A, B and C start a business each investing Rs. 20,000. After 5 months A withdraws Rs. 5000, B withdraws Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.

Answer

To solve the problem step by step, we will calculate the share of each partner (A, B, and C) based on their investments and the time for which they invested.

### Step 1: Calculate the initial investment of each partner

- A, B, and C each invest Rs. 20,000 at the start.

**Investment:**
- A = Rs. 20,000
- B = Rs. 20,000
- C = Rs. 20,000

### Step 2: Calculate the effective investment of each partner after 5 months

After 5 months:
- A withdraws Rs. 5,000, so his effective investment becomes Rs. 15,000.
- B withdraws Rs. 4,000, so his effective investment becomes Rs. 16,000.
- C invests an additional Rs. 6,000, so his effective investment becomes Rs. 26,000.

**Effective Investment after 5 months:**
- A = Rs. 15,000
- B = Rs. 16,000
- C = Rs. 26,000

### Step 3: Calculate the time period for which each partner's investment was active

- A's initial investment of Rs. 20,000 was active for 5 months.
- After 5 months, A's investment of Rs. 15,000 is active for the remaining 7 months (total 12 months).

- B's initial investment of Rs. 20,000 was active for 5 months.
- After 5 months, B's investment of Rs. 16,000 is active for the remaining 7 months (total 12 months).

- C's initial investment of Rs. 20,000 was active for 5 months.
- After 5 months, C's investment of Rs. 26,000 is active for the remaining 7 months (total 12 months).

### Step 4: Calculate the contribution of each partner in terms of "months of investment"

- A's contribution:
- For the first 5 months: \( 20,000 \times 5 = 100,000 \)
- For the next 7 months: \( 15,000 \times 7 = 105,000 \)
- Total contribution of A = \( 100,000 + 105,000 = 205,000 \)

- B's contribution:
- For the first 5 months: \( 20,000 \times 5 = 100,000 \)
- For the next 7 months: \( 16,000 \times 7 = 112,000 \)
- Total contribution of B = \( 100,000 + 112,000 = 212,000 \)

- C's contribution:
- For the first 5 months: \( 20,000 \times 5 = 100,000 \)
- For the next 7 months: \( 26,000 \times 7 = 182,000 \)
- Total contribution of C = \( 100,000 + 182,000 = 282,000 \)

### Step 5: Calculate the total contribution

Total contribution = A's contribution + B's contribution + C's contribution
Total contribution = \( 205,000 + 212,000 + 282,000 = 699,000 \)

### Step 6: Calculate the profit share for each partner

The total profit is Rs. 69,900. We will now find the share of each partner based on their contribution.

- A's share = \( \frac{205,000}{699,000} \times 69,900 \)
- B's share = \( \frac{212,000}{699,000} \times 69,900 \)
- C's share = \( \frac{282,000}{699,000} \times 69,900 \)

### Step 7: Calculate the individual shares

1. A's share:
\[ A's \, share = \frac{205,000}{699,000} \times 69,900 \approx 19,600 \]

2. B's share:
\[ B's \, share = \frac{212,000}{699,000} \times 69,900 \approx 20,200 \]

3. C's share:
\[ C's \, share = \frac{282,000}{699,000} \times 69,900 \approx 30,100 \]

### Final Shares:
- A's share = Rs. 19,600
- B's share = Rs. 20,200
- C's share = Rs. 30,100