New Profit Sharing Ratio

Correct answer: A. 35:25:12

C receives 1/6 of the profits, so 5/6 remains for A and B. This remainder is divided in the old ratio 7:5. Therefore, A's share is (5/6) × (7/12) = 35/72, and B's share is (5/6) × (5/12) = 25/72. C's share is 1/6 = 12/72. Hence, the new profit-sharing ratio is 35:25:12. Exam tip: When the incoming partner receives a specified share and the balance is divided in the old ratio, multiply each old partner's fraction by the remaining share.

Correct answer: A. 13:5:6

A and B’s old shares are 5/8 and 3/8 respectively. C’s 1/4 share is sacrificed by A and B in the ratio 1:2, so A sacrifices 1/12 and B sacrifices 1/6. Therefore, A’s new share is 5/8 − 1/12 = 13/24, B’s new share is 3/8 − 1/6 = 5/24, and C’s share is 1/4 = 6/24. Hence, the new ratio is 13:5:6. Exam tip: Subtract each existing partner’s sacrifice from the old share and then include the incoming partner’s share.

Correct answer: A. \(4:3:2\)

Initially, A’s share is \(4/9\) and B’s share is \(5/9\). Since C receives \(2/9\) of the total profit from B, A’s share remains \(4/9\), while B’s new share becomes \(5/9-2/9=3/9\). C’s share is \(2/9\). Therefore, the new ratio is \(4/9:3/9:2/9=4:3:2\). Option B is incorrect because it does not deduct C’s share from B’s original share. Exam tip: If the incoming partner acquires a share from only one old partner, reduce the share of only that partner.

Correct answer: A. (2:1)

Direct answer: Option A, 2:1, is correct. A and B originally share in 3:2, so their total is 5 parts: A’s old share is 3/5 = 9/15 and B’s old share is 2/5 = 6/15. After admission, the new ratio is 7:5:3, whose total is 15. Thus A’s new share is 7/15 and B’s new share is 5/15. A sacrifices 9/15 − 7/15 = 2/15. B sacrifices 6/15 − 5/15 = 1/15. The sacrificing ratio is therefore 2/15:1/15 = 2:1. Option A works. Option B repeats the old profit-sharing ratio, but sacrifice is based on the difference between old and new shares. Option C uses the new shares rather than the amounts surrendered. Option D reverses the calculated sacrifice amounts. Check also that C receives 3/15 and the final shares total 15/15. Memory cue: put old and new shares over a common denominator, subtract, then simplify the sacrifices.

Correct answer: A. 7:5:4

The old ratio 11:5 has a total of 16 parts, so A’s old share is 11/16 and B’s share is 5/16. C receives 1/4 = 4/16 exclusively from A; therefore, A’s new share is 11/16 − 4/16 = 7/16. B’s share remains 5/16, while C receives 4/16. Hence, the new ratio is 7:5:4. Exam tip: When the incoming partner obtains the entire share from only one old partner, only that partner’s share is reduced.

Correct answer: A. 4:14:9

C receives 1/3 of the total profit, so the remaining share for A and B is 2/3. A’s new share is \(\frac{2}{3}\times\frac{2}{9}=\frac{4}{27}\), while B’s new share is \(\frac{2}{3}\times\frac{7}{9}=\frac{14}{27}\). C’s share is \(\frac{1}{3}=\frac{9}{27}\). Therefore, the new ratio is 4:14:9. Exam tip: First subtract the incoming partner’s share from 1, then distribute the balance among the old partners in their old ratio.

Correct answer: A. By equal sacrifice

The governing concept is comparison of old and new shares after admission. Before C entered, A and B shared the total in the ratio 5:4, so A’s share was 5/9 and B’s was 4/9. The new ratio 4:3:2 totals 9, giving A 4/9, B 3/9, and C 2/9. A’s sacrifice is therefore 5/9 − 4/9 = 1/9. B’s sacrifice is 4/9 − 3/9 = 1/9. The combined sacrifice is 2/9, exactly equal to C’s new share. Since both A and B surrender the same amount, C’s share has come through equal sacrifice. Hence option A is correct; options B and C ignore one of the equal reductions, while D does not describe the calculated source.

