New Ratios

The governing rule is to add each partner’s acquired portion of the retiring partner’s share to that partner’s old share. The total old ratio is 4 + 2 + 4 = 10, so B’s share is 2/10 = 1/5. A and C acquire this 1/5 share in the ratio 3:1. A receives 3/4 × 1/5 = 3/20, while C receives 1/4 × 1/5 = 1/20. A’s new share is 4/10 + 3/20 = 8/20 + 3/20 = 11/20. C’s new share is 4/10 + 1/20 = 8/20 + 1/20 = 9/20. Therefore, the new ratio is 11:9, making option A correct. Other choices confuse the old, acquisition, or an incorrectly calculated ratio.

If no information is given the old mutual ratio of continuing partners becomes the new ratio. So A and B new ratio is 5:3.

The old ratio tells us how A, B, and C shared profit before B’s death. When B leaves and the question gives no special instruction, the remaining partners continue to share in the same mutual proportion in which they previously shared. Therefore, the relevant comparison is only between A’s old share of 6 and C’s old share of 5. B’s number is removed; it is not redistributed unless the question states a new arrangement.

Thus, A and C’s new ratio is obtained directly as A:C = 6:5. Option A is correct. Options B and C do not represent the proper remaining mutual ratio, while 1:1 would be possible only if an equal-sharing arrangement were specifically given. No such information is supplied, so the simplest valid assumption is that the old mutual ratio continues.

Taking the share in old ratio does not change the mutual ratio of continuing partners. B and C old mutual ratio is 3:5.

C share is 1/8 and equal taking gives 1/16 each to A and B. New shares are 9/16 and 7/16 so the ratio is 9:7.

C share 1/10 divided in 3:2 gives A 3/50 and B 2/50. New shares are 38/50 and 12/50 so the simplified ratio is 19:6.

C share 2/10 is divided in 1:3. A gets 1/20 and B gets 3/20 so new shares become 7/20 and 13/20.

First find the retiring partner's share and then distribute it according to the stated gaining ratio. The old ratio totals 5 + 1 + 4 = 10, so C's share is 4/10. Equal acquisition means A and B each receive 2/10. A's new share becomes 5/10 + 2/10 = 7/10, and B's new share becomes 1/10 + 2/10 = 3/10. Removing the common denominator gives the new ratio 7:3. Option B is only the old ratio and does not include C's share; option C gives the acquisition ratio rather than final shares; option D results from an incorrect addition. Therefore option A is the correct new ratio.

B share is 6/10. A gets 2/10 and C gets 4/10 so new shares are 4/10 and 6/10 with simplified ratio 2:3.

The governing method is to add the deceased partner's share to the continuing partners in the stated ratio. The old total is 1 + 4 + 5 = 10, so A's share is 1/10. B and C acquire it equally, receiving 1/20 each. B's new share is 4/10 + 1/20 = 8/20 + 1/20 = 9/20. C's new share is 5/10 + 1/20 = 10/20 + 1/20 = 11/20. Consequently, their new ratio is 9:11. Option B is the old ratio, option C wrongly assumes equal final shares, and option D does not follow the required fraction calculation. Hence option A is correct.

After C retires, A and B share profits in the new ratio 5:3. The total parts are \(5+3=8\), so A's new share is \(\frac{5}{8}\). The old ratio is not needed because the new ratio is given directly. Exam tip: Find a partner's fraction by dividing that partner's new ratio term by the sum of all terms in the new ratio.

After C’s retirement, the given new ratio of A and B is 6:6. Dividing both terms by their greatest common divisor, 6, gives 6 ÷ 6 : 6 ÷ 6 = 1:1. Thus, A and B will share profits equally. Option 6:6 is the unsimplified ratio, while 2:1 changes the relative shares. In exams, express a ratio in the smallest whole numbers.

The share of retiring or deceased partner is added to continuing partners. So new share is the sum of old share and gained share.

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

A new share is 7/12 and old share is 3/5. Difference 7/12 - 3/5 = -1/60 so A has actually sacrificed.

