New Profit Sharing Ratio

B’s old share was \(1/10\). Since C’s \(1/10\) share is sacrificed by A and B in the ratio \(4:1\), B sacrifices \(1/5\) of it, i.e. \(1/10 \times 1/5 = 1/50\). Therefore, B’s new share is \(1/10 - 1/50 = 5/50 - 1/50 = 4/50 = 2/25\). Exam tip: Divide the incoming partner’s share according to the sacrificing ratio before subtracting each partner’s sacrifice from the old share.

C receives 3/11 of the total profit, so the remaining share for A and B is 1 − 3/11 = 8/11. Dividing this remaining share in the old ratio 5:6 gives A's share as (8/11) × (5/11) = 40/121 and B's share as (8/11) × (6/11) = 48/121. C's share, 3/11, equals 33/121. Therefore, the new ratio is 40:48:33. Option B is incorrect because it simply combines the old ratio with C's stated fraction without allocating the remaining profit. Exam tip: calculate the balance share first, distribute it in the old ratio, and then express all partners' shares with a common denominator.

Taking the share in the old ratio means the sacrifice is also in the old ratio. If the question gives another basis follow it.

Under the old ratio 10:3, A and B receive 10/13 and 3/13, respectively. C’s 1/13 share is sacrificed by A and B in the ratio 3:2, so A sacrifices 3/65 and B sacrifices 2/65. Therefore, the new shares are A = 10/13 − 3/65 = 47/65, B = 3/13 − 2/65 = 13/65, and C = 1/13 = 5/65. Hence, the new profit-sharing ratio is 47:13:5. Exam tip: Convert the old shares to a common denominator before subtracting the sacrificed shares.

A and B's old shares are 6/11 and 5/11. C receives 1/11, which A and B sacrifice in the ratio 5:6, so their sacrifices are 5/121 and 6/121. Their new shares are 6/11 − 5/121 = 61/121 and 5/11 − 6/121 = 49/121; C's share is 1/11 = 11/121. Therefore, the new profit-sharing ratio is 61:49:11.

After allocating \(\frac{3}{11}\) of the profit to C, the remaining profit is \(1-\frac{3}{11}=\frac{8}{11}\). This remainder is shared by A and B in their old ratio of 7:4. Therefore, A’s new share is \(\frac{8}{11}\times\frac{7}{11}=\frac{56}{121}\). Option B is only A’s old share, not the revised share. Exam tip: first calculate the remaining profit, then multiply it by the concerned partner’s old fraction.

Both statements are correct. After admission future profits are shared by all old and new partners.

C’s share is \(\frac{4}{13}\), so the profit remaining for A and B is \(1-\frac{4}{13}=\frac{9}{13}\). A receives \(\frac{9}{13}\times\frac{6}{13}=\frac{54}{169}\), B receives \(\frac{9}{13}\times\frac{7}{13}=\frac{63}{169}\), and C receives \(\frac{4}{13}=\frac{52}{169}\). Therefore, the new ratio is \(54:63:52\). Option B is incorrect because \(4:13\) represents C’s share, not the new profit-sharing ratio. Exam tip: First subtract the new partner’s share from 1, then distribute the remainder in the old partners’ original ratio.

C receives 1/5 of the total profit, so 4/5 remains for A and B. Distributing this remainder in the old ratio 13:7 gives A \(\frac{4}{5}\times\frac{13}{20}=\frac{13}{25}\) and B \(\frac{4}{5}\times\frac{7}{20}=\frac{7}{25}\). C's share is \(\frac{1}{5}=\frac{5}{25}\). Therefore, the new ratio is 13:7:5. Option D incorrectly doubles the old components without making the required adjustment. Exam tip: first subtract the incoming partner's share from 1, then distribute the remainder in the old ratio.

A and B initially have shares \(3/11=15/55\) and \(8/11=40/55\), respectively. C’s share is \(2/11=10/55\). Since the sacrificing ratio is 4:1, A sacrifices \(8/55\) and B sacrifices \(2/55\). Thus, A’s new share is \(15/55-8/55=7/55\), B’s is \(40/55-2/55=38/55\), and C’s is \(10/55\). Therefore, the new ratio is 7:38:10. Exam tip: Convert all shares to a common denominator before distributing the new partner’s share in the sacrificing ratio.

A's sacrifice is (5/12-7/20=4/60) and B's sacrifice is (7/12-8/20=11/60). So the sacrificing ratio is (4:11).

The governing concept is source-specific sacrifice: when the incoming partner’s share is taken entirely from one old partner, the other old partner’s share does not change. The old ratio 9:8 has total 17, so A’s original share is 9/17 and B’s original share is 8/17. C receives 2/17 from A alone, reducing A to 7/17. B makes no sacrifice and therefore continues to receive 8/17. Hence option A is correct. Option C confuses B’s share with A’s original share; option D is C’s incoming share, and option B has no basis because nothing is deducted from B.

A's old share is \(\frac{6}{6+7}=\frac{6}{13}\). Since C receives a total share of \(\frac{1}{13}\) and the sacrifice ratio is \(2:3\), A's sacrifice is \(\frac{1}{13}\times\frac{2}{5}=\frac{2}{65}\). Therefore, A's new share is \(\frac{6}{13}-\frac{2}{65}=\frac{30-2}{65}=\frac{28}{65}\). Exam tip: Deduct the new partner's share from each old partner according to the stated sacrificing ratio.