Correct answer: A. \(\frac{9}{22}\)

B’s old share is \(\frac{5}{11}\). Since the total sacrifice of \(\frac{2}{11}\) is divided between A and B in the ratio 3:1, B’s sacrifice is \(\frac{2}{11}\times\frac{1}{3+1}=\frac{1}{22}\). Therefore, B’s new share is \(\frac{5}{11}-\frac{1}{22}=\frac{9}{22}\). Exam tip: A continuing partner’s new share equals the old share minus the share sacrificed.

Correct answer: A. B

A’s old share was 7/10, which decreased to 5/10, so A sacrificed 2/10. B’s old share was 3/10 and its new share is also 3/10; therefore, B made no sacrifice. The new partner C gained 2/10. Exam tip: calculate sacrifice by subtracting the new share from the old share.

Correct answer: A. 5:7:4

A’s old share is 3/8 and B’s old share is 5/8. C’s 1/4 share is contributed by A and B in the sacrificing ratio 1:3; therefore, A sacrifices 1/16 and B sacrifices 3/16. Thus, A’s new share is 3/8 − 1/16 = 5/16, B’s new share is 5/8 − 3/16 = 7/16, and C’s share is 1/4 = 4/16. Hence, the new profit-sharing ratio is 5:7:4. Exam tip: Convert the old ratio into fractions first, then distribute the incoming partner’s share according to the sacrificing ratio and subtract it. Option B fails to make this proper sacrifice adjustment.

Correct answer: A. 4:5:2

Under the old ratio 4:7, A’s share is \(\frac{4}{11}\) and B’s share is \(\frac{7}{11}\). Since C receives \(\frac{2}{11}\) entirely from B, B’s new share becomes \(\frac{7}{11}-\frac{2}{11}=\frac{5}{11}\). Thus, the new shares of A, B and C are \(\frac{4}{11}:\frac{5}{11}:\frac{2}{11}\), giving the new ratio 4:5:2. Option B is incorrect because it does not deduct C’s share from B. Exam tip: If an incoming partner obtains a share from only one old partner, subtract that share from that partner’s old share and leave the others unchanged.

Correct answer: A. 180:162:19

C receives 1/19 of the total profit, so the remaining profit for A and B is 18/19. This remainder is divided in the old ratio 10:9. Therefore, A receives (18/19) × (10/19) = 180/361 and B receives (18/19) × (9/19) = 162/361. C’s share, 1/19, is equal to 19/361. Hence, the new ratio is 180:162:19. Option B incorrectly combines the old ratio directly with C’s share without reducing A’s and B’s shares. Exam tip: If the incoming partner receives a specified share and the balance is divided in the old ratio, multiply each old partner’s fractional share by the remaining profit fraction.

Correct answer: A. 33:9:7

C’s share is \(\frac{1}{7}=\frac{7}{49}\). In the sacrificing ratio 2:5, A sacrifices \(\frac{2}{49}\) and B sacrifices \(\frac{5}{49}\). Their old shares were \(\frac{5}{7}=\frac{35}{49}\) and \(\frac{2}{7}=\frac{14}{49}\), respectively. Thus, A’s new share is \(\frac{33}{49}\), B’s is \(\frac{9}{49}\), and C’s is \(\frac{7}{49}\), giving the ratio 33:9:7. Exam tip: Distribute the incoming partner’s share in the sacrificing ratio and subtract each sacrifice from the respective old share.

Correct answer: A. 1/5

The total of the new ratio 13:11:6 is 30. Therefore, C's new share is 6/30 = 1/5. The old ratio is not required for this calculation because C's share is given directly in the new ratio. Exam tip: To find a partner's share under a new ratio, divide that partner's ratio term by the sum of all the new-ratio terms.

Correct answer: A. \(\frac{1}{3}\)

The partners’ new shares must add up to 1. Therefore, B’s share is \(1-\frac{7}{15}-\frac{1}{5}=1-\frac{7}{15}-\frac{3}{15}=\frac{5}{15}=\frac{1}{3}\).

Correct answer: A. \(O_i-N_i\)

Sacrifice is the portion of profit given up by an old partner; hence it equals old share minus new share, \(O_i-N_i\). For example, \(3/10-1/5=1/10\). In exams, first express old and new shares with a common denominator.

Correct answer: A. \(\frac{11}{35}\)

A’s old share is \(\frac{3}{3+4}=\frac{3}{7}\). A bears \(\frac{2}{5}\) of C’s 2/7 share because the sacrifice ratio is 2:3, so A’s sacrifice is \(\frac{2}{5}\times\frac{2}{7}=\frac{4}{35}\). A’s new share is therefore \(\frac{3}{7}-\frac{4}{35}=\frac{11}{35}\).

