Two partners A and B have started business with the capitals of Rs. 6,000 and Rs. 8,000 respectively. If they made profit of Rs. 5,600 then the share (in Rs.) of A is:
2,400
Problem Analysis: Partner Profit Sharing
The question describes a business partnership between two individuals, A and B, who started the venture with specific amounts of capital. They earned a total profit and we need to determine the share of this profit that belongs to partner A. In a partnership, profits are typically distributed among partners in the ratio of their investments, unless otherwise specified by an agreement.
Key information provided:
- Partner A's initial capital: Rs. 6,000
- Partner B's initial capital: Rs. 8,000
- Total profit made: Rs. 5,600
We need to find the share (in Rs.) of partner A from the total profit.
Step-by-Step Solution for Partner Profit Share
To find each partner's share of the profit, we first need to determine the ratio of their initial investments. The profit will be divided according to this investment ratio.
Understanding the Investment Ratio
The investments of A and B are Rs. 6,000 and Rs. 8,000 respectively. The ratio of their investments is calculated as the ratio of their capital amounts.
Investment Ratio of A to B $=$ Capital of A : Capital of B
Investment Ratio $=$ 6,000 : 8,000
Calculating the Ratio of Investments
We simplify the ratio by dividing both numbers by their greatest common divisor.
$$ \text{Ratio} = \frac{6000}{8000} $$
We can cancel out common factors:
$$ \text{Ratio} = \frac{6}{8} $$
Further simplifying by dividing both numerator and denominator by 2:
$$ \text{Ratio} = \frac{3}{4} $$
So, the investment ratio of A : B is 3 : 4.
Determining Total Ratio Parts
The total number of parts in the ratio is the sum of the individual parts for A and B.
Total Ratio Parts = Ratio part of A + Ratio part of B
Total Ratio Parts = 3 + 4 = 7
The total profit of Rs. 5,600 is to be divided into 7 equal parts.
Finding the Value of Each Ratio Part
To find the value of one ratio part, we divide the total profit by the total number of ratio parts.
Value of one ratio part $$ = \frac{\text{Total Profit}}{\text{Total Ratio Parts}} $$
Value of one ratio part $$ = \frac{5600}{7} $$
Value of one ratio part = Rs. 800
Each part in the ratio corresponds to Rs. 800 of the profit.
Calculating Partner A's Profit Share
Partner A's share in the profit is equal to their ratio part multiplied by the value of one ratio part.
A's Share = A's Ratio Part $\times$ Value of one ratio part
A's Share = 3 $\times$ 800
A's Share = Rs. 2,400
Therefore, partner A's share of the profit is Rs. 2,400.
| Detail | Amount/Ratio |
|---|---|
| A's Capital | Rs. 6,000 |
| B's Capital | Rs. 8,000 |
| Total Profit | Rs. 5,600 |
| Investment Ratio (A:B) | 3:4 |
| Total Ratio Parts | 7 |
| Value of one ratio part | Rs. 800 |
| A's Profit Share | Rs. 2,400 |
Revision Table: Key Concepts in Partnership Profit Distribution
| Concept | Description |
|---|---|
| Partnership | A business owned by two or more individuals who agree to share in the profits or losses of the business. |
| Capital | The money or assets invested by each partner into the business. |
| Profit Sharing Ratio | The agreed-upon proportion in which profits or losses are divided among partners. Often based on capital invested, time invested, or specific agreements. |
| Investment Ratio Method | If no specific agreement exists, profits are typically shared in the ratio of the partners' capital contributions. |
Additional Information: Partnership Agreements and Profit Sharing
While profits are commonly shared in the ratio of investments, a partnership agreement (or deed) can specify a different method for distributing profits. This agreement is a legal document that outlines the terms and conditions of the partnership.
Possible clauses in a partnership agreement regarding profit distribution include:
- Sharing profits equally, regardless of capital contribution.
- Sharing profits based on both capital and time contributed.
- Providing interest on capital before distributing remaining profits based on a ratio.
- Allowing a salary or commission to a working partner before profit distribution.
In the absence of a partnership agreement, the Indian Partnership Act, 1932 (or equivalent legislation in other regions) usually stipulates that profits (and losses) must be shared equally among partners, irrespective of their capital contribution. However, the question implies sharing based on capital by providing initial investments, which is a standard approach taught in many basic problems unless equal sharing is explicitly stated.
Important Questions from Partnership
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
Sumit, Ravi and Puneet invest Rs. 45000, Rs. 81000 and Rs. 90000 respectively to start a business. At the end of the year the total profit is Rs. 4800. 30% of the total profit gives in charity and rest is divided among them. What will be the share of Sumit?
A sum of ₹ 159250 is divided among A, B, C, and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 2 : 5, and that of C and D is 2 : 3. The share (in ₹) of A is:
A and B start a business by investing Rs. 1,00,000 and Rs. 1,50,000 respectively. Find the respective share of each out of a total profit of Rs. 24, 000.
A, B and C are partners in a business with a total capital of Rs. 33,000. The profit at the end of the year is Rs. 1 5,000 that is to be divided in proportion to their capitals. A receives Rs. 4,500 and B receives Rs. 5,500 as their shares in profit. Find C's capital (in Rs.).
