New Ratios

Correct answer: A. \(\frac{1}{9}\)

B’s old share was \(\frac{3}{4+3+2}=\frac{3}{9}\). After C’s death, the new ratio of A and B is 5:4, so B’s new share is \(\frac{4}{5+4}=\frac{4}{9}\). Therefore, B’s gaining share = new share − old share = \(\frac{4}{9}-\frac{3}{9}=\frac{1}{9}\). Option C is only B’s old share, not the gain. Exam tip: Calculate a gaining share as the new share minus the old share.

Correct answer: A. 1:1

Under the old ratio 3:5:2, A’s share was 3/10 and B’s share was 5/10. Under the new ratio 2:3, A’s share becomes 2/5 = 4/10 and B’s share becomes 3/5 = 6/10. Thus, A gains 4/10 − 3/10 = 1/10, while B gains 6/10 − 5/10 = 1/10. Therefore, their gaining ratio is 1/10:1/10 = 1:1. Remember that 2:3 is the new ratio, not the gaining ratio.

Correct answer: A. 1:1

The old shares are A = 2/10, B = 3/10 and C = 5/10. When C retires, C’s 5/10 share is acquired by A and B in the ratio 3:2. Hence A receives 3/10 and B receives 2/10 from C’s share. Their new shares become A = 2/10 + 3/10 = 5/10 and B = 3/10 + 2/10 = 5/10.

Both continuing partners therefore receive equal portions of future profits. The final ratio is 5:5, which reduces to 1:1. The ratio 3:2 is only the acquisition ratio and cannot be used alone as the new ratio. Thus option A, 1:1, is correct; option D expresses the same ratio before simplification but is not the selected answer.

Correct answer: A. 2:3

C’s original share is \(3/10\). Since A and B acquire it in the ratio 1:2, A receives \(1/10\) and B receives \(2/10\). A’s new share is \(3/10+1/10=4/10\), while B’s new share is \(4/10+2/10=6/10\). Therefore, the new ratio is \(4:6=2:3\). Remember that 1:2 is the ratio in which the retiring partner’s share is acquired, not the new profit-sharing ratio.

Correct answer: A. 19:11

A’s original share is \(2/10=1/5\). B acquires \(2/3\) of A’s share, i.e. \(2/15\), while C acquires \(1/3\), i.e. \(1/15\). Thus, B’s new share is \(5/10+2/15=19/30\), and C’s new share is \(3/10+1/15=11/30\). Therefore, the new ratio is \(19/30:11/30=19:11\). Exam tip: First calculate the retiring partner’s share, then distribute it among the gaining partners in the stated gaining ratio.

Correct answer: A. 17:3

The direct answer is option A, 17:3. Take the total profit as 10 equal parts. A has 8/10, B has 1/10 and C has 1/10. B dies, and A and C take B's 1/10 equally. Half of 1/10 is 1/20, so A receives 1/20 and C also receives 1/20. A's new share is 8/10 + 1/20 = 16/20 + 1/20 = 17/20. C's new share is 1/10 + 1/20 = 2/20 + 1/20 = 3/20. Removing the common denominator 20 gives the new ratio 17:3. Option A is correct. Option B, 8:1, merely keeps A's old part and C's old part and ignores the transferred share. Option C, 9:2, incorrectly adds whole parts instead of half of B's share. Option D, 1:1, ignores that A already had a much larger share. Exam cue: first convert the old ratio into fractions, divide the deceased partner's share as instructed, and add each gain to the continuing partner's old share.

Correct answer: A. 2:3:1

The direct answer is option A, 2:3:1. The old ratio is A:B:C:D = 2:3:1:4. When D retires, only D leaves; the question gives no special instruction about how D's share will be acquired. In this standard partnership-accounting situation, the continuing partners' old mutual ratio remains unchanged unless another ratio is specifically stated. Therefore A, B and C continue in the ratio 2:3:1. Option A is correct. Option B, 2:3:4, incorrectly includes D's four parts even though D has retired. Option C, 3:1:4, changes the order and again includes D, so it cannot be the ratio of A, B and C after D's retirement. Option D, 1:1:1, assumes equal sharing, which is not given and conflicts with the old mutual ratio. The total old parts were 10, but the common factor is not important; after D's share is dealt with without any stated change, the relative shares of A, B and C remain 2, 3 and 1. Memory cue: no information means preserve the continuing partners' old mutual ratio.

Correct answer: A. 7:10:13

D’s old share was 4 out of 10, i.e. 4/10. Since this share is acquired equally by A, B and C, each receives 4/30. Therefore, their new shares are 1/10 + 4/30 = 7/30, 2/10 + 4/30 = 10/30, and 3/10 + 4/30 = 13/30. Hence, the new ratio is 7:10:13. Exam tip: When the retiring partner’s share is acquired equally, add an equal fraction of that share to each continuing partner’s old share.

