New Profit Sharing Ratio

Since A and B share profits in the ratio 11:9, their old shares are 11/20 and 9/20, respectively. A’s new share is 11/20 − 3/20 = 8/20, and B’s new share is 9/20 − 1/20 = 8/20. C’s share is 1/5 = 4/20. Therefore, the new ratio is 8/20 : 8/20 : 4/20 = 8:8:4. Option B is incorrect because it adds C’s share without reducing A’s and B’s shares. Exam tip: subtract the portion surrendered by each old partner from that partner’s original share.

B’s old share was 7/(5 + 7) = 7/12. Since A and B sacrifice for C in the ratio 2:3, B bears 3/5 of C’s 1/6 share: (3/5) × (1/6) = 1/10. So B’s new share is 7/12 − 1/10 = 35/60 − 6/60 = 29/60.

A's old share was (2/5=8/20) and new share is (7/20) so sacrifice is (1/20). Total sacrifice is (1/4=5/20) so the part is (1/5).

The new profit shares of A, B and C must add up to 1. Therefore, B’s new share = \(1-\frac{1}{4}-\frac{1}{6}=\frac{12-3-2}{12}=\frac{7}{12}\). Hence, option A is correct. The old ratio of 1:2 is useful for checking consistency, but once A’s new share and C’s share are given, B’s share is the remaining portion of the total profit.

After C receives 3/16, the total share left for A and B is 13/16. Dividing this in their old ratio of 5:3 gives A’s share as (13/16) × (5/8) = 65/128 and B’s share as (13/16) × (3/8) = 39/128. C’s share is 3/16 = 24/128. Therefore, the new ratio is 65:39:24. Exam tip: Subtract the incoming partner’s share from 1, then distribute the balance among the old partners in their old ratio.

The original ratio 3:3:2 has a total of 8 parts, so A and B each have 3/8 and C has 2/8. Since D’s 1/8 share is taken equally from A and B, subtract 1/16 from each: A = 3/8 − 1/16 = 5/16, B = 5/16, C = 2/8 = 4/16, and D = 1/8 = 2/16. Therefore, the new ratio is 5:5:4:2. Exam tip: reduce the shares only of those existing partners who sacrifice a portion for the incoming partner.

A’s old share is \(\frac{3}{3+7}=\frac{3}{10}\). Since A and B sacrifice C’s \(\frac{1}{5}\) share in the ratio 1:3, A’s sacrifice is \(\frac{1}{5}\times\frac{1}{1+3}=\frac{1}{20}\). Therefore, A’s new share is \(\frac{3}{10}-\frac{1}{20}=\frac{6}{20}-\frac{1}{20}=\frac{1}{4}\). Thus, A’s share decreases to \(\frac{1}{4}\). Option D is incorrect because it treats the entire sacrificed share as A’s sacrifice, whereas A sacrifices only one-fourth of it. Exam tip: Subtract the sacrificing partner’s share of the incoming partner’s share from the old share.

Direct answer: The new ratio is A:B:C = 5:5:4, so option A is correct. C receives \(2/7\), so A and B together retain \(1−2/7=5/7\). The question says they share this remainder equally, so A gets \(5/14\) and B also gets \(5/14\). C's share is \(2/7=4/14\). Thus the common-denominator shares are 5/14, 5/14, and 4/14, giving 5:5:4. Option A is correct. Option B wrongly continues the old ratio 4:3, although the question expressly says the remainder is equal. Option C has equal old-partner numbers but incorrectly doubles the new partner's share. Option D gives C 2/14 instead of 4/14. Read the condition about equal sharing carefully.

C’s 1/11 share is sacrificed by A and B in their old ratio of 6:5. Thus, A’s sacrifice is 6/11 × 1/11 = 6/121 and B’s sacrifice is 5/11 × 1/11 = 5/121. A’s new share is 6/11 − 6/121 = 60/121, B’s new share is 5/11 − 5/121 = 50/121, and C’s share is 1/11 = 11/121. Therefore, the new ratio is 60:50:11. Exam tip: If the incoming partner’s share is sacrificed in the old ratio, distribute the sacrifice among the old partners in that same ratio.

