A and B started a business with capitals Rs. 4000 and Rs. 6000. After 5 months C joins with a capital of Rs. 8000. At the end of a year they got a profit of Rs. 1760. Find the share of B.

Business Profit Sharing Solution

A and B started a business with capitals Rs. 4000 and Rs. 6000. After 5 months C joins with a capital of Rs. 8000. At the end of a year they got a profit of Rs. 1760. Find the share of B.

Step 1: Determine the investment and time for each person.

• A's investment: Rs. 4000 for the entire year (12 months).
• B's investment: Rs. 6000 for the entire year (12 months).
• C's investment: Rs. 8000, but C joins after 5 months, so C invests for 7 months.

Step 2: Calculate the effective capital invested by each person.

The effective capital is calculated by multiplying the amount of capital by the time it was invested.

• A's effective capital: 4000 × 12 = 48,000
• B's effective capital: 6000 × 12 = 72,000
• C's effective capital: 8000 × 7 = 56,000

Step 3: Calculate the total effective capital.

Total effective capital = A's effective capital + B's effective capital + C's effective capital

48,000 + 72,000 + 56,000 = 176,000

Step 4: Calculate the profit-sharing ratio.

The ratio of the investments is:

• A: 48,000
• B: 72,000
• C: 56,000

Simplifying the ratio, we divide each term by 8,000:

48,000 ÷ 8,000 : 72,000 ÷ 8,000 : 56,000 ÷ 8,000 = 6 : 9 : 7

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

The total profit is Rs. 1760, and B’s share of the profit is in the ratio of 9 out of the total of 6 + 9 + 7 = 22 parts.

B's share of the profit:

(9 / 22) × 1760 = 720

Final Answer:

The share of B is Rs. 720.