Question

A, B, and C are partners sharing profits in the ratio of 3:3:4. They decide to share future profits equally. The sacrifice or gain of partners are

• A. A gains 1/30; B gains 1/30; C sacrifices 2/30
• B. A gains 2/30; B gains 1/30; C sacrifices 3/30
• C. A sacrifices 1/30; B gains 3/30; C sacrifices 2/30
• D. A gains 2/30; B gains 3/30; C sacrifices 5/30

Answer 1

The Correct Option is D

Calculating Partner Gain or Sacrifice: Profit-Sharing Ratio Change

When a partnership agreement is modified to change the profit-sharing ratio among the partners, it's essential to determine the gain or sacrifice for each partner. This helps to ensure a fair allocation of future profits and losses. 

1. Original Profit-Sharing Ratio

The original profit-sharing ratio is A : B : C = 3 : 3 : 4. This means:

• A's original share: \( \frac{3}{10} \)
• B's original share: \( \frac{3}{10} \)
• C's original share: \( \frac{4}{10} \)

2. New Profit-Sharing Ratio

The future profits are to be shared equally among A, B, and C. Therefore, the new profit-sharing ratio for each partner is:

\( \frac{1}{3} = \frac{10}{30} \)

3. Calculating Gain or Sacrifice

To determine the gain or sacrifice for each partner, subtract their original share from their new share:

• A's Change: New share - Original share \( = \frac{10}{30} - \frac{9}{30} = \frac{1}{30} \) (Gain)
• B's Change: New share - Original share \( = \frac{10}{30} - \frac{9}{30} = \frac{1}{30} \) (Gain)
• C's Change: New share - Original share \( = \frac{10}{30} - \frac{12}{30} = -\frac{2}{30} \) (Sacrifice)

Conclusion

Thus, A gains \( \frac{1}{30} \), B gains \( \frac{1}{30} \), and C sacrifices \( \frac{2}{30} \), making Option (1) the correct answer.

Answer 2

Partner Sacrifice or Gain on Profit Ratio Change 

A, B, and C are partners sharing profits in the ratio of 3:3:4. They decide to share future profits equally.

Calculating Sacrifice/Gain:

• Old Ratio: A (3/10), B (3/10), C (4/10)
• New Ratio: A (1/3), B (1/3), C (1/3)

Sacrifice/Gain Calculation:

• A's Sacrifice/Gain: (3/10) - (1/3) = (9 - 10)/30 = -1/30 (Gain)
• B's Sacrifice/Gain: (3/10) - (1/3) = (9 - 10)/30 = -1/30 (Gain)
• C's Sacrifice/Gain: (4/10) - (1/3) = (12 - 10)/30 = 2/30 (Sacrifice)

Therefore:

• A gains 1/30
• B gains 1/30
• C sacrifices 2/30

Note: A negative result indicates a gain, while a positive result indicates a sacrifice.