New Ratios

A is correct. The new profit-sharing ratio specifies how the continuing partners divide the firm’s profits after the retiring partner leaves; it is not a capital or asset-value ratio.

A is correct. With no new agreement, A and B gain C’s share in their old ratio, 3:2. Their relative shares therefore remain 3:2.

After B’s death, only A and C remain. In the original ratio 5:3:2, A’s share was 5 and C’s share was 2. Since they continue in the same mutual ratio, their new ratio is 5:2. Exam tip: when the question states that the remaining partners continue in the old ratio, retain their original share numbers and omit the outgoing partner’s share.

The gaining ratio compares the increases in the profit shares of the continuing partners. The retiring partner leaves the firm and is not included in this ratio.

A continuing partner’s gain is the increase in that partner’s share: new share minus old share. For example, an increase from 1/4 to 1/3 gives a gain of 1/3 − 1/4 = 1/12.

The total old shares are 5 parts, so A and B each had 2/5. They divide C’s 1/5 equally, gaining 1/10 each. Each then has 2/5 + 1/10 = 1/2, so their new ratio is 1:1.

A’s old share was 4 parts and C’s share was 2 parts. When A takes over C’s entire share, A’s new share becomes 4 + 2 = 6 parts, while B’s share remains 3 parts. Thus, the new ratio is 6:3, or 2:1 in its simplest form. Exam tip: Add the retiring partner’s share to the old share of the partner who takes it over.

The old ratio is A:B:C = 3:3:2. Since B takes C’s entire share of 2, A’s share remains 3 while B’s share becomes 3 + 2 = 5. Therefore, the new ratio of A and B is 3:5. Exam tip: When one partner takes the whole share of the retiring partner, add the acquired share to that partner’s original share.

A and B acquire C’s 3/12 share in the ratio 5:4, so their gains are 5/36 and 4/36. Their new shares are 5/12 + 5/36 = 5/9 and 4/12 + 4/36 = 4/9. Thus, the new ratio is 5:4.

C’s profit share was \(1/10\). Half of it, \(1/20\), is acquired by A and the other half by B. Thus, A’s new share is \(6/10+1/20=13/20\), while B’s new share is \(3/10+1/20=7/20\). Therefore, the new ratio is \(13:7\). Option B reverses the two partners’ shares. Exam tip: When the retiring partner’s share is acquired equally, add half of that share to each continuing partner’s original share.

The governing concept is the calculation of a new profit-sharing ratio after retirement by adding each continuing partner’s gain from the retiring partner to that partner’s old share. C’s old share is 5/10. A and B acquire this share in the ratio 2:3, so A gains 2/5 × 5/10 = 2/10, while B gains 3/5 × 5/10 = 3/10. A’s new share is therefore 2/10 + 2/10 = 4/10, and B’s new share is 3/10 + 3/10 = 6/10. The ratio 4:6 simplifies to 2:3. Thus option A is correct. The acquisition ratio happens to equal A and B’s original relative ratio, so their mutual ratio remains unchanged; the other options do not total the whole profit correctly.

The gaining ratio compares how much each continuing partner gains. If they acquire equal portions of the retiring partner’s share, their gains are equal, so the gaining ratio is equal.

The gaining ratio shows the relative proportions in which the continuing partners obtain the outgoing partner’s profit share. The question explicitly states that the retiring partner’s share is acquired in the ratio 3:1. Therefore, the first continuing partner gains three parts for every one part gained by the second continuing partner, and the gaining ratio is 3:1. The old ratio would be relevant only if the question said that the share was acquired in the old proportion. The new ratio describes final profit entitlement, not necessarily the proportions of the gain. Option B reverses the stated order, while options C and D introduce ratios not supplied in the question. Hence option A is correct.

The governing concept is that each continuing partner’s new share equals the old share plus the share acquired from the retiring partner. Before retirement, A, B and C each have 1/3 of the profit. C’s 1/3 share is acquired equally by A and B, so each receives an additional 1/6. A’s new share becomes 1/3 + 1/6 = 1/2, and B’s new share also becomes 1/3 + 1/6 = 1/2. Therefore, their new ratio is 1/2:1/2, which simplifies to 1:1. Option A is correct. Ratios 2:1 and 1:2 would require unequal acquisition or unequal original shares, while 3:1 does not represent the stated equal sharing of C’s interest.

