A, B and C are partners. Their capital at the beginning ₹ 50,000, ₹ 60,000 and ₹ 70,000 respectively. A introduce additional capital ₹ 20,000 after 3 months, B ₹ 25,000 after 6 months, C ₹ 30,000 after 9 months. At the end profit for the year ₹ 25,800. Which is distributed in their capital ratio. What will be the share of profit of A ?

Question

Accepted Answer

Here's a detailed explanation justifying why Option 1 is correct and why the other options are incorrect:

**1. Justification for Option 1 (₹ 7,800) being correct:**

To distribute the profit in the capital ratio, we first need to calculate the "equivalent capital" for each partner for the entire year, considering the changes in their capital over time. This is done by multiplying the capital amount by the number of months it was invested and summing these products.

*   **Calculation for Partner A:**
    *   Initial capital of ₹ 50,000 was invested for 3 months. (₹ 50,000 × 3 months = ₹ 150,000)
    *   After 3 months, A introduced an additional ₹ 20,000. So, A's capital became ₹ 50,000 + ₹ 20,000 = ₹ 70,000 for the remaining 9 months of the year. (₹ 70,000 × 9 months = ₹ 630,000)
    *   A's equivalent capital for the year = ₹ 150,000 + ₹ 630,000 = ₹ 780,000

*   **Calculation for Partner B:**
    *   Initial capital of ₹ 60,000 was invested for 6 months. (₹ 60,000 × 6 months = ₹ 360,000)
    *   After 6 months, B introduced an additional ₹ 25,000. So, B's capital became ₹ 60,000 + ₹ 25,000 = ₹ 85,000 for the remaining 6 months of the year. (₹ 85,000 × 6 months = ₹ 510,000)
    *   B's equivalent capital for the year = ₹ 360,000 + ₹ 510,000 = ₹ 870,000

*   **Calculation for Partner C:**
    *   Initial capital of ₹ 70,000 was invested for 9 months. (₹ 70,000 × 9 months = ₹ 630,000)
    *   After 9 months, C introduced an additional ₹ 30,000. So, C's capital became ₹ 70,000 + ₹ 30,000 = ₹ 100,000 for the remaining 3 months of the year. (₹ 100,000 × 3 months = ₹ 300,000)
    *   C's equivalent capital for the year = ₹ 630,000 + ₹ 300,000 = ₹ 930,000

**Determining the Capital Ratio:**
The equivalent capital ratio for A, B, and C is:
A : B : C = ₹ 780,000 : ₹ 870,000 : ₹ 930,000
Dividing by 10,000, we get: 78 : 87 : 93
Further dividing by 3, we get the simplified ratio: 26 : 29 : 31

The sum of the ratio parts = 26 + 29 + 31 = 86

**Calculating A's Share of Profit:**
Total profit for the year = ₹ 25,800
A's share of profit = (A's ratio part / Total ratio parts) × Total profit
A's share = (26 / 86) × ₹ 25,800
A's share = 26 × (₹ 25,800 / 86)
A's share = 26 × ₹ 300
A's share = ₹ 7,800

Therefore, A's share of profit is ₹ 7,800, which matches Option 1.

**2. Explanation for why other options are incorrect:**

*   **Option 2: ₹ 8,700**
    This amount represents B's share of profit based on the calculated capital ratio.
    B's share = (29 / 86) × ₹ 25,800 = 29 × ₹ 300 = ₹ 8,700.
    Since the question asks for A's share, this option is incorrect.

*   **Option 3: ₹ 9,300**
    This amount represents C's share of profit based on the calculated capital ratio.
    C's share = (31 / 86) × ₹ 25,800 = 31 × ₹ 300 = ₹ 9,300.
    Since the question asks for A's share, this option is incorrect.

*   **Option 4: ₹ 7,084**
    This value does not correspond to the calculated share of profit for any partner based on the correct method of distributing profit according to the time-weighted capital ratio. It is likely the result of an incorrect calculation or an erroneous method of profit distribution.