Under the old ratio 3:2, B’s old share was \(\frac{2}{3+2}=\frac{2}{5}\). Under the new ratio 7:5, B’s new share was \(\frac{5}{7+5}=\frac{5}{12}\). Therefore, B’s gaining share = new share − old share = \(\frac{5}{12}-\frac{2}{5}=\frac{25-24}{60}=\frac{1}{60}\). The value \(\frac{5}{12}\) is B’s new share, not the gain. Exam tip: Calculate gaining share by subtracting the old share from the new share.

The gaining ratio is calculated by subtracting each continuing partner's old share from the corresponding new share. The old total is 10, so A's old share is 4/10 and B's is 3/10. The new ratio 5:4 has total 9, so A's new share is 5/9 and B's is 4/9. A's gain is 5/9 - 4/10 = 50/90 - 36/90 = 14/90. B's gain is 4/9 - 3/10 = 40/90 - 27/90 = 13/90. The common denominator cancels, producing a gaining ratio of 14:13. Option B is the new ratio, while C is the old ratio and D assumes equal gains. Therefore option A is correct.

Under the old ratio 5:2:3, A’s share is 5/10 and B’s share is 2/10. Under the new ratio 3:2, A’s share becomes 3/5 = 6/10 and B’s share becomes 2/5 = 4/10. Therefore, A’s gain is 6/10 − 5/10 = 1/10, while B’s gain is 4/10 − 2/10 = 2/10. Hence, the gaining ratio is 1/10 : 2/10 = 1:2. Exam tip: To find the gaining ratio, subtract each continuing partner’s old share from their new share.

The direct answer is A, B. The old ratio A:B:C is 2:1:7, so the total is 10 parts. A’s old share is 2/10 and B’s is 1/10. After C retires, A and B share equally, so each receives 1/2, or 5/10. A’s gain is 5/10 − 2/10 = 3/10. B’s gain is 5/10 − 1/10 = 4/10. Since 4/10 is greater than 3/10, B gained more. Option A is correct. Option B is wrong because A gained only 3/10. Option C is wrong because the gains are unequal. Option D is wrong because both partners together take C’s share, but each does not gain nothing. Exam cue: calculate each new share minus that partner’s old share; never compare only the new ratio.

A, B, and C originally share profits in the ratio 7:1:2. The total parts are 10, so A’s old share is 7/10 and B’s old share is 1/10. After C retires, A and B share the remaining profit in the new ratio 4:1. Thus A’s new share is 4/5 and B’s new share is 1/5. A’s gain is 4/5 − 7/10 = 8/10 − 7/10 = 1/10. B’s gain is 1/5 − 1/10 = 2/10 − 1/10 = 1/10. Both gain equally, so the gaining ratio is 1:1 and option A is correct.

The retired partner’s share is redistributed through the increase in the continuing partners’ shares. Since A and B each gain 1/10, their relative gains are equal. The new ratio 4:1 itself is not the gaining ratio; it shows their final shares, not the amounts by which their shares increased. Therefore, option A follows directly from comparing old and new shares.

C’s old share is 5/10, which is gained by A and B after C’s retirement. A’s old share was 3/10 and his new share is 2/5 = 4/10, so A gained 1/10. B’s old share was 2/10 and his new share is 3/5 = 6/10, so B gained 4/10. Therefore, B gained more than A. Exam tip: Calculate each continuing partner’s gain as new share minus old share.

Under the old ratio, A's share was 3/10 and B's share was 2/10. Converting the new ratio 2:3 into tenths gives A's share as 4/10 and B's share as 6/10. Therefore, A's gain is 4/10 − 3/10 = 1/10, while B's gain is 6/10 − 2/10 = 4/10. Hence, the gaining ratio is 1:4. Exam tip: Gain = New share − Old share.

Gaining ratio is the same ratio in which continuing partners take the retiring partner share. Hence it is 4:5.

When share is taken equally the increase of continuing partners is equal. Therefore gaining ratio will be equal.

Taking share in old ratio does not change the mutual ratio of continuing partners. So new ratio remains their old mutual ratio.