Question

A and B entered into a partnership investing `16,000 and `12,000 respectively. After 3 months, A withdrew `5000 while B invested `5000 more. After 3 more months, C joins the business with a capital of `21,000. The share of B exceeds that of C, out of a total profit of `26,400 after one after by:

• A. 2400
• B. 3000
• C. 3600
• D. 4800

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the profit share each partner receives based on their capital investment and the time for which the capital was invested.

Step 1: Determine the capital investment duration for each:

• A's Investment: A invested `16,000 for the first 3 months. After 3 months, A withdrew `5,000, remaining `11,000 for the next 9 months. Hence, A's capital contribution can be calculated as follows: \( (16000 \times 3) + (11000 \times 9) = 48000 + 99000 = 147000 \) (capital-months).
• B's Investment: B invested `12,000 initially. After 3 months, B added `5,000, bringing it to `17,000 for 9 months. Thus, B's capital is: \( (12000 \times 3) + (17000 \times 9) = 36000 + 153000 = 189000 \) (capital-months).
• C's Investment: C joined after 6 months with `21,000 for 6 months. Thus, C's capital is: \( 21000 \times 6 = 126000 \) (capital-months).

Step 2: Calculate total capital-months and individual shares:

• Total Capital-Months: \( 147000 + 189000 + 126000 = 462000 \)
• Profit Sharing Ratio:
  • A : \( \frac{147000}{462000} \)
  • B : \( \frac{189000}{462000} \)
  • C : \( \frac{126000}{462000} \)

Step 3: Calculate the Profit Share:

• Total Profit: `26,400
• Share for B: \( 26400 \times \frac{189000}{462000} = 10800 \)
• Share for C: \( 26400 \times \frac{126000}{462000} = 7200 \)

The difference in profit share between B and C is \( 10800 - 7200 = 3600 \).

Conclusion: B's share exceeds C's by `3600. Therefore, the correct answer is 3600.