A started a business with a capital of Rs. 7000 in the beginning of the year. After 4 months, he admitted B with a capital of Rs. 6000; after 6 months they admitted C with a capital of Rs. 8000. If…

Solution: Profit Sharing Ratio

This problem involves calculating the individual profits of partners A, B, and C based on their investments and the time period for which the capital was invested. The profit is shared in the ratio of their capital × time.

Step 1: Calculate the Investment Period for Each Partner

• A invested Rs. 7000 for the entire year (12 months).
• B joined after 4 months, so his investment period is 12 − 4 = 8 months.
• C joined after 6 months, so his investment period is 12 − 6 = 6 months.

Step 2: Compute the Weighted Capital (Capital × Time)

• A’s share = 7000 × 12 = 84,000
• B’s share = 6000 × 8 = 48,000
• C’s share = 8000 × 6 = 48,000

Step 3: Determine the Profit Sharing Ratio

The ratio of their shares is: A : B : C = 84,000 : 48,000 : 48,000

Simplify the ratio by dividing each term by 12,000: A : B : C = 7 : 4 : 4

Step 4: Calculate Individual Profits

Total profit = Rs. 15,000 Total parts in the ratio = 7 + 4 + 4 = 15

• A’s profit = (7/15) × 15,000 = Rs. 7,000
• B’s profit = (4/15) × 15,000 = Rs. 4,000
• C’s profit = (4/15) × 15,000 = Rs. 4,000

Final Answer

• A’s profit = Rs. 7,000
• B’s profit = Rs. 4,000
• C’s profit = Rs. 4,000