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.