Mohan invested Rs. 100,000 in a garment business. After few months, Sohan joined him with Rs. 40000. At the end of the year, the total profit was divided between them in ratio 3 : 1. After how many months did Sohan join the business?
2
Partnership Profit Sharing Calculation
This problem involves calculating the duration of investment in a business partnership based on the profit-sharing ratio. In a partnership, profits are typically divided among partners in proportion to the product of their investment amount and the time period for which the investment was made.
Understanding Business Partnership Profit Share
When partners invest different amounts for different durations, the share of profit for each partner is determined by the ratio of their respective (Investment × Time) values. The formula used is:
$$ \frac{\text{Profit}_1}{\text{Profit}_2} = \frac{\text{Investment}_1 \times \text{Time}_1}{\text{Investment}_2 \times \text{Time}_2} $$
In this scenario, we have two partners, Mohan and Sohan.
Analyzing the Given Information
- Mohan's investment: Rs. 100,000
- Mohan stayed in the business for the entire year. A year has 12 months. So, Mohan's time in the business is 12 months.
- Sohan joined after a few months with an investment of Rs. 40,000.
- Let's assume Sohan stayed in the business for $x$ months.
- The total profit at the end of the year was divided in the ratio 3 : 1 (Mohan : Sohan).
We can summarize the information in a table:
| Partner | Investment (Rs.) | Time in Business (Months) | Profit Ratio Share |
|---|---|---|---|
| Mohan | 100,000 | 12 | 3 |
| Sohan | 40,000 | $x$ | 1 |
Setting up the Profit Ratio Equation
Using the formula for profit sharing based on Investment × Time:
$$ \frac{\text{Mohan's Profit}}{\text{Sohan's Profit}} = \frac{\text{Mohan's Investment} \times \text{Mohan's Time}}{\text{Sohan's Investment} \times \text{Sohan's Time}} $$
Substitute the given values:
$$ \frac{3}{1} = \frac{100000 \times 12}{40000 \times x} $$
Solving for Sohan's Time in Business
Now, we solve the equation to find the value of $x$, which represents the number of months Sohan was in the business.
$$ 3 = \frac{100000 \times 12}{40000 \times x} $$
We can simplify the fraction on the right side by canceling out common factors.
$$ 3 = \frac{100 \times 12}{40 \times x} $$
$$ 3 = \frac{10 \times 12}{4 \times x} $$
$$ 3 = \frac{120}{4x} $$
Cross-multiply:
$$ 3 \times 4x = 120 $$
$$ 12x = 120 $$
Divide by 12:
$$ x = \frac{120}{12} $$
$$ x = 10 $$
This means Sohan's investment was in the business for 10 months.
Calculating When Sohan Joined
The question asks "After how many months did Sohan join the business?". The total duration is one year, which is 12 months. If Sohan was in the business for the last 10 months of the year, he must have joined after the first $12 - 10$ months.
Number of months after which Sohan joined = Total time - Sohan's time in business
Number of months after which Sohan joined = $12 - 10 = 2$ months.
Therefore, Sohan joined the business after 2 months.
Revision Table - Partnership Profit Sharing
| Concept | Description |
|---|---|
| Partnership | A business structure where two or more individuals agree to share in the profits or losses of a business. |
| Profit Sharing Ratio | The agreed-upon proportion in which profits are divided among partners. |
| Investment × Time | The product used to determine each partner's effective contribution when investments are made for different durations. Profit shares are proportional to this value. |
Additional Information - Business Partnership Concepts
Understanding partnership dynamics is crucial for solving such problems. Here are some related concepts:
- Active vs. Sleeping Partner: An active partner participates in the daily management of the business, while a sleeping partner only contributes capital. Profit sharing principles usually apply regardless of this distinction, based on the partnership deed.
- Partnership Deed: A written agreement among partners outlining the terms and conditions of the partnership, including profit/loss sharing, investment details, duration, etc.
- Types of Partnerships: Includes General Partnership, Limited Partnership (LP), and Limited Liability Partnership (LLP), each with different structures regarding liability and management roles.
Problems like this help reinforce the understanding of how investment duration impacts profit distribution in a business partnership.
Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
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)?
