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 gains 2/30; B gains 3/30; C sacrifices 5/30
- A gains 2/30; B gains 1/30; C sacrifices 3/30
- A sacrifices 1/30; B gains 3/30; C sacrifices 2/30
- A gains 1/30; B gains 1/30; C sacrifices 2/30
The Correct Option is D
Approach Solution - 1
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.
Approach Solution -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.
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