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**Question:**
In a business, there are two partners X and Y. X started the business with a capital of Rs. 15,000, and after 4 months, Y joined him with a capital of Rs. 18,000. At the end of the year, find the profit share of Y out of the total profit of Rs. 6,300.

The options are:
1. Rs. 2,800
2. Rs. 3,000
3. Rs. 3,500
4. Rs. 4,000
5. Rs. 2,400

**Solution:**

The profit share is distributed in proportion to the amount of capital and the time the capital was invested.

1. X's capital was invested for 12 months, so his capital-time is:
   \( 15,000 \times 12 = 180,000 \)

2. Y's capital was invested for 8 months (since he joined after 4 months), so his capital-time is:
   \( 18,000 \times 8 = 144,000 \)

3. The total capital-time is:
   \( 180,000 + 144,000 = 324,000 \)

4. The ratio of X's share to Y's share is:
   \( X : Y = 180,000 : 144,000 = 5 : 4 \)

5. Y's share of the total profit of Rs. 6,300 is:
   \[
   Y's \, Share = \frac{4}{9} \times 6,300 = 2,800
   \]

Thus, Y's share of the profit is **Rs. 2,800**.

The correct answer is **Option 1: Rs. 2,800**.

Let me know if you need further details, or have any questions!

### Related Questions:
1. If X's capital was Rs. 20,000, how would the profit share change?
2. How would the result change if Y joined after 6 months instead of 4 months?
3. What if the total profit was Rs. 10,000 instead of Rs. 6,300?
4. If Y invested Rs. 25,000 instead of Rs. 18,000, how would the profit share change?
5. What is the importance of time when distributing profit among partners?

### Tip:
Always calculate the capital-time (capital × time) when dividing profits in a partnership.

In a business, there are two partners X and Y. X started the business with a capital of Rs. 15,000, and after 4 months, Y joined him with a capital of Rs. 18,000. At the end of the year, find the profit share of Y out of the total profit of Rs. 6,300.

Learn how to calculate the profit share in a partnership where two partners invest Rs. 15,000 and Rs. 18,000. This problem involves key mathematical concepts such as proportional distribution, capital-time, and the formula for profit sharing. Suitable for students in Grades 9-12.

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