C receives a total profit share of 1/5, so the combined sacrifice of A and B must also be 1/5. Since A sacrifices 1/10, B’s sacrifice is 1/5 − 1/10 = 1/10. Therefore, the sacrificing ratio is 1/10 : 1/10 = 1:1. Exam tip: the new partner’s share equals the total sacrifice made by the old partners.

A's new share is (2/3\times2/5=4/15) while old share was (5/9). So A sacrifices (5/9-4/15=13/45).

Old partners retain (3/4) and in (2:1) A's new share is (1/2). A's old share was also (1/2) so A did not gain and B sacrificed.

The governing concept is that the admitted partner’s share is deducted from the specified sacrificing partner, while the other existing partner’s share remains unchanged. The old ratio 2:5 totals 7, so A’s old share is 2/7 and B’s old share is 5/7. C receives 1/7 entirely from B. Therefore B’s new share is 5/7 − 1/7 = 4/7, while A continues to receive 2/7. The new mutual ratio of A and B is 2/7:4/7 = 2:4, which simplifies to 1:2. Hence option A is correct. Option B is merely the old ratio. Options C and D do not represent the stated deduction of 1/7 from B’s share.

B’s old share was 1/6 because A and B shared profits in the ratio 5:1. B sacrifices 1/12 in favour of C, so B’s new share = 1/6 − 1/12 = 2/12 − 1/12 = 1/12. Therefore, option A is correct. Exam tip: Subtract the portion sacrificed by an old partner from that partner’s old share to find the new share.

A's and B's old shares are 7/10 and 3/10. C's 1/5 share is sacrificed in the ratio 4:1, so A sacrifices 1/5 × 4/5 = 4/25 and B sacrifices 1/5 × 1/5 = 1/25. Their new shares are 7/10 − 4/25 = 27/50 and 3/10 − 1/25 = 13/50; C has 1/5 = 10/50. Therefore, the new ratio is 27:13:10.

The sum of all partners’ new profit shares must be 1. Therefore, A’s new share = \(1-\frac{3}{7}-\frac{2}{7}=\frac{2}{7}\). Hence, option A is correct. Option B is B’s given new share, not A’s share. Exam tip: subtract the known partners’ shares from the total share of 1 to find the unknown share.

The governing principle is that the incoming partner’s share is supplied through the sacrifices of the old partners. The old shares are A = 4/9 and B = 5/9. C receives 1/9, and A sacrifices 1/18. Therefore B must sacrifice the balance of C’s share: 1/9 − 1/18 = 1/18. A’s new share is 4/9 − 1/18 = 8/18 − 1/18 = 7/18. B’s new share is 5/9 − 1/18 = 10/18 − 1/18 = 9/18. C’s share is 1/9 = 2/18. Hence the new ratio is 7:9:2, so option A is correct. B ignores the required reductions, C reduces A incorrectly, and D merely preserves the old ratio.

Direct answer: The new ratio is A:B:C:D = 25:20:15:12, so option A is correct. The old partners together retain \(1−1/6=5/6\), because D receives \(1/6\). D's share is sacrificed by all old partners in their old ratio 5:4:3. Their fractional parts of the old total are 5/12, 4/12, and 3/12. Thus A gets \(5/6×5/12=25/72\), B gets \(5/6×4/12=20/72\), and C gets \(5/6×3/12=15/72\). D gets \(1/6=12/72\). Hence 25:20:15:12. Option A is correct. B wrongly leaves old shares unchanged. C multiplies old shares without reducing them. D gives incorrect old-partner amounts. Use: retained share × old ratio fraction.

