Analyzing Capital Allocation and Profit Distribution in a Partnership

In the business world, understanding the dynamics of capital allocation and profit distribution is crucial for both partners and stakeholders. The given problem involves a unique scenario where one partner's capital is twice that of another and thrice that of the third. This article will break down the problem and provide a step-by-step solution with an analysis of the calculations.

Problem Statement

A business is formed by three partners: A, B, and C. Partner B's capital is twice that of Partner A and thrice that of Partner C. In one year, the profit amounts to Rs. 330, which is 1/10th of the total capital. The question asks for Partner A's capital, and the options provided should be scrutinized.

Solution

The problem can be solved by first determining the total capital and then allocating it based on the given ratios. Let's start by defining the capital contributions of A, B, and C with the given ratios:

Step 1: Define Variables

Let's denote the capital of Partner A as A. According to the problem, Partner B's capital is twice that of Partner A, which can be represented as 2A. Additionally, Partner B's capital is thrice that of Partner C, which means Partner C's capital is a third of Partner B's capital, represented as C 1/3 * 2A 2A/3.

Step 2: Calculate Total Capital

The total capital is the sum of the individual capitals of A, B, and C:

Total Capital A 2A 2A/3

To simplify, we find a common denominator and combine the terms:

Total Capital A 2A 2A/3 (3A 6A 2A) / 3 11A / 3

Step 3: Use Given Profit Information

It is given that the profit of Rs. 330 is 1/10th of the total capital. Therefore, we can write:

330 1/10 * Total Capital

Substituting the expression for total capital:

330 1/10 * (11A / 3)

Solving for A:

330 (11A / 30)

Multiplying both sides by 30:

9900 11A

Dividing both sides by 11:

A 900

Therefore, Partner A's capital is Rs. 900.

Conclusion

The solution demonstrates that the correct capital allocation leads to Partner A having Rs. 900, Partner B having Rs. 1800, and Partner C having Rs. 600. This detailed step-by-step analysis ensures clarity and accuracy in solving the problem, providing a strong foundation for understanding capital allocation and profit distribution in partnerships.

Keywords: Capital Allocation, Profit Distribution, Mathematical Problem