New Profit Sharing Ratio

Correct answer: A. (1:1:1)

The old partners' remaining share is (2/3), so each gets (1/3). The new partner also gets (1/3).

Correct answer: A. (8:5:5:2)

The total of the old ratio is 20, so the old shares are 9/20, 6/20 and 5/20. The new partner’s share is 1/10 = 2/20. Since it is acquired equally from the first and second partners, each of them sacrifices 1/20. The revised shares are therefore 8/20, 5/20, 5/20 and 2/20, giving the new ratio 8:5:5:2. Option B is incorrect because it adds the new partner without reducing the old partners’ shares. Exam tip: when the sacrifice is equal, divide the incoming partner’s share equally among the contributing partners before forming the ratio.

Correct answer: A. \(\frac{1}{5}\)

After admission, the new shares of all partners must add up to 1. Therefore, the second old partner's share is \(1-\frac{3}{5}-\frac{1}{5}=\frac{1}{5}\). Choosing \(\frac{2}{5}\) would make the total exceed 1, so it is incorrect. Exam tip: For a missing-share question, subtract the sum of all given shares from 1.

Correct answer: A. (3:4:8:5)

The old partners’ shares are \(1/5, 3/10, 1/2\). The new partner’s \(1/4\) share is surrendered in the ratio 1:2:2, so the sacrifices are \(1/20, 1/10, 1/10\), respectively. Thus, the old partners’ new shares are \(1/5-1/20=3/20\), \(3/10-1/10=1/5\), and \(1/2-1/10=2/5\). The new partner retains \(1/4\). Multiplying all shares by 20 gives the ratio 3:4:8:5. Option B results from assuming equal sacrifice, so it is incorrect. Exam tip: Convert the old ratio into fractions first, then distribute the incoming partner’s share according to the sacrificing ratio.

Correct answer: A. 99:81:40

Teena receives 2/11, so the share left for the old partners is 1 − 2/11 = 9/11. Distributing this in the old ratio 11:9 gives Reena (9/11) × (11/20) = 9/20 = 99/220 and Meena (9/11) × (9/20) = 81/220. Teena’s share is 2/11 = 40/220. Therefore, the new ratio is 99:81:40. Option B is incorrect because it treats 2/11 directly as a ratio term instead of allocating the remaining profit in the old ratio. Exam tip: find the remaining share first, then distribute it according to the old ratio.

Correct answer: A. (12:8:5:5)

The first and second sacrifice in (3:2). Their sacrifices are (1/10) and (1/15), and the new shares are (2/5,4/15,1/6,1/6).

Correct answer: A. (25:16)

Old shares are (5/8,3/8) and new shares are (7/16,4/16). The sacrifices are (3/16) and (1/8), so the sacrificing ratio is (3:2).

Correct answer: A. पुराने लाभ-विभाजन अनुपात में

When the sacrificing ratio is unavailable, goodwill brought by the incoming partner is credited to old partners in their old profit-sharing ratio, reflecting their existing profit rights. The new ratio applies after admission. Exam tip: check the sacrificing ratio first.

Correct answer: A. (50:30:20:30)

The old partners' total share is (10/13). Dividing it in (5:3:2) gives (5/13,3/13,2/13) and the new partner gets (3/13).

Correct answer: A. 4:2:1:3

The old shares are 5/10, 2/10 and 3/10. The new partner takes 1/10 from the first, leaving 4/10, and takes 1/5=2/10 from the third, leaving 1/10. The second partner is unchanged at 2/10. The new partner receives 1/10+2/10=3/10. Hence the new ratio is 4:2:1:3, so option A is correct.

Correct answer: A. (1:3:4:2)

The correct answer is option A: (1:3:4:2). The old ratio 1:2:2 means the original shares are 1/5, 2/5 and 2/5. The new partner receives 1/5, and the first two old partners sacrifice equally. Their total sacrifice must be 1/5, so each sacrifices 1/10. The first partner keeps 1/5 − 1/10 = 1/10. The second keeps 2/5 − 1/10 = 3/10. The third sacrifices nothing and keeps 2/5. The new partner gets 1/5. Taking denominator 10 gives 1:3:4:2. Option A exactly matches. Option B gives the first partner 2/12, not 1/10, and its total is not based on the calculation. Option C leaves the second partner unchanged, although that partner must sacrifice 1/10. Option D makes the first partner’s share too large and does not show equal sacrifice by the first two. Exam cue: distribute the incoming partner’s share among sacrificing partners according to the stated sacrifice condition.