Correct answer: A. 6:4:3

The old ratio 8:5 gives A a share of 8/13 and B a share of 5/13. C’s 3/13 share is sacrificed by A and B in the ratio 2:1, so A sacrifices 2/13 and B sacrifices 1/13. Therefore, A’s new share is 8/13 − 2/13 = 6/13, B’s is 5/13 − 1/13 = 4/13, and C’s is 3/13. Hence, the new ratio is 6:4:3. Exam tip: subtract each partner’s sacrifice from their old share; do not simply append the newcomer’s share to the old ratio.

Correct answer: A. 30:100:39

C receives 3/13 of the profit, so the remaining share for A and B is 10/13. Distributing this remainder in the old ratio 3:10 gives A: (10/13) × (3/13) = 30/169 and B: (10/13) × (10/13) = 100/169. C’s share, 3/13, equals 39/169. Therefore, the new ratio is 30:100:39. Exam tip: Multiply each old-ratio term by the remaining fraction, then express all three shares with a common denominator.

Correct answer: A. Only from A

Under the old ratio, A’s share was \(\frac{7}{9}\) and B’s share was \(\frac{2}{9}\). Under the new ratio 5:2:2, A gets \(\frac{5}{9}\), B remains at \(\frac{2}{9}\), and C gets \(\frac{2}{9}\). A therefore sacrifices \(\frac{7}{9}-\frac{5}{9}=\frac{2}{9}\), while B sacrifices nothing. Hence, C’s entire share comes from A; option B is incorrect because B’s share does not change. Exam tip: Compare each old partner’s old and new fractions to identify who has sacrificed a share.

Correct answer: A. 1/5 and 4/5

The total number of ratio parts is 11+9+5=25. G's share is 5/25=1/5. The combined share of old partners A and B is (11+9)/25=20/25=4/5. Option B incorrectly gives their combined share as 15/25; the correct sum is 20/25. Exam tip: Add the ratio parts of the relevant old partners first, then divide by the total parts.

Correct answer: A. 4:9:2

The old ratio 4:11 gives A and B shares of 4/15 and 11/15, respectively. Since C receives 2/15 entirely from B, A’s share remains 4/15, while B’s new share becomes 11/15 − 2/15 = 9/15. Thus, the new ratio of A, B and C is 4:9:2. Exam tip: When the incoming partner obtains a share from only one existing partner, only that partner’s share is reduced.

Correct answer: A. 21:39:20

Since the old ratio is 5:11, A’s and B’s old shares are 5/16 and 11/16. C receives 1/4, so A sacrifices 1/20 and B sacrifices 1/5 because the sacrificing ratio is 1:4. Therefore, A’s new share is 5/16 − 1/20 = 21/80, B’s new share is 11/16 − 1/5 = 39/80, and C’s share is 1/4 = 20/80. Hence, the new ratio is 21:39:20. Exam tip: Subtract each old partner’s sacrifice and add the admitted partner’s share; verify that the resulting shares total 1.

Correct answer: A. \(\frac{13}{22}\)

The old ratio 2:9 has a total of 11 parts, so B’s old share is \(\frac{9}{11}\). The total share sacrificed for C is \(\frac{3}{11}\). Since A:B sacrifice in the ratio 1:5, B’s sacrifice is \(\frac{3}{11}\times\frac{5}{6}=\frac{5}{22}\). Therefore, B’s new share is \(\frac{9}{11}-\frac{5}{22}=\frac{18}{22}-\frac{5}{22}=\frac{13}{22}\). Exam tip: A partner’s new share equals the old share minus the share sacrificed for the incoming partner.

Correct answer: A. 72:27:22

The governing concept is proportional distribution of the residual profit. C receives 2/11, so the profit remaining for A and B together is 1 − 2/11 = 9/11. This remainder is divided in their old ratio 8:3, whose total is 11. Therefore A receives (9/11) × (8/11) = 72/121, while B receives (9/11) × (3/11) = 27/121. C’s share, 2/11, expressed with denominator 121, is 22/121. The common-denominator ratio is therefore 72:27:22, making option A correct. The shares add to 121/121, confirming the calculation. Options B, C and D either use the old ratio without adjusting the remainder or fail to distribute 9/11 proportionately.