New Profit Sharing Ratio

The old ratio is (2:1) and old partners retain (2/3). Shares are (4/9) (2/9) and (3/9) so the ratio is (4:2:3).

The governing rule is equal sacrifice: when the incoming partner’s share is surrendered equally by the old partners, each old partner sacrifices half of the incoming share. C receives 1/5, so A and B each sacrifice (1/5) × (1/2) = 1/10. Under the old ratio 9:1, B’s old share was 1/(9+1) = 1/10. Therefore B’s new share is old share minus sacrifice: 1/10 − 1/10 = 0. Hence option A, Zero, is correct. Option B is B’s old share before admission, not the remaining share. Option C is C’s share, while option D does not follow from equal sacrifice and does not reconcile with the transferred 1/5.

C receives 1/5 of the profit, so A and B each sacrifice 1/10. A’s new share is 9/10 − 1/10 = 8/10, while B’s new share is 1/10 − 1/10 = 0. Therefore, the new ratio is 8/10 : 0 : 1/5 = 8 : 0 : 2 = 4 : 0 : 1. B’s entire original share is sacrificed, which is why B has a zero share in the new ratio. Exam tip: when the new partner’s share is sacrificed equally, subtract half of that share from each old partner’s share.

A's sacrifice is (4/5-3/5=1/5) and total sacrifice is also (1/5). So B's sacrifice is zero and sacrificing ratio is (1:0).

C's (1/4) share is sacrificed in (2:3) so A gives (1/10) and B gives (3/20). The new shares are (8/20) (5/20) and (5/20).

D's (1/6) share is sacrificed in (3:2:1) so sacrifices are (1/12) (1/18) and (1/36). New shares are (23/72) (20/72) (17/72) and (12/72).

G's total share is (1/5) so Kh's sacrifice is (1/5-1/9=4/45). The new shares are (15/45) (21/45) and (9/45).

The direct answer is 1/6, so option A is correct. Sacrifice is calculated as old share minus new share. Mohan and Sohan originally share in the ratio 5:7, so Sohan’s old share is 7/(5+7)=7/12. Rohan receives 1/4, leaving 1−1/4=3/4 for Mohan and Sohan. They divide this balance in the new mutual ratio 4:5, so Sohan receives 5/9 of the balance. His new share is (3/4)×(5/9)=15/36=5/12. Therefore Sohan’s sacrifice is 7/12−5/12=2/12=1/6. Option B is only Sohan’s old share, not his sacrifice. Option C is Rohan’s share. Option D results from using the new ratio or subtraction incorrectly. The important distinction is that the 4:5 ratio applies only to the remaining 3/4, not to the entire profit. A quick check is that Sohan’s share falls from 7/12 to 5/12, and the difference is exactly 1/6.

The governing principle is that sacrifice equals the old share minus the revised share. Sohan’s old share is 7/12 from the ratio 5:7. Rohan receives 1/4, so the balance for the two existing partners is 3/4. Under the revised ratio 4:5, Sohan receives 5/9 of that balance: 3/4 × 5/9 = 5/12. Hence Sohan’s sacrifice is 7/12 − 5/12 = 2/12 = 1/6. Option A is the corrected answer. Option B is too small, option C is Sohan’s new share rather than his sacrifice, and option D is the incoming partner’s share. The revised shares also total 4/12 + 5/12 + 3/12 = 1.

Take the total profit as 1. Reema’s and Neema’s new shares are \(\frac{1}{3}\) and \(\frac{1}{8}\), respectively. Therefore, Seema’s new share is \(1-\frac{1}{3}-\frac{1}{8}=\frac{24-8-3}{24}=\frac{13}{24}\). \(\frac{5}{8}\) may relate to the old arrangement, but the new shares must add up to 1. Exam tip: After admission of a partner, verify that all the new profit shares together equal the whole profit.

Old partners retain (4/5) and in (7:5) A's new share is (7/15). A's old share was (3/5=9/15) so sacrifice is (2/15).

The governing concept is construction of the new ratio from the precise sacrifices made by the old partners. A’s old share is 5/9. He gives one-fifth of this old share to C, so A sacrifices (5/9) × (1/5) = 1/9. C’s total share is 1/3 = 3/9; therefore B contributes the remaining 2/9. A’s new share is 5/9 − 1/9 = 4/9, while B’s new share is 4/9 − 2/9 = 2/9. C receives 3/9. Multiplying all shares by 9 gives A:B:C = 4:2:3. Thus option A is correct. The other options fail to preserve the stated contributions to C.

Payal’s old share was \(7/(4+7)=7/11\). Out of Riya’s \(1/11\) share, Payal sacrifices \(2/(1+2)\times1/11=2/33\). Therefore, Payal’s new share is \(7/11-2/33=21/33-2/33=19/33\). Option B is only Payal’s old share because it does not deduct her sacrifice. Exam tip: Divide the incoming partner’s share according to the sacrificing ratio and subtract each partner’s sacrifice from their old share.

