By selling 12 oranges for 60, a man loses 25%. The number of oranges he has to sell for 100, so as to gain 25% is

Options

A. A) 10
B. B) 11
C. C) 12
D. D) 15

Answer

To solve the problem step by step, we need to first understand the relationship between selling price, cost price, profit, and loss.

### Step-by-Step Solution:

1. **Identify the Selling Price and Loss Percentage**:
- Selling Price (SP) of 12 oranges = Rs. 60
- Loss Percentage = 25%

2. **Calculate the Cost Price (CP)**:
- We know that if there is a loss, the formula to find the Cost Price is:
\[ CP = \frac{SP \times 100}{100 - \text{Loss Percentage}} \]
- Substituting the values:
\[ CP = \frac{60 \times 100}{100 - 25} = \frac{60 \times 100}{75} = \frac{6000}{75} = 80 \]
- So, the Cost Price of 12 oranges = Rs. 80.

3. **Calculate the Cost Price of One Orange**:
- To find the Cost Price of one orange:
\[ CP \text{ of one orange} = \frac{80}{12} = \frac{20}{3} \text{ Rs.} \]

4. **Determine the Selling Price for a Gain of 25%**:
- To find the Selling Price (SP) for a gain of 25%, we use the formula:
\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
- Substituting the values:
\[ SP = \frac{20}{3} \times \left(1 + \frac{25}{100}\right) = \frac{20}{3} \times \left(1 + 0.25\right) = \frac{20}{3} \times \frac{5}{4} = \frac{100}{12} = \frac{25}{3} \text{ Rs.} \]

5. **Calculate the Number of Oranges to Sell for Rs. 100**:
- We need to find how many oranges (let's call this \( A_2 \)) need to be sold for Rs. 100 at the new Selling Price of \( \frac{25}{3} \):
\[ A_2 = \frac{100}{SP \text{ of one orange}} = \frac{100}{\frac{25}{3}} = 100 \times \frac{3}{25} = 12 \]

### Final Answer:
The number of oranges he has to sell for Rs. 100 to gain 25% is **12**.