To solve the problem step by step, we will calculate the share of B in the profit based on the investments and the time each partner invested in the business.
### Step 1: Calculate the investment of B
A's investment = Rs 16,000
B's investment = (3/5) * A's investment
B's investment = (3/5) * 16,000 = Rs 9,600
**Hint:** To find B's investment, multiply A's investment by 3/5.
### Step 2: Identify the investment of C
C's investment = Rs 8,000
**Hint:** C's investment is given directly in the problem.
### Step 3: Determine the time each partner invested
- A invested for 10 months (from the start).
- B invested for 8 months (joined after 2 months).
- C invested for 6 months (joined after 4 months).
**Hint:** Calculate the time each partner invested based on when they joined the business.
### Step 4: Calculate the effective capital contribution for each partner
- A's contribution = Investment * Time = 16,000 * 10 = Rs 160,000
- B's contribution = Investment * Time = 9,600 * 8 = Rs 76,800
- C's contribution = Investment * Time = 8,000 * 6 = Rs 48,000
**Hint:** Multiply each partner's investment by the number of months they invested.
### Step 5: Find the total capital contribution
Total capital contribution = A's contribution + B's contribution + C's contribution
Total = 160,000 + 76,800 + 48,000 = Rs 284,800
**Hint:** Add the contributions of all partners to find the total.
### Step 6: Calculate the profit-sharing ratio
The profit-sharing ratio is based on their effective contributions:
- A's ratio = 160,000 / 284,800
- B's ratio = 76,800 / 284,800
- C's ratio = 48,000 / 284,800
**Hint:** Divide each partner's contribution by the total contribution to find their ratio.
### Step 7: Simplify the ratios
To simplify:
- A's ratio = 160,000 / 284,800 = 50 / 89
- B's ratio = 76,800 / 284,800 = 24 / 89
- C's ratio = 48,000 / 284,800 = 15 / 89
**Hint:** Simplifying the fractions helps in understanding the share of profit.
### Step 8: Calculate each partner's share of the profit
Total profit = Rs 6,230
B's share of profit = (B's ratio) * Total profit
B's share = (24/89) * 6,230
**Hint:** Multiply B's ratio by the total profit to find B's share.
### Step 9: Calculate B's share of the profit
B's share = (24/89) * 6,230 = Rs 1,680
**Hint:** Perform the multiplication carefully to find the exact amount.
### Final Answer
B's share in the profit is Rs 1,680.