New Profit Sharing Ratio

After Chetan takes (1/5) the remaining (4/5) is divided in (3:2). Exam tip: first find the remaining share.

Meena's (1/4) share is given equally so each old partner sacrifices (1/8). New share of each old partner is (1/2-1/8=3/8).

Rohit had (5/8) and he gives (1/4). So the shares become Rohit (3/8) Mohit (3/8) and Sohit (2/8).

Charu’s share is 1/6, so the share remaining for the old partners is 1 − 1/6 = 5/6. This remaining share is divided between Anshu and Binu in their old ratio of 7:5. Anshu’s new share = 5/6 × 7/12 = 35/72, and Binu’s new share = 5/6 × 5/12 = 25/72. Charu’s share, 1/6, equals 12/72. Therefore, the new ratio is 35:25:12. Exam tip: Subtract the incoming partner’s share from 1 first, then distribute the remainder in the old ratio.

Manoj's (1/3) is sacrificed equally so each old partner gives (1/6). The new shares are (1/2) (1/6) and (1/3).

Pankaj's old share was (1/5) and the whole share goes to the new partner. So Pankaj's new share becomes zero.

Falgun receives 1/4 of the profits, leaving 3/4 for Deepak and Isha. Since they contribute Falgun’s share in their old ratio of 3:1, Deepak retains 3/4 of the remaining share. Thus, Deepak’s new share is (3/4) × (3/4) = 9/16.

Geeta’s old profit share was \(\frac{1}{2}\). Since Ira’s \(\frac{1}{6}\) share is sacrificed equally by the two old partners, Geeta sacrifices \(\frac{1}{6} \div 2=\frac{1}{12}\). Therefore, Geeta’s new share is \(\frac{1}{2}-\frac{1}{12}=\frac{5}{12}\). \(\frac{1}{2}\) is her old share, not her new share. Exam tip: When a new partner’s share is sacrificed equally, divide that share by the number of sacrificing old partners to find each partner’s sacrifice.

Karan gives no sacrifice so his share remains unchanged. In this case only the sacrificing partner's share is reduced.

Om receives 1/9 of the total profit, so Meera and Neelam together retain 8/9. They sacrifice this one-ninth in their old ratio, which means their retained shares remain proportional to 5:4. Meera’s new share is (8/9)×(5/9) = 40/81, and Neelam’s new share is (8/9)×(4/9) = 32/81. Om’s share is 1/9 = 9/81. Therefore, the new ratio is 40:32:9, making option A correct. Option B fails to reduce the old partners’ shares. Option C uses the wrong retained fraction, and option D gives both old partners more than their proper shares. The three parts total 81, confirming that the entire profit is distributed.

Siya's (1/10) share is sacrificed in (1:2) so sacrifices are (1/30) and (2/30). New shares are (11/30) (16/30) and (3/30).

The governing rule is that a continuing partner’s new share equals the old share minus the sacrifice made for the incoming partner. Ajay’s old share is 3/4 = 12/16. After sacrificing 1/16, his new share is 11/16. Vijay’s old share is 1/4 = 4/16; after sacrificing 1/16, his new share is 3/16. Sanjay receives 1/8 = 2/16. Comparing all shares with denominator 16 gives Ajay:Vijay:Sanjay = 11:3:2. Therefore option A is correct. The other options either fail to subtract the stated sacrifices, assign an incorrect continuing share, or do not preserve the total profit. Indeed, 11/16 + 3/16 + 2/16 = 1, confirming the result.

The governing concept is expressing every partner’s share with a common denominator while forming the final ratio. Payal’s admitted share is 1/7. The old partners retain 6/7, and this retained amount is divided between Kamal and Nirmal in their old ratio 4:3. Kamal therefore receives (6/7)×(4/7) = 24/49, while Nirmal receives (6/7)×(3/7) = 18/49. Payal’s share is converted to the same denominator: 1/7 = 7/49. Thus the final ratio is 24:18:7, so Payal’s numerical part is 7. Option A is correct. Option B is the unreduced fractional share, option C represents the old partners’ combined retained numerator, and option D incorrectly uses Kamal’s old ratio number.

The total profit is taken as 1. Therefore, the combined share of the old partners = 1 − 1/4 = 3/4. Hence, option A is correct. Option B is the new partner’s share, not the remaining share of the old partners. Exam tip: Remaining share of old partners = 1 − new partner’s share.

Admission changes the way profit is shared. Therefore a new profit sharing ratio is calculated.

The new profit-sharing ratio is the ratio in which all partners, including the newly admitted partner, share future profits and losses after admission. It is different from the old profit-sharing ratio and from the partners’ capital ratio. Exam tip: the new ratio applies from the date of admission and includes the new partner.

The governing concept is that the complete profit of the reconstituted partnership represents one whole, or 100 percent. Admission changes the distribution among partners but does not change the total amount available for sharing. Thus, if the incoming partner receives 1/5, the existing partners together receive the remaining 4/5, and 1/5 + 4/5 = 1. Therefore the total of all partners' new shares must be 1, making option A correct. Option B is only the new partner's share, C is only the combined share of the old partners, and D is an unnormalized expression rather than the total share.

Direct answer: The new ratio is A:B:C = 10:5:3, so option A is correct. C receives \(1/6\), leaving \(1-1/6=5/6\) for A and B together. They must divide this remainder in their old ratio 2:1. Thus A receives \(5/6×2/3=10/18\), and B receives \(5/6×1/3=5/18\). C receives \(1/6=3/18\). Therefore the ratio is 10:5:3. Option A is correct. Option B wrongly keeps the old numbers and gives C one whole part without adjusting the total. Option C gives A and B the wrong scaled shares. Option D makes A and B equal, contrary to the old ratio. Memory cue: first subtract the incoming partner's share from one, then distribute the remainder in the old ratio.

From the old ratio 3:2, