A and B started a business by investing X 35000 and X 20000, respectively. After 5 months B left the business and C joined the business with a sum of X 15000. The profit earned at the end of year is X 84125. What is the share of B in profit ?

Options

A. X 14133
B. X 15000
C. X 13460
D. Couldn't be determined

Answer

To find B's share in the profit, we will follow these steps:

### Step 1: Determine the investment and time for each partner
- A's investment: ₹35,000 for 12 months
- B's investment: ₹20,000 for 5 months
- C's investment: ₹15,000 for 7 months (since C joined after B left, which was after 5 months)

### Step 2: Calculate the effective capital contribution for each partner
- A's contribution = Investment × Time = ₹35,000 × 12 = ₹420,000
- B's contribution = Investment × Time = ₹20,000 × 5 = ₹100,000
- C's contribution = Investment × Time = ₹15,000 × 7 = ₹105,000

### Step 3: Determine the total effective capital
Total effective capital = A's contribution + B's contribution + C's contribution
= ₹420,000 + ₹100,000 + ₹105,000 = ₹625,000

### Step 4: Calculate the ratio of their contributions
The ratio of A : B : C = ₹420,000 : ₹100,000 : ₹105,000

### Step 5: Simplify the ratio
To simplify the ratio, we can divide each term by ₹5,000:
- A's ratio = 420,000 ÷ 5,000 = 84
- B's ratio = 100,000 ÷ 5,000 = 20
- C's ratio = 105,000 ÷ 5,000 = 21

Thus, the simplified ratio is A : B : C = 84 : 20 : 21.

### Step 6: Calculate the total parts in the ratio
Total parts = 84 + 20 + 21 = 125 parts.

### Step 7: Determine B's share of the profit
Total profit = ₹84,125
B's share = (B's ratio / Total parts) × Total profit
= (20 / 125) × 84,125

### Step 8: Calculate B's share
B's share = (20 / 125) × 84,125 = ₹13,460.

### Final Answer
B's share in the profit is ₹13,460.

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