New Profit Sharing Ratio

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

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.

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.

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.

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.

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).

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).

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.

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).

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.

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.

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.

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.

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.

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.

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

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

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).

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.

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).

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

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).

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).

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.

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.