Sirai and Hiten started a business with investment of Rs. 15000 and Rs. 18000, respectively. After one year, Siraj increased his investment by 10% while Hiten decreased his investment by 10%. At the end of two years, total profit made by the business is Rs. 13140. Find the share of profit of Hiten.

To solve this problem, we need to determine the profit share of Hiten based on their investments over the two-year period.

### Step 1: Initial Investments
- Siraj's initial investment: Rs. 15,000
- Hiten's initial investment: Rs. 18,000

### Step 2: Investments After One Year
After one year:
- Siraj increases his investment by 10%.
- Hiten decreases his investment by 10%.

New investments:
- Siraj's new investment = \( 15,000 + 0.10 \times 15,000 = 15,000 + 1,500 = Rs. 16,500 \)
- Hiten's new investment = \( 18,000 - 0.10 \times 18,000 = 18,000 - 1,800 = Rs. 16,200 \)

### Step 3: Calculate the Average Investment
To determine their respective shares of the profit, we first calculate the average investment over the two years:

For Siraj:
- First year investment: Rs. 15,000
- Second year investment: Rs. 16,500

Average investment of Siraj:
\[
\text{Average investment of Siraj} = \frac{15,000 + 16,500}{2} = \frac{31,500}{2} = Rs. 15,750
\]

For Hiten:
- First year investment: Rs. 18,000
- Second year investment: Rs. 16,200

Average investment of Hiten:
\[
\text{Average investment of Hiten} = \frac{18,000 + 16,200}{2} = \frac{34,200}{2} = Rs. 17,100
\]

### Step 4: Calculate the Ratio of Investment
The ratio of their average investments over the two years is:
\[
\text{Ratio of Siraj to Hiten} = \frac{15,750}{17,100} = \frac{15,750}{17,100} \approx \frac{525}{570} = \frac{35}{38}
\]

### Step 5: Total Profit and Hiten's Share
Given that the total profit is Rs. 13,140, the share of Hiten is calculated as:
\[
\text{Hiten's share} = \frac{38}{35 + 38} \times 13,140 = \frac{38}{73} \times 13,140
\]

\[
\text{Hiten's share} = \frac{498,120}{73} \approx Rs. 6,820
\]

Thus, Hiten's share of the profit is **Rs. 6,820**.

Would you like more details on any part of the solution, or have any questions?

Here are 5 related questions to consider:
1. How would the profit share change if Hiten increased his investment instead of decreasing it?
2. What would be Siraj's share of the profit?
3. How does changing the percentage of investment affect the profit distribution?
4. What if the profit was distributed based on their initial investments alone?
5. How would the total profit change if both had kept their initial investments unchanged?

**Tip:** When calculating profit shares, it's crucial to consider both the amount invested and the time period over which it was invested.

Learn how to calculate profit share based on initial investments and changes over time. Solve a business problem involving investments, percentage changes, and profit distribution. Suitable for students in Grades 7-9.

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