New Profit Sharing Ratio

The old ratio 2:3:5 has a total of 10 parts, so A, B and C hold 2/10, 3/10 and 5/10 respectively. D’s 1/10 share is taken entirely from C; therefore, C’s new share is 5/10 − 1/10 = 4/10. The new ratio is 2/10:3/10:4/10:1/10, or 2:3:4:1. Exam tip: When a new partner’s share is acquired entirely from one old partner, the shares of the other partners remain unchanged.

A’s old share is 4/7 = 12/21. After giving 2/21 to C, A’s new share is 12/21 − 2/21 = 10/21. B’s old share is 3/7 = 9/21; after giving 1/21, B retains 8/21. C receives 1/7 = 3/21. Therefore, the new ratio is 10/21 : 8/21 : 3/21 = 10 : 8 : 3. Exam tip: Convert all shares to a common denominator before subtracting the sacrificing portions.

A's sacrifice is (5/9-4/9=1/9). Total sacrifice is (2/9) so B's sacrifice is also (1/9) and the ratio is (1:1).

A's sacrifice is (1/9) and B's new share is (1-4/9-2/9=3/9). B's sacrifice is (4/9-3/9=1/9) so the ratio is (1:1).

C's (1/6) share is sacrificed in (3:2) so A gives (1/10) and B gives (1/15). New shares are (58/120) (42/120) and (20/120) so simplified ratio is also (29:21:10).

A's new share is (7/12-1/10=29/60) and B's is (5/12-1/15=21/60). C is (10/60) so the correct ratio is (29:21:10).

The correct answer is A. D receives 1/9, and this is sacrificed in the ratio 2:1:1. The total sacrifice parts are 4, so A sacrifices 2/36 = 1/18, while B and C each sacrifice 1/36. Convert the old ratio 4:3:2 into denominator 36: A = 16/36, B = 12/36 and C = 8/36. Subtract the sacrifices: A = 14/36, B = 11/36 and C = 7/36. D receives 1/9 = 4/36. Therefore the new ratio is 14:11:7:4. B shows old shares without the correct sacrifice, C simply appends D, and D has incorrect deductions. Check: 14+11+7+4 = 36.

G's total share is (1/5) and Kh gives the balance (1/5-1/8=3/40). With common denominator the new ratio is (31:25:18).

K's share is (5/9-1/8=31/72) and Kh's is (4/9-3/40=133/360) so the common ratio is (155:133:72). None of these options is fully correct so this type needs careful option checking.

C receives \(\frac{1}{4}\) of the profits, and A and B sacrifice this share in the ratio \(1:3\). Therefore, A’s sacrifice is \(\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}\), while B’s sacrifice is \(\frac{1}{4}\times\frac{3}{4}=\frac{3}{16}\). Their old shares are A = \(\frac{3}{5}\) and B = \(\frac{2}{5}\). Hence, A’s new share is \(\frac{3}{5}-\frac{1}{16}=\frac{43}{80}\), B’s new share is \(\frac{2}{5}-\frac{3}{16}=\frac{17}{80}\), and C’s share is \(\frac{1}{4}=\frac{20}{80}\). Thus, the new ratio is \(43:17:20\). Option B is incorrect because it retains the old shares of A and B without deducting their sacrifices. Exam tip: Distribute the incoming partner’s share according to the sacrifice ratio and subtract those amounts from the old partners’ shares.

D's total share is (1/5) and the balance from C is (1/20). The new shares are (40/100) (25/100) (15/100) and (20/100).

Sacrifice is governed by the rule: old share minus new share. Sohan’s old share under the ratio 4:5 was 5/(4+5) = 5/9. Rohan receives 2/9, leaving 1 − 2/9 = 7/9 for Mohan and Sohan. This balance is divided in their new ratio 5:2, whose total is 7. Sohan therefore receives (7/9) × (2/7) = 2/9 as his new share. His sacrifice is 5/9 − 2/9 = 3/9 = 1/3. Thus option A is correct. Option B is only Sohan’s new share, option C does not represent the difference between old and new shares, and option D is his old share rather than his sacrifice.

The shares of all partners in the reconstituted firm must add up to 1. Therefore, Seema’s share is \(1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\). If Seema’s share were \(\frac{3}{8}\), the total would become \(\frac{9}{8}\), which is impossible. Exam tip: subtract the known shares from 1 to find a missing share in the new profit-sharing ratio.

