Nisha bought a number of orang es at 2 for a rupee and an equal number at 3 for a rupee. To make a profit of 20% she should sell a dozen for

Options

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

Answer

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

### Step 1: Determine the number of oranges bought
Nisha bought oranges in two batches:
- The first batch: 2 oranges for 1 rupee.
- The second batch: 3 oranges for 1 rupee.

Let’s assume she bought 'x' oranges in each batch. Therefore, the total number of oranges she bought is:
\[ \text{Total oranges} = x + x = 2x \]

### Step 2: Calculate the cost price (CP) of the oranges
1. **Cost of the first batch**:
- Since she bought 'x' oranges at 2 for 1 rupee, the number of pairs of oranges is \( \frac{x}{2} \).
- Therefore, the cost for the first batch is:
\[ \text{Cost of first batch} = \frac{x}{2} \times 1 = \frac{x}{2} \text{ rupees} \]

2. **Cost of the second batch**:
- She bought 'x' oranges at 3 for 1 rupee, so the number of groups of oranges is \( \frac{x}{3} \).
- Therefore, the cost for the second batch is:
\[ \text{Cost of second batch} = \frac{x}{3} \times 1 = \frac{x}{3} \text{ rupees} \]

3. **Total cost price (CP)**:
\[ \text{Total CP} = \frac{x}{2} + \frac{x}{3} \]
To add these fractions, we need a common denominator, which is 6:
\[ \text{Total CP} = \frac{3x}{6} + \frac{2x}{6} = \frac{5x}{6} \text{ rupees} \]

### Step 3: Calculate the selling price (SP) for a profit of 20%
To achieve a profit of 20%, we need to calculate the selling price based on the cost price:
\[ \text{Selling Price (SP)} = \text{CP} + 20\% \text{ of CP} \]
\[ \text{SP} = \text{CP} \times \left(1 + \frac{20}{100}\right) = \text{CP} \times 1.2 \]
Substituting the value of CP:
\[ \text{SP} = \frac{5x}{6} \times 1.2 = \frac{5x \times 1.2}{6} = \frac{6x}{6} = x \text{ rupees} \]

### Step 4: Selling price for a dozen oranges
Since Nisha bought '2x' oranges, we need to find the selling price for a dozen (12) oranges. If 'x' is the number of oranges in one batch, then:
- If she bought 'x' oranges in each batch, we can assume she bought 12 oranges in total. Thus, \( x = 12/2 = 6 \).

Now, substituting \( x = 6 \) into the selling price:
\[ \text{SP for 12 oranges} = x = 6 \text{ rupees} \]

### Final Answer:
Nisha should sell a dozen oranges for **6 rupees**.

---