Understanding Profit Sharing and Salary in Partnerships

This question involves a partnership where two individuals, P and Q, contribute capital to start a business. The profit generated is typically shared based on the ratio of their investments. However, in this case, one partner, P, also receives a fixed amount as a salary in addition to his share of the profit. We need to determine the amount of salary P received.

Calculating Profit Share Based on Investment Ratio

In a partnership, when investments are made for the same duration (as indicated by "After a year"), the profit is usually divided among the partners in the ratio of their respective capital contributions.

• P's capital = Rs. 1,50,000
• Q's capital = Rs. 4,50,000

The ratio of their investments is:

$$ \text{Ratio of P's capital to Q's capital} = 1,50,000 : 4,50,000 $$

To simplify this ratio, we can divide both numbers by the greatest common divisor. Both are divisible by 1,50,000:

$$ \text{Ratio} = \frac{1,50,000}{1,50,000} : \frac{4,50,000}{1,50,000} $$

$$ \text{Ratio} = 1 : 3 $$

So, P and Q share the profit in the ratio of 1:3. This means for every 1 part of the profit P gets, Q gets 3 parts. The total number of parts is $1 + 3 = 4$.

Determining P's Share of the Total Profit

The total profit earned after a year is Rs. 1,60,000.

P's share of this profit is calculated based on his share in the investment ratio:

$$ \text{P's profit share} = \left(\frac{\text{P's ratio part}}{\text{Total ratio parts}}\right) \times \text{Total Profit} $$

$$ \text{P's profit share} = \left(\frac{1}{4}\right) \times 1,60,000 $$

$$ \text{P's profit share} = \frac{1,60,000}{4} $$

$$ \text{P's profit share} = 40,000 $$

So, P's share of the profit based on the capital contribution is Rs. 40,000.

Calculating P's Salary

The question states that P gets a total amount of Rs. 70,000, which includes his share of the profit plus some money as salary.

• P's total earnings = Rs. 70,000
• P's total earnings = P's profit share + P's salary

We know P's total earnings and his profit share. We can rearrange the formula to find the salary:

$$ \text{P's salary} = \text{P's total earnings} - \text{P's profit share} $$

Substitute the values:

$$ \text{P's salary} = 70,000 - 40,000 $$

$$ \text{P's salary} = 30,000 $$

Therefore, the salary P received is Rs. 30,000.

Step-by-Step Summary

1. Find the ratio of the capital invested by P and Q.
2. Calculate the total number of parts in the ratio.
3. Calculate P's share of the total profit based on this ratio.
4. Subtract P's profit share from his total earnings to find his salary.

Revision Table: Partnership Profit & Salary

Additional Information: Partnership Basics

A partnership is a type of business where two or more individuals agree to share the profits or losses of a business carried on by all or any of them acting for all. Key aspects include:

• Agreement: Partnerships are formed through an agreement, which can be oral or written. A written agreement (Partnership Deed) is highly recommended to avoid future disputes.
• Capital Contribution: Partners contribute capital, which can be in the form of money, assets, or services. The capital ratio is crucial for profit sharing.
• Profit and Loss Sharing: Profits and losses are shared among partners according to the terms of the partnership agreement. If there is no agreement, profits and losses are shared equally.
• Management: Partners can participate in the management of the business.
• Liability: In most traditional partnerships, partners have unlimited liability, meaning their personal assets can be used to pay off business debts.

Understanding the terms agreed upon regarding profit sharing, salaries, interest on capital, etc., is essential when solving partnership problems.