Correct answer: A. 7:10:3

B’s share is 2/10. Dividing it in the ratio 1:2:1 gives A an additional 1/20, C an additional 1/10, and D an additional 1/20. Therefore, the new shares are A = 3/10 + 1/20 = 7/20, C = 4/10 + 1/10 = 10/20, and D = 1/10 + 1/20 = 3/20. Hence, the new ratio is 7:10:3. The ratio 1:2:1 represents only the distribution of B’s acquired share, not the final profit-sharing ratio. Exam tip: First calculate the retiring partner’s share, then distribute it according to the stated acquisition ratio.

Correct answer: A. 2:1:1

C share is 3/10. A gets 1/10 B gets 3/20 and D gets 1/20 so new shares are 10/20 5/20 and 5/20.

Correct answer: A. 5:2:2

When share is taken in old ratio the mutual ratio of continuing partners remains unchanged. Therefore A B C new ratio is 5:2:2.

Correct answer: A. 9:3:8

Direct answer: Option A, 9:3:8. The total old ratio is 2+4+1+3=10. A’s share is 2/10. This share is taken by B, C and D in 1:1:2, whose total is 4. B receives (2/10)×(1/4)=1/20; C also receives 1/20; D receives (2/10)×(2/4)=1/10. B’s new share is 4/10+1/20=8/20+1/20=9/20. C’s new share is 1/10+1/20=2/20+1/20=3/20. D’s new share is 3/10+1/10=6/20+2/20=8/20. Thus the ratio is 9:3:8. Option A is correct. Option B, 4:1:3, is only the old ratio of B, C and D. Option C, 1:1:2, is their receiving ratio, not the final ratio. Option D, 8:2:6, is an incorrect scaling and totals only 16 units rather than 20. Check that 9+3+8=20.

Correct answer: A. To share future profits and losses

After retirement only continuing partners run the firm. Therefore future profits and losses are shared in new ratio.

Correct answer: A. Goodwill compensation of retiring partner

Gaining ratio shows who received extra profit share. Therefore goodwill compensation is made in this ratio.

Correct answer: A. Old mutual ratio of continuing partners will be new ratio

Without extra information continuing partners remain in their old mutual ratio. This is the common exam rule.

Correct answer: A. 4:7

Gaining ratio is the same ratio in which continuing partners acquire extra share. Hence it will be 4:7.

Correct answer: A. In the given new ratio

When new ratio is clearly given future profits and losses are shared in that ratio. Gaining ratio only shows extra share.

Correct answer: A. Sacrifice

When a continuing partner’s new share is lower than his old share, he gives up a part of his profit share. Therefore, sacrifice = old share − new share. Gain applies when the new share is greater than the old share. In examinations, an increase in share indicates gain, while a decrease indicates sacrifice.

Correct answer: A. ३:२

Under the old ratio, A’s share was 2/10 and B’s share was 3/10. Under the new 5:5 ratio, each receives 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, the gaining ratio is 3:2. Exam tip: Calculate each partner’s gain as new share minus old share; the new ratio itself is not the gaining ratio.

Correct answer: A. Using gaining ratio for future profits

Future profits are shared in new ratio. Gaining ratio is used only for extra share and goodwill adjustment.

Correct answer: A. 7:3

C share is 4/15. Dividing it in 5:3 makes A and B new shares 7/10 and 3/10 so the ratio is 7:3.

Correct answer: A. 11:14

B’s share is 2/10. A and C acquire it in the ratio 1:4, so A gains 2/10 × 1/5 = 1/25 and C gains 2/10 × 4/5 = 4/25. A’s new share is 4/10 + 1/25 = 11/25, while C’s new share is 4/10 + 4/25 = 14/25. Therefore, the new ratio is 11:14. Exam tip: First divide the deceased partner’s share according to the gaining ratio, then add each gain to the partner’s old share.

Correct answer: A. 1/15

The total old ratio is 9+5+1=15, so A’s old share is 9/15. After C’s retirement, A’s new share is 2/(2+1)=2/3=10/15. Therefore, A’s gaining share = new share − old share = 10/15−9/15=1/15. Option C represents A’s old share, not the share gained. Exam tip: Always calculate the gain by subtracting the old share from the new share.

Correct answer: A. B sacrificed 1/15 share

B old share is 5/15 and new share is 1/3 or 5/15. There is no change so no gain or sacrifice occurs.

Correct answer: A. Only A gained share

A share increased from 9/15 to 10/15 and B share remained 5/15. Therefore only A gained C share.