New Profit Sharing Ratio

Correct answer: A. \(\frac{1}{5}\)

B's old share was 1/5. After C receives 2/5, 3/5 remains for A and B. B gets 2/3 of that remainder, so B's new share is (2/3 × 3/5) = 2/5. B's gain is the new share minus the old share: 2/5 − 1/5 = 1/5.

Correct answer: A. 3/16

The incoming partner’s share is equal to the total sacrifice made by the old partners. Therefore, A and B together sacrifice 1/4 = 4/16. Since A’s sacrifice is 1/16, B’s sacrifice is 4/16 − 1/16 = 3/16. Option 1/8 is incorrect because the total sacrifice need not be divided equally between the old partners. Exam tip: First find the total sacrifice equal to the incoming partner’s share, then subtract the given partner’s sacrifice.

Correct answer: A. A : B : C = 9 : 3 : 4

C's \(\frac{1}{4}\) share is sacrificed by A and B in the ratio 1 : 3. Thus, A sacrifices \(\frac{1}{16}\) and B sacrifices \(\frac{3}{16}\). A's old share was \(\frac{5}{8}=\frac{10}{16}\), so the new share is \(\frac{9}{16}\). B's new share is \(\frac{3}{8}-\frac{3}{16}=\frac{3}{16}\), while C receives \(\frac{4}{16}\). Hence, the new ratio is 9 : 3 : 4. Option B fails to deduct the correct sacrifice from the old shares. Exam tip: The total reduction in the old partners' shares must equal the new partner's admitted share.

Correct answer: A. A B C D (7:6:3:4)

D's share comes from A and C in (3:1) so A sacrifices (3/20) and C (1/20). New shares are (7/20) (6/20) (3/20) and (4/20).

Correct answer: A. (5/18)

The direct answer is A, 5/18. A and B originally share 5:4, so B’s old share is 4/9. C receives 1/3, leaving 2/3 for the old partners. Their new mutual ratio is 3:1, so B receives one of four parts of the remaining 2/3: (2/3) × (1/4) = 1/6. B’s sacrifice is old share minus new share: 4/9 − 1/6 = 8/18 − 3/18 = 5/18. Option A is correct. Option B, 1/9, is too small and does not result from subtraction. Option C, 1/3, is C’s admitted share, not B’s sacrifice. Option D, 4/9, is B’s old share, not the amount surrendered. Exam cue: first distribute the remaining share according to the new mutual ratio.

Correct answer: A. 1/18

The governing rule is that sacrifice equals the old share minus the new share. A’s old share under the 5:4 ratio was 5/9. After C receives 1/3, the balance for A and B is 2/3. Their new mutual ratio is 3:1, so A receives 3/4 of that balance: (2/3) × (3/4) = 1/2. Therefore A’s sacrifice is 5/9 − 1/2. Taking 18 as the common denominator gives 10/18 − 9/18 = 1/18. Hence option A is correct. Option B is not the actual difference, option C is C’s share, and option D is A’s old share. The result also confirms that A’s share decreases after admission.

Correct answer: A. A : B : C = 3 : 1 : 2

C receives \(1/3\) of the profit, so the balance left for A and B is \(1 - 1/3 = 2/3\). This balance is divided in the ratio 3:1; therefore, A receives \(2/3 \times 3/4 = 1/2\) and B receives \(2/3 \times 1/4 = 1/6\). Thus, A:B:C = \(1/2:1/6:1/3\) = 3:1:2. Option B incorrectly uses the old ratio 7:2 directly as part of the new ratio. Exam tip: subtract the incoming partner’s share from one, then divide the remaining share according to the specified ratio of the old partners.

Correct answer: A. No one gained

A falls from (7/9) to (1/2) and B falls from (2/9) to (1/6). Both shares decrease so no old partner gained.

