New Ratios

D share is 1/8 and when divided in 1:1:2 A gets 1/32 B gets 1/32 and C gets 2/32. New shares are 13/32 9/32 and 10/32 so the ratio is 13:9:10.

If no information is given continuing partners share in their old mutual ratio. So A and B new ratio will be 4:3.

The correct answer is A: 7:3. The old ratio is A:B:C = 7:5:3. When B dies, B’s share is removed. No information is given that A and C take that share in any special ratio. Therefore, the continuing partners retain their old mutual relationship: A:C = 7:3. Option A is correct. Option B incorrectly uses B’s old share with C. Option C includes the deceased partner’s share and is therefore not a ratio between the continuing partners. Option D assumes equal sharing, but the question gives no such fact. Remember: when no gaining information is supplied, preserve the old mutual ratio of the remaining partners.

When the share is taken in old ratio the mutual ratio of continuing partners does not change. B and C old ratio 2:3 becomes new ratio.

C share is 1/6 and equal taking gives 1/12 each to A and B. New shares are 7/12 and 5/12 so the ratio is 7:5.

C share 1/10 divided in 2:1 gives A 1/15 and B 1/30. New shares are 2/3 and 1/3 so ratio is 2:1.

C’s old share is 3/10. A acquires 3/5 of C’s share, which is 9/50, while B acquires 2/5, which is 6/50. A’s new share is 2/10 + 9/50 = 10/50 + 9/50 = 19/50, and B’s new share is 5/10 + 6/50 = 25/50 + 6/50 = 31/50. Therefore, the new ratio is 19:31. Exam tip: Divide the retiring partner’s share according to the gaining ratio and add the gains to the old shares.

Direct answer: Option A, 21:29. The total old ratio is 4+5+1=10. Thus A has 4/10, B has 5/10 and C has 1/10. C’s share is taken by A and B in 1:4, so the five parts give A (1/10)×(1/5)=1/50 and B (1/10)×(4/5)=4/50. A’s new share is 4/10+1/50=20/50+1/50=21/50. B’s new share is 5/10+4/50=25/50+4/50=29/50. Hence their ratio is 21:29. Option A is correct. Option B, 4:5, is only their old ratio and forgets the transfer. Option C, 5:9, has no correct calculation from the given data. Option D, 1:4, is only the gaining proportion, not the final ratio. Since A and B receive all of C’s share, their new shares add to 50/50. Exam cue: first find the retired partner’s fraction, then divide it in the gaining ratio.

B’s share is 3/10 of the total profit. A acquires 2/3 of it, which is 2/10, while C acquires 1/3, which is 1/10. Thus, A’s new share is 5/10 + 2/10 = 7/10 and C’s new share is 2/10 + 1/10 = 3/10. Therefore, the new ratio is 7:3. Exam tip: Divide the retiring partner’s share according to the given acquisition ratio and add the respective portions to the partners’ old shares.

The governing concept is redistribution of the deceased partner’s share among the surviving partners. The old ratio totals 1 + 3 + 2 = 6, so A’s share is 1/6. B and C acquire this share equally; each receives half of 1/6, which is 1/12. B’s new share is 3/6 + 1/12 = 6/12 + 1/12 = 7/12. C’s new share is 2/6 + 1/12 = 4/12 + 1/12 = 5/12. Thus, the new ratio of B and C is 7:5, so option A is correct. Option B merely repeats their old ratio. Options C and D fail to add one-half of A’s share to each surviving partner and therefore do not preserve the whole profit share.

After C’s retirement, A and B share profits in the new ratio 3:2. The total parts are 3 + 2 = 5, and A has 3 parts. Therefore, A’s new share is 3/5. The old ratio is not required because the new ratio is given directly. Exam tip: Divide a partner’s ratio part by the sum of all the new ratio parts to find the partner’s share.

After C’s retirement, the new ratio of A and B is given as 5:5. Dividing both terms by their greatest common divisor, 5, gives 5:5 = 1:1. Hence, the simplest new ratio is 1:1. In exams, always reduce a ratio to the smallest whole numbers.

