Understanding Business Profit Sharing Based on Investment

This problem involves calculating the share of profit for one partner (C) in a business, based on the initial investments made by three friends: A, B, and C.

The fundamental principle is that profit is distributed among partners in the same ratio as their investments.

Investment Details

Here's a summary of the investments made by each friend:

Calculating the Ratio of Investments

First, we need to determine the ratio of their investments. This ratio will represent how the total profit is divided.

Ratio of Investments = Investment of A : Investment of B : Investment of C

Ratio = ₹6,000 : ₹8,000 : ₹10,000

To simplify the ratio, we can divide each part by the greatest common divisor, which is 2,000:

Simplified Ratio = (6,000 / 2,000) : (8,000 / 2,000) : (10,000 / 2,000)

Simplified Ratio = 3 : 4 : 5

Determining C's Share of Profit

The total profit is ₹12,000. This profit needs to be divided according to the ratio 3 : 4 : 5.

First, find the total number of parts in the ratio:

Total Parts = 3 + 4 + 5 = 12 parts

Next, calculate the value of one part of the profit:

Value of 1 Part = Total Profit / Total Parts

Value of 1 Part = ₹12,000 / 12

Value of 1 Part = ₹1,000

Now, we can calculate C's share. C has 5 parts in the ratio.

C's Share = C's Ratio Part × Value of 1 Part

C's Share = 5 × ₹1,000

C's Share = ₹5,000

Conclusion

Therefore, C's share of the total profit of ₹12,000 is ₹5,000.