Correct answer: C. 6:1

The governing principle is that when the incoming partner’s entire share is taken from one old partner, only that partner’s share changes. A’s old share under the ratio 8:1 was 8/9. C receives 2/9 entirely from A, so A’s new share becomes 8/9 − 2/9 = 6/9. B does not sacrifice and retains his old share of 1/9. The new mutual ratio of A and B is therefore 6/9:1/9 = 6:1. Hence option C is correct. Option B is merely the old ratio, option D does not subtract the full amount transferred by A, and option A results from an incorrect reduction. The shares also remain consistent with C’s 2/9 admission share.

Correct answer: A. 6:1

In the old ratio 8:1, A’s share was 8/9 and B’s share was 1/9. Since C’s 2/9 share is taken entirely from A, A’s new share becomes 8/9 − 2/9 = 6/9, while B’s share remains 1/9. Therefore, A and B’s new mutual ratio is 6/9 : 1/9 = 6:1. Exam tip: when the incoming partner acquires the share entirely from one existing partner, reduce only that partner’s share.

Correct answer: A. 27/100

B's sacrifice is 1/5 × 1/4 = 1/20, because B contributes one-fourth of the total sacrifice under the 3:1 sacrifice ratio. B's old share was 8/25. Therefore, B's new share = 8/25 − 1/20 = 32/100 − 5/100 = 27/100. Option 8/25 is the old share and does not account for B's sacrifice. Exam tip: first divide the incoming partner's share according to the sacrifice ratio, then subtract each partner's sacrifice from the old share.

Correct answer: A. A : B : C = 53 : 27 : 20

C’s share is \(1/5\), and the sacrificing ratio is 3:1. Therefore, A sacrifices \(3/20\) and B sacrifices \(1/20\). A’s new share is \(17/25-3/20=53/100\), while B’s new share is \(8/25-1/20=27/100\). C’s share is \(1/5=20/100\). Hence, the new ratio is \(53:27:20\). Exam tip: first distribute the incoming partner’s share according to the sacrificing ratio, then subtract each sacrifice from the corresponding old share.

Correct answer: A. New ratio of A, B, C and D: 5:10:3:2

D’s 1/10 share is taken equally from A and C, so each sacrifices 1/20. The original shares are A = 6/20, B = 10/20 and C = 4/20. After the sacrifice, their shares are A = 5/20, B = 10/20 and C = 3/20; D receives 2/20. Therefore, the new profit-sharing ratio is 5:10:3:2.

Correct answer: A. 1:1

Sacrificing ratio = A’s sacrifice : B’s sacrifice = 1/12 : 1/12 = 1:1. Hence, option A is correct. The ratio 7:5 is the old profit-sharing ratio, not the sacrificing ratio. In an exam, compare the actual shares sacrificed by the old partners, rather than their old profit-sharing ratio.

Correct answer: A. A : B : C = 3 : 2 : 1

A and B’s old shares are \(7/12\) and \(5/12\), respectively. C receives \(1/6=2/12\) of the total profit. Since A and B sacrifice this share equally, each sacrifices \(1/12\). Therefore, A’s new share is \(7/12-1/12=6/12\), B’s is \(5/12-1/12=4/12\), and C’s is \(2/12\). The new ratio is \(6:4:2\), which simplifies to \(3:2:1\). Exam tip: Always verify that the new shares add up to the whole profit. The unchanged ratio in option D ignores the sacrifice made by A and B.

Correct answer: A. 4/35

A and B’s old shares were 3/7 and 4/7, respectively. Since C receives 1/7 and A’s new share is 2/5, B’s new share is 1 − 2/5 − 1/7 = 16/35. Therefore, B’s sacrifice = old share − new share = 4/7 − 16/35 = 20/35 − 16/35 = 4/35. Hence, option A is correct. Exam tip: Calculate a partner’s sacrifice by subtracting the new share from the old share.

Correct answer: A. 1:4

The old shares are A = 3/7 and B = 4/7. A’s sacrifice is 3/7 − 2/5 = 1/35. Since C receives 1/7 = 5/35, B’s sacrifice is 5/35 − 1/35 = 4/35. Therefore, A’s and B’s sacrificing ratio is 1/35 : 4/35 = 1:4. The ratio 3:4 is only the old profit-sharing ratio, not the sacrificing ratio. Exam tip: Sacrifice of an old partner = old share − new share.