A's old share was (4/9) and new share is (5/15). Both old partners' shares decrease so the correct answer should be none.

Under the old ratio, A’s share was 4/9 = 20/45, while B’s share was 5/9 = 25/45. Under the new ratio, A’s share is 7/15 = 21/45 and B’s share is 6/15 = 18/45. Therefore, A’s share has increased by 1/45, whereas B’s share has decreased. Hence, A is the correct answer. Exam tip: Convert the old and new shares to a common denominator before comparing them.

The governing concept is the new profit-sharing ratio after admission. C receives 3/19, so the balance for A and B is 1 − 3/19 = 16/19. This balance must be divided in their old ratio, 14:5, whose total is 19. Therefore, A receives 16/19 × 14/19 = 224/361, while B receives 16/19 × 5/19 = 80/361. C’s share is 3/19 = 57/361. Taking the common denominator 361, the new ratio is 224:80:57, so option A is correct. Options B and C fail to apply the reduced balance correctly, while D does not preserve the stated shares.

After C’s admission, the sum of the new profit shares of A, B and C must be 1. Therefore, B’s new share = \(1-\frac{4}{11}-\frac{2}{11}=\frac{5}{11}\). The old ratio 5:6 provides context, but B’s new share can be found directly from the given new shares of A and C. Exam tip: subtract the known new shares from the total profit share, 1.

C’s share is 1/5, so A and B together sacrifice 1/5. In the sacrificing ratio 3:2, A sacrifices \(\frac{3}{25}\) and B sacrifices \(\frac{2}{25}\). Therefore, A’s new share is \(\frac{11}{20}-\frac{3}{25}=\frac{43}{100}\), and B’s new share is \(\frac{9}{20}-\frac{2}{25}=\frac{37}{100}\). C receives \(\frac{1}{5}=\frac{20}{100}\). Hence, the new profit-sharing ratio is 43:37:20. Option B does not correctly subtract the sacrificed portions from the old shares. Exam tip: Calculate each partner’s sacrifice first, then subtract it from the partner’s original share.

A's share changed from (5/8) to (6/10) so A gained. B's share fell from (3/8) to (3/10), so C's effective share came from B.

A's share changed from (5/8) to (6/10), so A gained. B's share decreased from (3/8) to (3/10), so only B sacrificed.

The governing rule is that each existing partner’s sacrifice equals the incoming partner’s share multiplied by that partner’s fraction in the sacrificing ratio. C’s share is 1/10. Since A and B sacrifice in 1:4, A sacrifices 1/10 × 1/5 = 1/50 and B sacrifices 1/10 × 4/5 = 4/50 = 2/25. A’s old share is 7/10 = 35/50, so A’s new share is 34/50. B’s old share is 3/10 = 15/50, so B’s new share is 11/50; C has 5/50. Thus the ratio is 34:11:5. Therefore the supplied option set needs correction: none of the original options is correct.

The direct answer is option B, 7/35 and 28/35. The ratio 17:11:7 has total parts 17 + 11 + 7 = 35. C is the partner represented by the last number, 7, so C’s share is 7/35, which simplifies to 1/5. The old partners are represented by 17 and 11, so their combined share is (17 + 11)/35 = 28/35, which simplifies to 4/5. Option B gives both required fractions exactly. Option A, 1/5 and 4/5, is mathematically equivalent, but it is not written in the ratio’s common denominator form; if only one answer is expected, B is the more exact listed form. Option C, 7/28 and 21/28, totals only 1 for a different division and does not use the given total parts correctly. Option D, 7/35 and 17/35, leaves out 11/35. Add all shares to check: 7/35 + 28/35 = 1.

B’s old share is \(\frac{11}{20}\). Since the sacrificing ratio of A and B is 2:1, B sacrifices \(\frac{1}{3}\) of C’s share, i.e. \(\frac{1}{3}\times\frac{3}{20}=\frac{1}{20}\). Therefore, B’s new share is \(\frac{11}{20}-\frac{1}{20}=\frac{10}{20}=\frac{1}{2}\). Exam tip: a sacrificing partner’s new share is calculated by subtracting the share sacrificed from the old share.

A's sacrifice is (8/15-9/20=5/60) and B's sacrifice is (7/15-6/20=10/60). The correct sacrificing ratio is (1:2).

The governing concept is the distribution of the incoming partner’s share according to the sacrificing ratio. C receives 3/18 of the total profit, and A contributes 5 parts out of the total 5 + 4 = 9 parts of the sacrifice. Therefore, A’s sacrifice is 3/18 × 5/9 = 15/162. Reducing this fraction by 3 gives 5/54. Hence option A is correct. Option B is C’s entire share and ignores the stated 5:4 division. Option C assigns B’s proportion of the sacrifice to A, while option D incorrectly applies the ratio without dividing by the total of its parts. The individual sacrifices together equal 5/54 + 4/54 = 9/54 = 1/6, which is exactly 3/18.