Ajay started a business investing X 25000.After 3 months, Vijay joined him with a capital of X 30000. At the end of the year, they made a profit of X 38000. What will be the Ajay's share in the profit?

Options

A. ? 10000
B. ? 18000
C. ? 15000
D. ? 20000

Answer

To solve the problem step by step, we need to determine Ajay's share of the profit based on their investments and the time each partner was involved in the business.

### Step 1: Determine the capital invested by each partner and the duration of their investment.
- **Ajay's Investment**: X 25,000 for 12 months.
- **Vijay's Investment**: X 30,000 for 9 months (since he joined after 3 months).

### Step 2: Calculate the effective capital contribution for each partner.
The effective capital contribution can be calculated by multiplying the amount invested by the time (in months) it was invested.

- **Ajay's Contribution**:
\[ 25,000 \times 12 = 300,000 \]

- **Vijay's Contribution**:
\[ 30,000 \times 9 = 270,000 \]

### Step 3: Calculate the total capital contribution.
- **Total Contribution**:
\[ 300,000 + 270,000 = 570,000 \]

### Step 4: Determine the profit-sharing ratio.
The profit-sharing ratio is based on the effective capital contributions of Ajay and Vijay.

- **Ajay's Share**:
\[ \text{Ajay's Share} = 300,000 \]

- **Vijay's Share**:
\[ \text{Vijay's Share} = 270,000 \]

- **Profit-sharing Ratio**:
\[ \text{Ratio} = 300,000 : 270,000 = 10 : 9 \]

### Step 5: Calculate Ajay's share of the profit.
The total profit made at the end of the year is X 38,000. We will now calculate Ajay's share based on the profit-sharing ratio.

- **Ajay's Share of Profit**:
\[ \text{Ajay's Share} = \frac{10}{10 + 9} \times 38,000 = \frac{10}{19} \times 38,000 \]

Calculating Ajay's share:
\[ \text{Ajay's Share} = \frac{10 \times 38,000}{19} = \frac{380,000}{19} \approx 20,000 \]

### Final Answer:
Ajay's share in the profit is X 20,000.

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