Old partners retain (4/5) and in (3:1) A's new share is (3/5). A's old share was (8/15) so the gain is (1/15).

A's sacrifice is (7/10\times1/7=1/10). B gives the balance (1/10) so the new shares are (6/10) (2/10) and (2/10).

Payal’s old profit share was \(5/8\). Since the sacrifice ratio is 3:1, Payal sacrifices \(1/4\) of Riya’s \(1/8\) share, i.e. \(1/8 \times 1/4 = 1/32\). Therefore, Payal’s new share is \(5/8 - 1/32 = 20/32 - 1/32 = 19/32\). Option B is only Payal’s old share and does not account for the sacrifice. Exam tip: For each old partner, individual sacrifice equals the incoming partner’s share multiplied by that partner’s proportion in the sacrifice ratio.

A and C do not change. B becomes (5/10-1/10=4/10) so old partners' new mutual ratio is (2:4:3).

The old shares of A and B are \(11/20\) and \(9/20\), respectively. C receives \(1/4\) of the total profit. Since A and B sacrifice this share equally, each sacrifices \(1/8\). Therefore, A’s new share is \(11/20 - 1/8 = 17/40\), B’s new share is \(9/20 - 1/8 = 13/40\), and C’s share is \(1/4 = 10/40\). Hence, the new ratio is \(17 : 13 : 10\). Exam tip: Under equal sacrifice, subtract half of the incoming partner’s share from each existing partner’s share.

A's old share is 4/7 = 12/21, and B's old share is 3/7 = 9/21. After giving up 1/21 and 2/21 respectively, their new shares are 11/21 and 7/21. C receives 1/7 = 3/21. Thus, the new ratio is 11:7:3.

The sacrificing ratio is (1:2) so A gives (1/3) of the total sacrifice. In exams first add the total of the ratio.

C’s total profit share is \(\frac{1}{4}\), and B bears \(\frac{2}{3}\) of this sacrifice according to the ratio 1:2. Hence, B’s actual sacrifice is \(\frac{1}{4}\times\frac{2}{3}=\frac{1}{6}\). The fraction \(\frac{1}{12}\) is A’s sacrifice, not B’s. Exam tip: Divide the incoming partner’s share according to the sacrifice ratio to find each old partner’s individual sacrifice.

After C receives \(\frac{2}{11}\) of the profit, the share remaining for A and B is \(1-\frac{2}{11}=\frac{9}{11}\). A receives \(\frac{4}{7}\) of this remaining profit because A and B share it in the ratio 4:3. Therefore, A’s new share is \(\frac{9}{11}\times\frac{4}{7}=\frac{36}{77}\). The value \(\frac{4}{7}\) represents A’s share of the remaining profit only, not of the total profit. In such questions, first calculate the balance profit and then multiply it by the relevant part of the new ratio.

The governing concept is comparison of an existing partner’s old share with the new share after admission. B’s old share in the ratio 6:5 was 5/11, which is 35/77. C receives 2/11, leaving 9/11 for A and B. Their new mutual ratio is 4:3, so B receives 3/7 of this balance: (9/11) × (3/7) = 27/77. B’s sacrifice is therefore old share minus new share, or 35/77 − 27/77 = 8/77. Since the new share is smaller, B sacrifices rather than gains. Hence option A is correct. Option B reverses the comparison, option C uses an incorrect difference, and option D ignores the change in the ratio.

The old shares of A and B are 6/11 and 5/11. C receives 2/11, so the balance left for A and B is 9/11. This remaining profit is divided between A and B in the new ratio 4:3. Thus B’s new share is \\(9/11\\times3/7=27/77\\). To compare fairly, B’s old share becomes \\(5/11=35/77\\).

Sacrifice is calculated as old share minus new share. Therefore B sacrifices \\(35/77-27/77=8/77\\). This agrees with option A. The answer is not 16/77 because that would double the actual difference, and 2/11 is C’s share rather than B’s sacrifice. The ratio and the admission share must be handled separately.

Old partners retain (5/6) and it is divided in (3:4:5). The new shares are (15/72) (20/72) (25/72) and (12/72).