Jiya, Varun, and Sofia invested Rs18, 000, Rs 6,000 and Rs14, 000 respectively to open a business. Jiya left after four months. If after nine months, there was a gain of Rs 4480,
then what will be the share of Sofia?
1,850
2,240
2,520
None of these

To determine Sofia's share of the profit, we need to calculate the ratio of each person's investment and time in the business. Here's how we proceed step by step:

### Step 1: Calculate the time-weighted investments
The total profit-sharing is based on the product of the amount invested and the time each person stayed in the business.

- **Jiya**: Invested Rs 18,000 but left after 4 months, so her time-weighted investment is:
  \[
  \text{Jiya's investment} = 18,000 \times 4 = 72,000
  \]

- **Varun**: Invested Rs 6,000 for the entire 9 months, so his time-weighted investment is:
  \[
  \text{Varun's investment} = 6,000 \times 9 = 54,000
  \]

- **Sofia**: Invested Rs 14,000 for the entire 9 months, so her time-weighted investment is:
  \[
  \text{Sofia's investment} = 14,000 \times 9 = 126,000
  \]

### Step 2: Calculate the total of all time-weighted investments
\[
\text{Total investment} = 72,000 + 54,000 + 126,000 = 252,000
\]

### Step 3: Calculate the share of Sofia in the profit
Sofia's share of the total profit (Rs 4480) is proportional to her time-weighted investment:
\[
\text{Sofia's share} = \frac{126,000}{252,000} \times 4480 = \frac{1}{2} \times 4480 = 2240
\]

Thus, **Sofia's share** of the profit is **Rs 2240**.

### Final Answer:
The correct option is:
**2240**

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Would you like further clarification on any part of this solution? Here are five related questions for practice:

1. What would Varun's share be in this profit?
2. If Jiya had stayed for the entire 9 months, what would her share have been?
3. How would Sofia's share change if her investment was Rs 10,000 instead of Rs 14,000?
4. What would be Sofia's share if the total profit was Rs 5000 instead of Rs 4480?
5. How would the share calculation change if there were no time differences in the investments?

**Tip:** Always calculate the time-weighted investment when there are different time periods involved in profit sharing.

Jiya, Varun, and Sofia invested Rs 18,000, Rs 6,000 and Rs 14,000 respectively to open a business. Jiya left after four months. If after nine months, there was a gain of Rs 4480, then what will be the share of Sofia? 1,850 2,240 2,520 None of these

Solve a profit-sharing problem where Jiya, Varun, and Sofia invest different amounts and stay in a business for varying time periods. Learn how to calculate Sofia's share of the Rs 4480 profit using time-weighted investment and proportional distribution. Suitable for Grades 9-10.

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