A started a business investing Rs.35,000. After six months B joined him with a capital of Rs. 60,000. At the end of the year the total profit was Rs. 26,000. What will be the difference between the share of profits of A and B ?

Options

A. Rs. 4,000
B. Rs. 2,000
C. Rs. 1,500
D. None of these

Answer

To solve the problem step by step, we will calculate the profit shares of A and B based on their investments and the time they invested in the business.

### Step 1: Calculate the capital contribution of A and B
- A invested Rs. 35,000 for 12 months.
- B invested Rs. 60,000 for 6 months.

### Step 2: Calculate the effective capital contribution
To find the effective capital contribution, we multiply the capital invested by the time (in months) for which it was invested.

- For A:
\[ \text{Effective capital of A} = 35,000 \times 12 = 420,000 \]

- For B:
\[ \text{Effective capital of B} = 60,000 \times 6 = 360,000 \]

### Step 3: Determine the ratio of their effective capital contributions
Now, we can find the ratio of A's and B's effective capital contributions.

- The ratio of A's contribution to B's contribution is:
\[ \text{Ratio} = \frac{420,000}{360,000} = \frac{42}{36} = \frac{7}{6} \]

### Step 4: Calculate the total profit shares
Let the profit share of A be \(7x\) and the profit share of B be \(6x\). The total profit is given as Rs. 26,000.

- Therefore, we have:
\[ 7x + 6x = 26,000 \]
\[ 13x = 26,000 \]

### Step 5: Solve for \(x\)
To find the value of \(x\):
\[ x = \frac{26,000}{13} = 2,000 \]

### Step 6: Calculate the individual profit shares
Now we can calculate the profit shares for A and B:
- A's share:
\[ 7x = 7 \times 2,000 = 14,000 \]
- B's share:
\[ 6x = 6 \times 2,000 = 12,000 \]

### Step 7: Find the difference between the shares of A and B
Finally, we find the difference between A's and B's profit shares:
\[ \text{Difference} = 14,000 - 12,000 = 2,000 \]

### Conclusion
The difference between the share of profits of A and B is Rs. 2,000.

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