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 analyze changes in profit-sharing for partners A, B, and C, we first establish their current and proposed profit-sharing ratios. The current ratio is 3:3:4. The proposed ratio is an equal distribution among the three partners, which is 1:1:1, meaning each partner will receive 1/3 of the profits.

The calculation of current and future profit shares is as follows:

• 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)

To facilitate comparison, all fractions are converted to a common denominator of 30:

• The least common multiple 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)

The gain or sacrifice for each partner is calculated as follows:

• 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

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

This outcome corresponds to the option: A gains 1/30; B gains 1/30; C sacrifices 2/30.