A’s old share is 8/15 and B’s old share is 7/15. C receives 1/5 = 6/30, contributed equally by A and B through 1/10 each. Thus, A’s new share is 8/15 − 1/10 = 13/30, while B’s new share is 7/15 − 1/10 = 11/30. Therefore, the new ratio is 13/30 : 11/30 : 6/30 = 13 : 11 : 6. Exam tip: Convert the old ratio into fractional shares first, then subtract each partner’s sacrifice.

After C receives \(\frac{1}{4}\) of the profits, \(\frac{3}{4}\) remains for A and B. Under their new mutual ratio of 3:2, A’s new share is \(\frac{3}{4}\times\frac{3}{5}=\frac{9}{20}\), whereas A’s old share was \(\frac{2}{5}=\frac{8}{20}\). Therefore, A gains \(\frac{9}{20}-\frac{8}{20}=\frac{1}{20}\). B’s new share is \(\frac{3}{4}\times\frac{2}{5}=\frac{3}{10}\), which is less than B’s old share of \(\frac{3}{5}\), so B sacrifices. Exam tip: First subtract the incoming partner’s share from 1, then distribute the remainder according to the continuing partners’ new mutual ratio.

After C receives 1/5 of the total profit, the remaining share for A and B is 4/5. Under their new mutual ratio of 7:1, B receives \((4/5)\times(1/8)=1/10\). B’s old share was 4/10, or 2/5. Therefore, B’s sacrifice = old share − new share = 2/5 − 1/10 = 3/10. Exam tip: First calculate the profit left for the old partners, then distribute that remainder according to their new mutual ratio.

Under the old ratio 1:3, A's share is 1/4 and B's is 3/4. Since A makes no sacrifice, A retains 1/4. B therefore sacrifices C's entire 1/4 share, leaving B with 3/4 − 1/4 = 1/2. The shares are 1/4:1/2:1/4, which simplify to 1:2:1.

The governing concept is equal sacrifice. C receives 1/5, so A and B each surrender half of that amount: (1/5) ÷ 2 = 1/10. Initially, A’s share is 9/10 and B’s share is 1/10 because their ratio is 9:1. After sacrifice, A’s share becomes 9/10 − 1/10 = 8/10, while B’s share becomes 1/10 − 1/10 = 0. C receives 1/5 = 2/10. Consequently, the new ratio is 8/10:0:2/10, or 8:0:2. Option A is correct. Although a zero share may look unusual, it follows directly from the stated equal-sacrifice condition; option B ignores the sacrifice and the remaining options give incorrect deductions.

The governing concept is that the incoming partner’s share equals the combined sacrifices of the existing partners. A’s old share is 3/5, and A gives up 1/6 of that old share. Thus A’s actual sacrifice is (3/5) × (1/6) = 3/30 = 1/10. C receives a total share of 1/4, so B’s sacrifice is the balance: 1/4 − 1/10. With denominator 20, this is 5/20 − 2/20 = 3/20. Therefore option A is correct. Option B is only A’s sacrifice, option C is C’s total share rather than B’s sacrifice, and option D results from an incorrect subtraction. The calculation also shows that both old partners together surrender exactly 1/4.

Direct answer: Option A, 1/5, is correct. A and B originally share in 7:8, so their old shares are 7/15 and 8/15. C receives 1/3, leaving 2/3 for A and B together. Their new mutual ratio is 1:1, so each receives half of 2/3, which is 1/3. B’s sacrifice is therefore his old share minus his new share: 8/15 − 1/3 = 8/15 − 5/15 = 3/15 = 1/5. Option A is correct. Option B, 1/3, is B’s new share, not his sacrifice. Option C, 2/15, does not follow from subtracting the correct shares. Option D, 1/15, would be the difference between one incorrectly chosen pair of fractions and is not B’s loss. A common mistake is to assume B sacrifices 1/3 merely because C receives 1/3; the incoming share is divided between old partners according to their new mutual ratio. Memory cue: sacrifice = old share − new share.