Correct answer: A. Share (1/6), sacrifice (1:1)

The old partners' new shares are (2/6) and (3/6), and the new partner has (1/6). Comparing with old shares shows equal sacrifice.

Correct answer: A. 1/8

The new profit shares of all partners must add up to 1. Therefore, the third partner’s share is 1 − 3/8 − 1/4 − 1/4 = 1/8. Thus, option A is correct. Exam tip: After admission, always verify that the sum of all partners’ new shares, including the incoming partner’s share, equals 1.

Correct answer: A. (10/27)

The correct answer is option A: 10/27. The new partner receives 1/6, so the old partners together retain 1 − 1/6 = 5/6. They divide this remaining share in the old ratio 4:3:2. The total of these ratio parts is 9, so the first partner receives 4/9 of the remaining share. Thus the first partner’s new share is (5/6) × (4/9) = 20/54 = 10/27. Option A is therefore correct. Option B, 4/9, is only the first partner’s fraction within the old group; it forgets that the old group now has only 5/6 of the firm. Option C, 5/12, uses an incorrect multiplier. Option D, 8/27, does not follow from 4/9 of 5/6. The safe method is: subtract the newcomer’s share from one, then multiply the remainder by the concerned old partner’s ratio fraction.

Correct answer: A. 0:1

The sacrificing ratio is the ratio of the shares surrendered by the old partners. Here, the new partner obtains the entire 1/5 share from the second partner; therefore, the first partner sacrifices nothing while the second partner sacrifices 1/5. Hence, the sacrificing ratio is 0:1. Exam tip: If the entire new partner’s share is taken from one old partner, the sacrificing ratio is 0:1 or 1:0 accordingly.

Correct answer: C. Third partner

The third partner's old share was (1/2) and new share is (2/5). Actually no old partner has gained.

Correct answer: B. (1:1:2:1)

The first two sacrifice equally because their old ratio is (3:3). The new shares are (1/5,1/5,2/5,1/5).

Correct answer: A. (15:3:4)

The old partners' total share is (3/4). Dividing it in (5:1) gives (5/8) and (1/8), and the new partner has (1/4).

Correct answer: A. 1/10

The new partner’s 3/10 share is the old partners’ total sacrifice. The first partner gives up 1/5 = 2/10, so the second partner gives up the remainder: 3/10 − 2/10 = 1/10.

Correct answer: A. (15:9:4:6)

The second sacrifices (1/18) and the third sacrifices (1/9). The new shares are (5/12,5/18,5/36,1/6), giving (15:10:5:6).

Correct answer: A. (1:1:1:1)

The old partners' remaining total is (3/4). The three old partners share it equally, so each gets (1/4).

Correct answer: A. (28:21:14:9)

The old partners' total share is (7/8). Dividing it in (4:3:2) gives (28/72,21/72,14/72), and the new partner has (9/72).

Correct answer: A. (1:1:1)

The first becomes (1/2). The second sacrifices (1/10) to complete the total sacrifice and becomes (3/10), while the new partner has (1/5).

Correct answer: A. 1:4:3:2

The old partners hold 2/10, 5/10 and 3/10, respectively. The first partner's revised share is 2/10 − 1/10 = 1/10, while the second partner's revised share is 5/10 − 1/10 = 4/10. The third partner's share remains 3/10, and the new partner receives 1/10 + 1/10 = 2/10. Therefore, the new ratio is 1:4:3:2. Option B is incorrect because it does not deduct the transferred shares from the first two partners. Exam tip: When the incoming partner obtains shares from specified partners, deduct each specified portion from its respective source partner before forming the final ratio.

Correct answer: A. 15:20:14

The new partner’s 2/7 share is sacrificed by the old partners in the ratio 3:4. Their original shares are 3/7 and 4/7, while their sacrifices are 6/49 and 8/49 respectively. Thus, their new shares become 15/49 and 20/49. The new partner’s share is 2/7 = 14/49. Therefore, the new ratio is 15:20:14. Exam tip: Deduct the incoming partner’s share from the old partners in the old ratio before writing the new ratio.