A and B started a business by investing Rs. 36000 and Rs. 45000 respectively. After 4 months B withdraws 4/9 of his investment. Its 5 months After she again invested 11/9 of its original investment. If the total earned profit at the end of the year, is Rs. 117240, then who will get more money as a share of profit and how much?

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the effective capital contribution of A and B.

**A's Investment:**
- A invests Rs. 36,000 for 12 months.

**B's Investment:**
- B invests Rs. 45,000 for the first 4 months.
- After 4 months, B withdraws \( \frac{4}{9} \) of his investment.

Calculating B's remaining investment after withdrawal:
- \( \text{Withdrawal} = \frac{4}{9} \times 45,000 = 20,000 \)
- Remaining investment = \( 45,000 - 20,000 = 25,000 \)

B's remaining investment of Rs. 25,000 is held for the next 5 months (from month 5 to month 9).

After 9 months, B reinvests \( \frac{11}{9} \) of his original investment:
- \( \text{Reinvestment} = \frac{11}{9} \times 45,000 = 55,000 \)

B's total investment after reinvestment is Rs. 55,000, which he holds for the last 3 months (from month 9 to month 12).

### Step 2: Calculate the total capital contribution in terms of months.

**A's Contribution:**
- \( 36,000 \times 12 = 432,000 \)

**B's Contribution:**
- For the first 4 months: \( 45,000 \times 4 = 180,000 \)
- For the next 5 months: \( 25,000 \times 5 = 125,000 \)
- For the last 3 months: \( 55,000 \times 3 = 165,000 \)

Total contribution of B:
- \( 180,000 + 125,000 + 165,000 = 470,000 \)

### Step 3: Calculate the ratio of their investments.

- A's total investment = 432,000
- B's total investment = 470,000

The ratio of their investments is:
- \( \text{Ratio} = A : B = 432,000 : 470,000 \)

To simplify:
- Divide both by 1,000:
- \( 432 : 470 \)

### Step 4: Calculate the total profit and distribute it according to the ratio.

Given total profit = Rs. 117,240.

Total parts = \( 432 + 470 = 902 \)

Now, calculate the value of each part:
- Value of each part = \( \frac{117240}{902} \approx 130 \)

### Step 5: Calculate A's and B's share of the profit.

**A's Share:**
- \( A's \, share = 432 \times 130 = 56160 \)

**B's Share:**
- \( B's \, share = 470 \times 130 = 61140 \)

### Step 6: Determine who gets more money and by how much.

- B gets more money than A.
- The difference in their profits = \( 61140 - 56160 = 4980 \)

### Final Conclusion:
- B will get more money as a share of the profit, and the difference is Rs. 4,980.