's break it down step by step.

### Step 1: Determine the number of oranges bought
Let the number of oranges Nisha bought at 2 for a rupee be \( x \). Since she bought an equal number at 3 for a rupee, she also bought \( x \) oranges at that price.

### Step 2: Calculate the total cost of the oranges
- The cost for \( x \) oranges bought at 2 for a rupee:
\[ \text{Cost at 2 for 1 rupee} = \frac{x}{2} \text{ rupees} \]

- The cost for \( x \) oranges bought at 3 for a rupee:
\[ \text{Cost at 3 for 1 rupee} = \frac{x}{3} \text{ rupees} \]

- Therefore, the total cost for all oranges is:
\[ \text{Total Cost} = \frac{x}{2} + \frac{x}{3} \]

### Step 3: Find a common denominator and simplify
To add the fractions, we need a common denominator, which is 6:
\[ \frac{x}{2} = \frac{3x}{6} \quad \text{and} \quad \frac{x}{3} = \frac{2x}{6} \]
Thus,
\[ \text{Total Cost} = \frac{3x}{6} + \frac{2x}{6} = \frac{5x}{6} \text{ rupees} \]

### Step 4: Determine the selling price for a profit of 20%
To achieve a profit of 20%, Nisha needs to sell the oranges for:
\[ \text{Selling Price} = \text{Cost} + 20\% \text{ of Cost} \]
Calculating 20% of the total cost:
\[ 20\% \text{ of } \frac{5x}{6} = \frac{1}{5} \times \frac{5x}{6} = \frac{5x}{30} = \frac{x}{6} \]
Thus, the selling price becomes:
\[ \text{Selling Price} = \frac{5x}{6} + \frac{x}{6} = \frac{6x}{6} = x \text{ rupees} \]

### Step 5: Calculate the selling price per dozen
Since Nisha has bought \( 2x \) oranges in total (as she bought \( x \) at each price), the selling price for a dozen (12 oranges) would be:
\[ \text{Selling Price for a dozen} = \frac{x}{2x} \text{ rupees} \times 12 = \frac{12}{2} = 6 \text{ rupees} \]

### Final Answer
To make a profit of 20%, Nisha should sell a dozen oranges for **6 rupees**.

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