New Profit Sharing Ratio

Correct answer: A. A : B : C = 8 : 8 : 4

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.

Correct answer: A. 29/60

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.

Correct answer: A. (1/5)

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).

Correct answer: A. \(\frac{7}{12}\)

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.

Correct answer: A. 65:39:24

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.

Correct answer: A. A : B : C : D = 5:5:4:2

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.

Correct answer: A. It will decrease to \(\frac{1}{4}\)

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.

Correct answer: A. A B C (5:5:4)

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.

Correct answer: A. 60:50:11

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.

Correct answer: A. 1:1

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.

Correct answer: A. Sacrifice (13/45)

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).

Correct answer: A. A gained (0) and B sacrificed

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.

Correct answer: A. 1:2

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.

Correct answer: A. B’s new profit share will be 1/12

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.

Correct answer: A. A : B : C = 27 : 13 : 10

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.

Correct answer: A. \(\frac{2}{7}\)

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.

Correct answer: A. A:B:C = 7:9:2

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.

Correct answer: A. A B C D (25:20:15:12)

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.

Correct answer: A. A : B : C = 13 : 11 : 6

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.

Correct answer: A. A gains \(\frac{1}{20}\)

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.

Correct answer: A. 3/10

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.

Correct answer: A. A : B : C = 1 : 2 : 1

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.

Correct answer: A. A:B:C = 8:0:2

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.

Correct answer: A. 3/20

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.

Correct answer: A. (1/5)

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.