To solve the problem, we need to calculate the profit shares of A, B, and C based on their investments and the duration of those investments. Let's break it down step by step.
### Step 1: Calculate the total investment of each person for the first 4 months.
- A's investment: Rs. 18,000 for 4 months
- B's investment: Rs. 20,000 for 4 months
- C's investment: Rs. 24,000 for 4 months
### Step 2: Calculate the investment for the next 4 months.
For the next 4 months, each person invests an additional Rs. 2,000.
- A's new investment: Rs. 18,000 + Rs. 2,000 = Rs. 20,000 for 4 months
- B's new investment: Rs. 20,000 + Rs. 2,000 = Rs. 22,000 for 4 months
- C's new investment: Rs. 24,000 + Rs. 2,000 = Rs. 26,000 for 4 months
### Step 3: Calculate the effective investment for each person.
Now, we need to calculate the effective investment for the entire 8 months.
- A's effective investment = 18,000 * 4 + 20,000 * 4
\[
= 72,000 + 80,000 = 152,000
\]
- B's effective investment = 20,000 * 4 + 22,000 * 4
\[
= 80,000 + 88,000 = 168,000
\]
- C's effective investment = 24,000 * 4 + 26,000 * 4
\[
= 96,000 + 104,000 = 200,000
\]
### Step 4: Calculate the ratio of their investments.
Now we can find the ratio of their investments:
- A : B : C = 152,000 : 168,000 : 200,000
To simplify this ratio, we can divide each term by 8,000:
- A : B : C = 19 : 21 : 25
### Step 5: Calculate the total parts of the profit.
The total parts of profit = 19 + 21 + 25 = 65 parts.
### Step 6: Calculate the value of each part.
Given that A's profit share is Rs. 7,600, we can find the value of each part:
\[
\text{Value of each part} = \frac{7,600}{19} = 400
\]
### Step 7: Calculate the profit share of B and C.
Now we can calculate the profit share of B and C:
- B's profit share = 21 parts = 21 * 400 = Rs. 8,400
- C's profit share = 25 parts = 25 * 400 = Rs. 10,000
### Step 8: Calculate the total profit share of B and C together.
\[
\text{Total profit share of B and C} = 8,400 + 10,000 = Rs. 18,400
\]
### Final Answer:
The profit share of B and C together at the end of 8 months is Rs. 18,400.
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