Solving Partnership Profit Sharing Problem

This problem involves calculating the share of profit for one partner, Sumit, in a business where profits are shared based on investment, after a portion is donated to charity.

Let's break down the steps to find Sumit's share of the profit.

Understanding the Given Information

• Sumit's Investment: Rs. 45000
• Ravi's Investment: Rs. 81000
• Puneet's Investment: Rs. 90000
• Total Profit at the end of the year: Rs. 4800
• Amount given to Charity: 30% of the total profit
• Remaining profit is divided among Sumit, Ravi, and Puneet in the ratio of their investments.

Calculating Profit for Distribution

First, we need to find the amount of profit that is distributed among the partners after giving to charity.

Amount given to Charity = 30% of Rs. 4800

Charity Amount $= 0.30 \times 4800 = 1440$

So, Rs. 1440 is given to charity.

Remaining Profit for distribution among partners = Total Profit - Charity Amount

Remaining Profit $= 4800 - 1440 = 3360$

The remaining profit of Rs. 3360 will be divided among Sumit, Ravi, and Puneet.

Determining the Investment Ratio

The profit is divided in the ratio of their investments. Let's find the ratio of the investments made by Sumit, Ravi, and Puneet.

Investment Ratio = Sumit's Investment : Ravi's Investment : Puneet's Investment

Ratio $= 45000 : 81000 : 90000$

To simplify the ratio, we can divide all the numbers by a common factor. Dividing by 1000 first:

Ratio $= 45 : 81 : 90$

Now, we can see that all numbers are divisible by 9. Dividing by 9:

Ratio $= \frac{45}{9} : \frac{81}{9} : \frac{90}{9} = 5 : 9 : 10$

The investment ratio of Sumit, Ravi, and Puneet is $5 : 9 : 10$.

Calculating Sumit's Share of Profit

The remaining profit (Rs. 3360) is divided according to the $5 : 9 : 10$ ratio. The sum of the ratio parts is $5 + 9 + 10 = 24$.

Sumit's share is $\frac{5}{24}$ of the remaining profit.

Sumit's Share $= (\text{Sumit's Ratio Part} / \text{Sum of Ratio Parts}) \times \text{Remaining Profit}

Sumit's Share $= \frac{5}{24} \times 3360$

Now, perform the multiplication and division:

Sumit's Share $= 5 \times \frac{3360}{24}$

Sumit's Share $= 5 \times 140$

Sumit's Share $= 700$

So, Sumit's share of the profit is Rs. 700.

Let's verify the options provided:

• Option 1: Rs. 700
• Option 2: Rs. 1260 (This would be Ravi's share: $(9/24) \times 3360 = 9 \times 140 = 1260$)
• Option 3: Rs. 131 (Incorrect)
• Option 4: Rs. 1400 (Incorrect)

Our calculated share for Sumit, Rs. 700, matches Option 1.

Final Answer

Sumit's share of the total profit is Rs. 700.

Revision Table: Partnership Profit Sharing

Review the key aspects of solving this type of partnership problem.

Additional Information: Business Partnership Basics

A business partnership is a formal arrangement by two or more parties to manage and operate a business and share in its profits.

• Profit Sharing: Profits (and losses) are typically shared among partners based on the partnership agreement. Common methods include sharing based on investment ratio, a fixed ratio, or a combination of investment and active participation. If the agreement is silent, profits are often shared equally.
• Investment Capital: This is the initial money or assets contributed by each partner to start or grow the business. The amount invested often directly influences the share of profits.
• Partnership Deed: This is a written agreement among partners. It covers crucial aspects like profit/loss sharing ratio, capital contribution, roles and responsibilities, interest on capital/drawings, and rules for dissolution. Having a deed helps prevent disputes.

In this problem, the partnership agreement specifies profit sharing based on investment ratio after a charitable donation.