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

Answer 1

The Correct Option is D

To determine the changes in profit-sharing among partners A, B, and C, we first need to understand their current and future profit-sharing ratios. The current ratio is 3:3:4, and the future ratio is meant to be equal among the three partners, which would be 1:1:1 or each getting 1/3 of the profits. 

Let's calculate the partners' current and future profit shares:

• A's current share: (3/10)
• B's current share: (3/10)
• C's current share: (4/10)
• A's future share: (1/3)
• B's future share: (1/3)
• C's future share: (1/3)

Convert all fractions to have the same denominator for easier comparison:

• The common denominator of 10 and 3 is 30.
• A's current share: (3/10) = (9/30)
• B's current share: (3/10) = (9/30)
• C's current share: (4/10) = (12/30)
• A's future share: (1/3) = (10/30)
• B's future share: (1/3) = (10/30)
• C's future share: (1/3) = (10/30)

Now, calculate the gain or sacrifice for each partner:

• A's gain: (10/30) - (9/30) = 1/30
• B's gain: (10/30) - (9/30) = 1/30
• C's sacrifice: (10/30) - (12/30) = -2/30

Therefore, in the transition from the old ratio to the new one, A gains 1/30, B gains 1/30, and C sacrifices 2/30 of the profit-sharing ratio.

This aligns with Option: A gains 1/30; B gains 1/30; C sacrifices 2/30.

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.