Understanding Business Profit Sharing

This question involves calculating the share of profit for one partner (C) in a business, given the initial investments of three partners (A, B, and C) and the total profit earned. The fundamental principle here is that profit is distributed among partners in proportion to their investments.

Calculating Total Investment

First, let's find the total investment made by all three friends:

• Investment by A = ₹6,000
• Investment by B = ₹8,000
• Investment by C = ₹10,000
• Total Investment = Investment by A + Investment by B + Investment by C
• Total Investment = ₹6,000 + ₹8,000 + ₹10,000 = ₹24,000

Determining the Investment Ratio

Next, we determine the ratio of their investments. This ratio represents how the profit will be divided.

• Ratio of Investments (A : B : C) = ₹6,000 : ₹8,000 : ₹10,000

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

• Simplified Ratio = (6000/2000) : (8000/2000) : (10000/2000)
• Simplified Ratio = 3 : 4 : 5

Calculating the Total Ratio Parts

The sum of the parts in the simplified ratio gives us the total number of parts into which the profit is divided.

• Total Ratio Parts = 3 + 4 + 5 = 12

Calculating C's Share of Profit

Now, we can calculate C's share of the total profit based on their proportion in the investment ratio.

• C's share is calculated as: (C's Ratio Part / Total Ratio Parts) * Total Profit
• C's Investment Ratio Part = 5
• Total Profit = ₹12,000
• C's Share = (5 / 12) * ₹12,000
• C's Share = 5 * (12000 / 12)
• 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.