Correct answer: A. 7/22

The partners’ new shares must add up to 1. So A’s share is 1 − 1/2 − 2/11 = 22/22 − 11/22 − 4/22 = 7/22. The original 5:6 ratio does not change this calculation because B’s new share is given.

Correct answer: A. \(\frac{3}{22}\)

A’s old profit share was \(\frac{5}{11}=\frac{10}{22}\). C receives \(\frac{2}{11}=\frac{4}{22}\), and B’s new share is \(\frac{1}{2}=\frac{11}{22}\). Therefore, A’s new share is \(1-\frac{4}{22}-\frac{11}{22}=\frac{7}{22}\). Hence, A’s sacrifice is \(\frac{10}{22}-\frac{7}{22}=\frac{3}{22}\). The share \(\frac{2}{11}\) belongs to C and is not A’s sacrifice. Exam tip: Sacrifice = old share − new share.

Correct answer: A. Sacrifice \(\frac{1}{22}\)

B’s old profit share was \(\frac{6}{11}=\frac{12}{22}\), whereas his new share is \(\frac{1}{2}=\frac{11}{22}\). Since the new share is smaller by \(\frac{1}{22}\), B sacrifices \(\frac{1}{22}\). Use the rule \(\text{Sacrifice} = \text{Old Share} - \text{New Share}\); if the new share is larger, it represents a gain.

Correct answer: A. A : B : C : D = 6:7:2:3

With the old ratio 2:3:1, A, B and C hold 6/18, 9/18 and 3/18 respectively. D’s share is 1/6 = 3/18. Since B and C surrender it in the ratio 2:1, B surrenders 2/18 and C surrenders 1/18. Their new shares are therefore 6/18, 7/18, 2/18 and 3/18, giving the new ratio 6:7:2:3. Exam tip: distribute the incoming partner’s share among the sacrificing partners in the stated surrender ratio before subtracting it.

Correct answer: A. A : B : C = 12 : 8 : 5

The old ratio of A and B is 15:10 = 3:2. After C receives 1/5, the old partners together retain 4/5. Therefore, A’s new share is 3/5 × 4/5 = 12/25 and B’s new share is 2/5 × 4/5 = 8/25. C’s share is 1/5 = 5/25. Hence, the new ratio is 12:8:5. Option C incorrectly retains the old ratio without reducing A’s and B’s shares for C’s admission. Exam tip: when the new partner’s share is sacrificed by old partners in the old ratio, multiply each old share by (1 − the new partner’s share).

Correct answer: C. 2/3

A’s and B’s old shares are 1/6 and 5/6, respectively. Since C receives 1/3 and A and B sacrifice equally, each sacrifices 1/3 ÷ 2 = 1/6. Therefore, B’s new share is 5/6 − 1/6 = 4/6 = 2/3. Hence, option C is correct. Exam tip: When sacrifice is equal, divide the incoming partner’s share equally among the sacrificing partners before subtracting it from each old share.

Correct answer: A. 2/3

Answer: option A, 2/3. The incoming partner C receives 1/3 of the total profit. Since A and B sacrifice equally, the total sacrifice of 1/3 is divided equally between them; each sacrifices 1/6. Before admission, B’s share from the ratio 1:5 was 5/(1+5)=5/6. Subtracting B’s sacrifice gives B’s new share=5/6−1/6=4/6=2/3. Therefore A is correct. Option C, 5/6, is B’s old share before C entered. Option D, 1/3, is C’s share. Option B, 1/2, does not follow from either the old ratio or the equal-sacrifice condition. A check confirms the result: A’s old share was 1/6 and he sacrifices 1/6, so A receives zero; B receives 2/3 and C receives 1/3. These shares total 1.

Correct answer: A. A B C (0:4:2)

A's old share was (1/6) and he sacrifices (1/6) so A becomes zero. B has (4/6) and C has (2/6).