If oranges are bought at the rate of 25 for a rupee, how many must be sold for a rupee so as to gain 25%?

To solve this problem, we can use the concept of cost price, selling price, and the desired percentage gain. Let's go through the steps systematically:

### 1. **Define the Cost Price (CP) and Selling Price (SP)**

- **Cost Price per Orange**: Since the oranges are bought at the rate of 25 for 1 rupee, the cost price (CP) of one orange is:
  \[
  \text{CP per orange} = \frac{1 \text{ rupee}}{25 \text{ oranges}} = \frac{1}{25} \text{ rupees}
  \]

- **Desired Gain**: The desired gain is 25%.

### 2. **Calculate the Required Selling Price (SP)**

To achieve a 25% gain, the selling price must be 25% more than the cost price.

- Let the selling price of one orange be \( x \) rupees.
  
  Since the gain is 25%, we can express the selling price per orange as:
  \[
  \text{SP per orange} = \text{CP per orange} + 25\% \text{ of CP per orange}
  \]
  \[
  \text{SP per orange} = \frac{1}{25} + 0.25 \times \frac{1}{25}
  \]
  \[
  \text{SP per orange} = \frac{1}{25} + \frac{0.25}{25}
  \]
  \[
  \text{SP per orange} = \frac{1 + 0.25}{25}
  \]
  \[
  \text{SP per orange} = \frac{1.25}{25}
  \]
  \[
  \text{SP per orange} = \frac{5}{100} = \frac{1}{20} \text{ rupees}
  \]

### 3. **Calculate the Number of Oranges Sold for 1 Rupee**

Now, we need to find out how many oranges must be sold for 1 rupee to achieve this selling price per orange.

- If each orange is sold for \(\frac{1}{20}\) rupees, then the number of oranges that must be sold for 1 rupee is:
  \[
  \text{Number of oranges} = \frac{1 \text{ rupee}}{\text{SP per orange}}
  \]
  \[
  \text{Number of oranges} = \frac{1 \text{ rupee}}{\frac{1}{20} \text{ rupees}}
  \]
  \[
  \text{Number of oranges} = 1 \times 20
  \]
  \[
  \text{Number of oranges} = 20
  \]

### Conclusion

To gain a 25% profit, the man must sell **20 oranges for 1 rupee**.

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Would you like further details or have any questions?

Here are some related questions you might be interested in:

1. How many oranges should be sold for a rupee to gain 50% profit instead of 25%?
2. If the purchase rate changes to 30 oranges per rupee, how does that affect the selling strategy for a 25% gain?
3. How much profit will be made if 30 oranges are sold for 1.5 rupees?
4. What is the profit percentage if 22 oranges are sold for 1 rupee?
5. How many oranges must be sold for 2 rupees to gain a 25% profit?

**Tip:** To determine the number of items to sell for a desired profit percentage, calculate the cost price and adjust the selling price accordingly.

Learn how to calculate the number of oranges that must be sold for 1 rupee to achieve a 25% profit. Understand the concepts of cost price, selling price, and percentage gain with a detailed step-by-step solution.

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