Partnership Profit Sharing Principle
In a business partnership, profit is distributed based on the ratio of investment value, which is calculated by multiplying the capital contributed by the duration of investment.
Investment Period Analysis
Kirti starts the business alone, while Vaishnavi joins later. We need to determine the duration each partner invested.
- Kirti's initial capital: ₹27,000
- Kirti's investment duration: 1 year = 12 months
- Vaishnavi joins after 7 months.
- Vaishnavi's investment duration: $12 \text{ months} - 7 \text{ months} = 5 \text{ months}$
Profit Ratio Application
The profit ratio between partners is equal to the ratio of their total investment values (Capital × Duration). Let Vaishnavi's capital contribution be $C_V$.
The ratio of Kirti's investment value to Vaishnavi's investment value is:
$ \frac{27000 \times 12}{C_V \times 5} $
This ratio is given as 8 : 9 (Kirti : Vaishnavi).
$ \frac{27000 \times 12}{C_V \times 5} = \frac{8}{9} $
Capital Calculation Method
To find Vaishnavi's capital ($C_V$), we solve the equation:
$ C_V \times 5 \times 8 = 27000 \times 12 \times 9 $
$ 40 \times C_V = 324000 \times 9 $
$ 40 \times C_V = 2916000 $
$ C_V = \frac{2916000}{40} $
$ C_V = \frac{291600}{4} $
$ C_V = 72900 $
Vaishnavi's Capital Value
Vaishnavi's contribution to the capital is ₹72,900.
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)?
