A, B and C started a business by investing 8,000, 12,800 and 16,000 respectively. After 6 months from the start of the business B and C withdrew half of their respective investments. If the difference between B's and C's share of annual profit is 900 what is total annual profit earned by all of them together?

Options

A. ₹12,901
B. ₹14,801
C. ₹11,100
D. ₹10,701

Answer

To solve the problem step by step, we will calculate the total investment of A, B, and C, determine their respective shares of the profit, and then find the total annual profit based on the given difference between B's and C's shares.

### Step 1: Calculate the initial investments and the duration of investments

- A's investment = 8,000 for 12 months
- B's investment = 12,800 for 12 months
- C's investment = 16,000 for 12 months

### Step 2: Calculate the investment after 6 months

After 6 months:
- B withdraws half of his investment:
- New investment = 12,800 / 2 = 6,400 for the next 6 months
- C withdraws half of his investment:
- New investment = 16,000 / 2 = 8,000 for the next 6 months
- A's investment remains the same at 8,000 for the entire year.

### Step 3: Calculate the effective investment for each partner

**For the first 6 months:**
- A's contribution = 8,000 * 6 = 48,000
- B's contribution = 12,800 * 6 = 76,800
- C's contribution = 16,000 * 6 = 96,000

**For the next 6 months:**
- A's contribution = 8,000 * 6 = 48,000
- B's contribution = 6,400 * 6 = 38,400
- C's contribution = 8,000 * 6 = 48,000

### Step 4: Calculate total contributions for the year

- Total contribution of A = 48,000 + 48,000 = 96,000
- Total contribution of B = 76,800 + 38,400 = 115,200
- Total contribution of C = 96,000 + 48,000 = 144,000

### Step 5: Calculate the ratio of their investments

Total investments:
- A : 96,000
- B : 115,200
- C : 144,000

To simplify the ratio, we can divide each by 1,000:
- A : 96
- B : 115.2
- C : 144

To eliminate decimals, we can multiply by 10:
- A : 960
- B : 1152
- C : 1440

Now, dividing by 48 (the GCD):
- A : 20
- B : 24
- C : 30

Thus, the ratio of their investments is:
**A : B : C = 20 : 24 : 30**

### Step 6: Calculate total parts in the ratio

Total parts = 20 + 24 + 30 = 74

### Step 7: Use the difference in profits to find the total profit

Given that the difference between B's and C's share of the profit is 900:
- B's share = 24 parts
- C's share = 30 parts

The difference in their shares:
30 parts - 24 parts = 6 parts = 900

### Step 8: Find the value of one part

Value of one part = 900 / 6 = 150

### Step 9: Calculate the total profit

Total profit = Total parts * Value of one part
= 74 * 150 = 11,100

### Conclusion

The total annual profit earned by A, B, and C together is **11,100**.

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