Retiring partner share goes to continuing partners so their share increases. In exams add old share and gained share.

Gaining ratio shows the ratio in which continuing partners acquired retiring partner share. It is important in goodwill adjustment.

A new share is 5/8 and old share is 2/3. Difference 5/8 - 2/3 = -1/24 so A has sacrificed not gained.

B’s old share was \(1/(2+1)=1/3\), while his new share is \(3/(5+3)=3/8\). Therefore, B’s gain is \(3/8-1/3=(9-8)/24=1/24\). The value 3/8 represents B’s new share, not the increase in his share. Exam tip: To calculate a partner’s gain, subtract the old share from the new share.

C’s retirement causes the remaining partners, A and B, to gain C’s share. A’s old share was \(3/6=6/12\), while the new share is \(7/12\); hence, A gains \(1/12\). B’s old share was \(2/6=4/12\), while the new share is \(5/12\); hence, B also gains \(1/12\). Therefore, the gaining ratio is \(1/12:1/12=1:1\). Remember that 7:5 is the new profit-sharing ratio, not the gaining ratio.

A gain is 5/9 - 4/10 = 14/90 and B gain is 4/9 - 3/10 = 13/90. Thus gaining ratio is 14:13 which is not among the options.

Under the old ratio, A’s share was 4/10 and B’s share was 3/10. Under the new ratio, A’s share is 5/9 and B’s share is 4/9. Thus, A’s gain is 5/9 − 4/10 = 14/90, while B’s gain is 4/9 − 3/10 = 13/90. Therefore, the gaining ratio is 14:13. Exam tip: Gaining ratio is calculated as new share minus old share.

A moved from 5/10 to 3/5 or 6/10 and B moved from 1/10 to 2/5 or 4/10. B gain 3/10 is more than A gain 1/10.

Before C’s retirement, A’s share was 6/10 and B’s share was 2/10. Under the new ratio, A’s share becomes 7/10 and B’s share becomes 3/10. Thus, A’s gain is 7/10 − 6/10 = 1/10, while B’s gain is 3/10 − 2/10 = 1/10. Since both partners gain equally, the gaining ratio is 1:1. Remember that 7:3 is the new ratio, not the gaining ratio; the gaining ratio is calculated from the increase in each partner’s share.

Gaining ratio measures the increase in each continuing partner’s share; it is not the final profit-sharing ratio. The old shares of A and B are 7/10 and 2/10. Under the new ratio 4:1, their shares are 4/5 = 8/10 and 1/5 = 2/10. A’s gain is 8/10 − 7/10 = 1/10, whereas B’s gain is 2/10 − 2/10 = 0. Therefore, the gaining ratio is 1/10:0, which simplifies to 1:0. Option A is correct. This shows that A alone acquires C’s entire 1/10 share, while B’s share remains unchanged. Option B reverses the result, option C assumes equal gains, and option D states the new ratio rather than the gaining ratio.

Under the old ratio, A’s share was 2/10 and B’s share was 3/10. In the new 1:1 ratio, each partner receives 1/2, or 5/10. Therefore, A’s gain is 5/10 − 2/10 = 3/10, while B’s gain is 5/10 − 3/10 = 2/10. Hence, A gained more than B. Exam tip: To compare gains on retirement, subtract each partner’s old share from the corresponding new share.

The gaining ratio equals each continuing partner’s new share minus his or her old share. A originally held 2/10 and B held 3/10. Under the new 1:1 ratio, each partner receives 1/2 = 5/10. Therefore, A’s gain is 5/10 − 2/10 = 3/10, and B’s gain is 5/10 − 3/10 = 2/10. The gaining ratio is consequently 3/10:2/10 = 3:2, so option A is correct. The total gain is 5/10, exactly equal to C’s former share. Option B is the new ratio, option C reverses the calculated gains, and option D incorrectly assumes that both partners gain equally despite their different old shares.

Gaining ratio is the ratio in which continuing partners take retiring partner share. Hence it will be 5:3.