Business Partnership Profit Calculation

Let's calculate the profit share for Mathur in this business partnership with Goyal. We need to consider their investments and the time they were involved, as well as how the total profit is distributed according to the given conditions.

First, let's identify the key information:

• Mathur's Investment: Rs. 6,76,000
• Mathur's Time in Business: 12 months (started at the beginning)
• Goyal's Investment: Rs. 5,07,000
• Goyal's Time in Business: Joined after 4 months, so \(12 - 4 = 8\) months
• Total Amount Received by Goyal: Rs. 2,60,000, including 25% of the total profit for conducting business.

We need to find out how much profit Mathur will get.

Calculating Equivalent Investments

Profit in a partnership is typically shared based on the product of the capital invested and the time period for which it was invested. This is called the equivalent investment or time-weighted capital.

• Mathur's Equivalent Investment: \(6,76,000 \times 12 = 81,12,000\)
• Goyal's Equivalent Investment: \(5,07,000 \times 8 = 40,56,000\)

Now, let's find the ratio of their equivalent investments, which will be the ratio for sharing the distributable profit:

\text{Ratio (Mathur : Goyal)} = 81,12,000 : 40,56,000

To simplify the ratio, we can divide both numbers by a common factor. Observing the numbers, 8112 is exactly double of 4056 (\(4056 \times 2 = 8112\)).

\text{Ratio (Mathur : Goyal)} = \frac{81,12,000}{40,56,000} : \frac{40,56,000}{40,56,000} = 2 : 1

So, the profit will be shared between Mathur and Goyal in the ratio 2:1 after accounting for the specific conditions mentioned.

Understanding Profit Distribution Rules

According to the question, the profit distribution has two parts for Goyal:

• A fixed amount for conducting business, which is 25% of the total profit.
• A share from the remaining profit, distributed based on the 2:1 investment ratio.

The total amount Goyal received from these two parts is Rs. 2,60,000.

Calculating Total Profit

Let the total profit of the business be \(P\).

Amount given to Goyal for conducting business = \(25\% \text{ of } P = 0.25P\)

The profit remaining for distribution after giving Goyal his fixed amount is:

\text{Remaining Profit} = P - 0.25P = 0.75P

This remaining profit (\(0.75P\)) is shared between Mathur and Goyal in the ratio 2:1. Goyal's share from this remaining profit is \(\frac{1}{3}\) of the remaining profit.

\text{Goyal's Share from Remaining Profit} = \frac{1}{2+1} \times 0.75P = \frac{1}{3} \times 0.75P = 0.25P

The total amount Goyal receives is the sum of the fixed amount for conducting business and his share from the remaining profit:

\text{Total Amount Goyal Gets} = 0.25P (\text{fixed}) + 0.25P (\text{share}) = 0.50P

We are given that the total amount Goyal gets is Rs. 2,60,000. So, we can write the equation:

\(0.50P = 2,60,000\)

To find the total profit \(P\), we solve this equation:

\(P = \frac{2,60,000}{0.50} = \frac{2,60,000}{1/2} = 2,60,000 \times 2 = 5,20,000\)

The total profit earned by the business at the end of the year is Rs. 5,20,000.

Calculating Mathur's Profit Share

Mathur receives his share from the remaining profit, which is \(0.75P\). The remaining profit is \(0.75 \times 5,20,000 = 3,90,000\).

Mathur's share from this remaining profit is based on the 2:1 ratio (Mathur : Goyal). Mathur gets \(\frac{2}{3}\) of the remaining profit.

\text{Mathur's Profit Share} = \frac{2}{2+1} \times (\text{Remaining Profit})

\text{Mathur's Profit Share} = \frac{2}{3} \times 3,90,000

\text{Mathur's Profit Share} = 2 \times \frac{3,90,000}{3} = 2 \times 1,30,000

\text{Mathur's Profit Share} = 2,60,000

So, Mathur will get Rs. 2,60,000 as his profit share.

Conclusion on Mathur's Profit

Based on our detailed calculations considering the investments, time periods, and the specific profit distribution rules, Mathur's share of the profit is found to be Rs. 2,60,000.

Let's review the provided options:

• Rs. 2,50,000
• Rs. 2,60,000
• Rs. 2,55,000
• More than one of the above
• None of the above

Our calculated profit for Mathur is Rs. 2,60,000, which matches Option 2. However, the provided correct answer is stated as 'None of the above'.