The old ratio 3:5:2 represents shares of 3/10, 5/10 and 2/10 for A, B and C respectively. Since D’s 1/10 share is taken entirely from B, B’s new share becomes 5/10 − 1/10 = 4/10. A’s and C’s shares remain unchanged. Therefore, the new mutual ratio of the old partners is 3:4:2. Option B is incorrect because it ignores B’s sacrifice. Exam tip: when the incoming partner’s share is taken solely from one old partner, subtract the entire incoming share from that partner’s original share.

A and B’s old shares are 13/20 and 7/20 because their ratio is 13:7. C receives 1/4 = 10/40 of the profits. Since A and B sacrifice this equally, each sacrifices 1/8 = 5/40. Thus, A’s new share is 26/40 − 5/40 = 21/40, B’s new share is 14/40 − 5/40 = 9/40, and C’s share is 10/40. Therefore, the new ratio is 21:9:10. Exam tip: When the new partner’s share is sacrificed equally, subtract half of that share from each old partner’s share.

In the old ratio 5:6, A’s share is \(\frac{5}{11}\) and B’s share is \(\frac{6}{11}\). Since C receives \(\frac{1}{11}\) from each partner, A’s new share is \(\frac{4}{11}\), B’s is \(\frac{5}{11}\), and C’s is \(\frac{2}{11}\). Therefore, the new ratio is 4:5:2. Option B is incorrect because it does not deduct C’s share from A and B. Exam tip: subtract each partner’s sacrifice from the old share, then write the new partner’s admitted share.

C’s share of \(\frac{1}{6}\) is sacrificed by A and B in the ratio 4:1. A therefore bears \(\frac{4}{4+1}=\frac{4}{5}\) of C’s share. A’s actual sacrifice is \(\frac{1}{6}\times\frac{4}{5}=\frac{2}{15}\). The old ratio of 7:5 is not needed because the sacrifice ratio is given.

B’s old share is \(\frac{5}{7+5}=\frac{5}{12}\). Since A and B sacrifice in the ratio 4:1, B sacrifices \(\frac{1}{5}\) of C’s \(\frac{1}{6}\) share, or \(\frac{1}{30}\). B’s new share is therefore \(\frac{5}{12}-\frac{1}{30}=\frac{25}{60}-\frac{2}{60}=\frac{23}{60}\).

After C receives \(\frac{2}{11}\), the remaining profit for A and B is \(1-\frac{2}{11}=\frac{9}{11}\). A's fraction of this remainder is \(\frac{5}{5+4}=\frac{5}{9}\). Therefore, A's new share is \(\frac{9}{11}\times\frac{5}{9}=\frac{5}{11}\). The value \(\frac{8}{11}\) results from incorrectly applying the old ratio directly. Exam tip: first calculate the remainder after the incoming partner's share, then multiply it by the relevant fraction of the new ratio.

After C receives 2/11, the remaining profit for A and B is 9/11. Under the new ratio 5:4, B’s new share is \(\frac{4}{9} \times \frac{9}{11}=\frac{4}{11}\). B’s old share was \(\frac{3}{11}\), so gain = new share − old share = \(\frac{4}{11}-\frac{3}{11}=\frac{1}{11}\). Therefore, B gains 1/11. Exam tip: For a gain, subtract the old share from the new share; for a sacrifice, subtract the new share from the old share.

Old partners retain (5/6) and it is divided in (4:5:3). The shares are (20/72) (25/72) (15/72) and (12/72).

A and B's old ratio, 12:8, simplifies to 3:2. After C receives 1/4 of the profits, 3/4 remains for A and B. Their new shares are therefore (3/4 × 3/5) = 9/20 for A and (3/4 × 2/5) = 6/20 for B; C's share is 1/4 = 5/20. The ratio 9:6:5 follows.

Old partners retain (2/3) and A's new share is (2/3\times2/5=4/15). A's sacrifice is (5/12-4/15=3/20).

Answer: option A, 11/60. Sacrifice means the share given up by an old partner, so we use: old share − new share. B’s old share was 7/(5+7)=7/12. C receives 1/3 of the total profit, so A and B together retain 1−1/3=2/3. Their new ratio is 2:3, whose total is 5. Therefore B receives 3/5 of the remaining 2/3, giving B’s new share=(3/5)×(2/3)=2/5. Hence B’s sacrifice=7/12−2/5. Taking 60 as the common denominator, 35/60−24/60=11/60. Thus A is correct. B is only B’s old share, not the amount sacrificed. C is B’s new share, and D is C’s share. A useful check is that the sacrificed shares of A and B together must equal C’s 1/3.

Old partners retain (3/5) and B's new share is (3/5\times2/3=2/5). B's old share was (1/5) so B gains.