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)?
10800
Understanding Business Profit Sharing
This problem involves calculating the profit share of a partner in a business, considering their investment ratio, a reinvestment of profit, and the status of one partner as a sleeping partner.
Initial Investment Ratio
The three partners, A, B, and C, invest in the business in the ratio:
\( A : B : C = 4 : 5 : 7 \)
This initial ratio usually dictates how profits are shared among working partners unless otherwise specified.
Total Profit and Reinvestment
The business makes a total profit of Rs 36,000. However, a portion of this profit is reinvested back into the business.
- Total Profit = \(\text{Rs } 36,000\)
- Percentage reinvested = \(25\%\)
- Amount reinvested = \(25\% \text{ of } 36,000\)
- Amount reinvested = \(\frac{25}{100} \times 36,000 = \frac{1}{4} \times 36,000 = 9,000\)
The profit available for distribution among the partners is the total profit minus the reinvested amount.
- Profit for distribution = Total Profit - Amount reinvested
- Profit for distribution = \(36,000 - 9,000 = 27,000\)
So, Rs 27,000 is the amount that will be shared among A, B, and C.
Impact of Sleeping Partner on Profit Share
The problem states that C is a sleeping partner and his share of profits will be half of what it would have been if he were a working partner. This changes the effective ratio in which the distributed profit is shared.
If all partners were working, the profit would be shared in the ratio 4:5:7. C's share would be proportional to 7 units.
Since C is a sleeping partner, his share is effectively proportional to half of his usual unit count:
\( \text{C's effective ratio unit} = 7 \times \frac{1}{2} = 3.5 \)
A and B are presumably working partners (as only C is specified as sleeping), so their ratio units remain 4 and 5, respectively.
The adjusted profit sharing ratio among A, B, and C is:
\( A : B : C = 4 : 5 : 3.5 \)
Calculating B's Share of Profit
To find B's share, we first need to find the total units in the adjusted ratio:
\( \text{Total units} = 4 + 5 + 3.5 = 12.5 \)
B's share of the distributed profit (Rs 27,000) is calculated based on B's units relative to the total units:
\( \text{B's share} = \frac{\text{B's ratio units}}{\text{Total units}} \times \text{Profit for distribution} \)
\( \text{B's share} = \frac{5}{12.5} \times 27,000 \)
To simplify the fraction \(\frac{5}{12.5}\), we can multiply the numerator and denominator by 10:
\( \frac{5}{12.5} = \frac{5 \times 10}{12.5 \times 10} = \frac{50}{125} \)
The fraction \(\frac{50}{125}\) can be simplified by dividing both by 25:
\( \frac{50 \div 25}{125 \div 25} = \frac{2}{5} \)
Now, substitute this simplified fraction back into the calculation for B's share:
\( \text{B's share} = \frac{2}{5} \times 27,000 \)
\( \text{B's share} = 2 \times \frac{27,000}{5} \)
\( \text{B's share} = 2 \times 5,400 \)
\( \text{B's share} = 10,800 \)
Summary of Calculation
| Description | Amount (Rs) |
|---|---|
| Total Profit | 36,000 |
| Amount Reinvested (25%) | 9,000 |
| Profit for Distribution | 27,000 |
| Initial Investment Ratio (A:B:C) | 4:5:7 |
| Adjusted Profit Sharing Ratio (A:B:C) considering Sleeping Partner | 4:5:3.5 |
| Total Units in Adjusted Ratio | 12.5 |
| B's Ratio Units | 5 |
| B's Share of Profit | \(\frac{5}{12.5} \times 27,000 = 10,800\) |
Therefore, B gets Rs 10,800 from the profit distribution.
Revision Table: Key Concepts
| Concept | Explanation | Relevance to Problem |
|---|---|---|
| Investment Ratio | The proportion in which partners invest capital. Often the basis for profit sharing. | 4:5:7 initial ratio provided. |
| Total Profit | The gross profit earned by the business before any distribution or reinvestment. | Given as Rs 36,000. |
| Reinvestment | A portion of the profit kept back in the business for future growth, not distributed to partners. | 25% reinvested, reducing distributable profit. |
| Profit for Distribution | The net profit amount that is actually shared among the partners after deductions like reinvestment. | Calculated as Total Profit - Reinvestment. |
| Sleeping Partner | A partner who contributes capital but does not participate in the day-to-day running of the business. Their profit share is often less than a working partner. | C is a sleeping partner, whose share is halved. |
| Adjusted Profit Sharing Ratio | The ratio in which the profit for distribution is actually shared, considering factors like sleeping partners, different levels of work contribution, or specific agreements, which may differ from the investment ratio. | Calculated as 4:5:3.5 based on the sleeping partner condition. |
Additional Information on Partnership Profit Sharing
Profit sharing in a partnership is typically governed by the partnership agreement. While investment ratio is a common basis, other factors can influence how profits are divided:
- Work Contribution: Partners actively involved in managing the business might receive a larger share or a salary in addition to profit share compared to sleeping partners.
- Specific Agreements: The partners can agree on any ratio for profit sharing, regardless of the investment ratio, provided it is documented in the partnership deed.
- Time Period: If partners join or leave during the year, the profit sharing might be calculated proportionally for the time they were partners.
- Guaranteed Profit: Sometimes, a partner might be guaranteed a minimum amount of profit, irrespective of the actual profit earned by the firm.
In this specific problem, the sleeping partner clause directly modified the proportion of profit C received, leading to an adjusted ratio for distribution. The calculation then simply involves dividing the distributable profit according to this adjusted ratio.
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 and B entered into a partnership with investments in the ratio 3 ∶ 5. After a few months, A withdrew and collected his money back. At the end of the year, they received profit in the ratio 2 ∶ 5. For how many months did A invest?