When there is no new agreement, the remaining partners, A and B, share the retiring partner C’s share in their old ratio. Therefore, their ratio remains 4:4, which simplifies to 1:1. The ratio 2:1 is incorrect because 4:4 simplifies equally for both partners. Exam tip: In the absence of a new agreement, the continuing partners retain their old mutual profit-sharing ratio.

The new ratio applies to profits for the period from the retirement date onward, when the continuing partners share profits under the reconstituted arrangement. The old ratio applies to the period before retirement.

After A retires, B and C continue as partners. In the absence of a new agreement, they continue to share profits in their existing mutual ratio. Their old mutual ratio was 5:2, so their profit-sharing ratio remains 5:2. The ratios 3:5 and 3:2 do not represent the continuing partners’ original mutual ratio, while 1:1 has no basis in the given information. Exam tip: On retirement, use the continuing partners’ old mutual ratio unless a new agreement specifies a different ratio.

In the absence of a new agreement, the retiring partner’s share is acquired by the continuing partners in their old profit-sharing ratio. Therefore, A and C continue to share profits in their old ratio of 2 : 3. Even B’s 5 parts are distributed between A and C in the ratio 2 : 3, so their resulting ratio remains 2 : 3. Hence, option A is correct. Exam tip: For retirement questions, first check whether a new ratio has been agreed upon; if not, use the continuing partners’ old ratio.

A’s old share is 7 and B’s share is 2. On B’s retirement, A acquires B’s entire share, so A’s new share becomes 7 + 2 = 9. C’s share remains 1. Therefore, the new ratio of A and C is 9:1. Exam tip: When one partner acquires another partner’s entire share, add the acquired share to the acquiring partner’s old share. 7:3 is incorrect because B’s share has not been added correctly to A’s share.

The total initial ratio is 10. B’s share is 1 part and C’s share is 5 parts. On B’s retirement, C acquires B’s 1 part, so C’s new share becomes 5 + 1 = 6, while A’s share remains 4. Therefore, the new ratio A:C is 4:6, or 2:3 in simplified form. Option C is incorrect because it ignores the transfer of B’s share to C. Exam tip: Add the retiring partner’s share to the share of the partner who acquires it.

C’s original share is 3/10. A and B acquire this share in the ratio 1:2, so A gains 1/10 and B gains 2/10. Therefore, A’s new share is 5/10 + 1/10 = 6/10, while B’s new share is 2/10 + 2/10 = 4/10. Thus, the new ratio is 6:4, which simplifies to 3:2. Exam tip: Convert the old ratio into fractions, calculate the retiring partner’s share, and distribute it according to the gaining ratio.

C’s old share was 3/10. When this share is acquired by A and B in the ratio 2:1, A gains 2/10 and B gains 1/10. Thus, A’s new share is 6/10 + 2/10 = 8/10, while B’s new share is 1/10 + 1/10 = 2/10. Therefore, the new ratio is 8:2 = 4:1. Exam tip: always reduce the final ratio to its simplest form.

The total ratio is 12, so A’s share is 3 parts. B and C acquire these 3 parts in the ratio 1:2; therefore, B gains 1 part and C gains 2 parts. Their new shares are B = 4+1 = 5 and C = 5+2 = 7. Hence, the new ratio is 5:7. Exam tip: Add each partner’s gain from the retiring partner’s share to that partner’s old share.

A’s share is 2 parts, and it is divided equally between B and C, so each receives 1 additional part. B’s new share is 7+1=8 and C’s new share is 1+1=2. Therefore, the new ratio is 8:2, which simplifies to 4:1. Exam tip: when a retiring partner’s share is acquired equally, add half of that share to each acquiring partner’s original share.

The new ratio is the ratio in which the continuing partners will share future profits. The gaining ratio shows the additional share acquired by each continuing partner from the retiring partner’s share, compared with the old ratio. It is generally calculated as new ratio − old ratio. Therefore, the two ratios need not be the same. Exam tip: new ratio means total future profit-sharing ratio, while gaining ratio means the additional share gained.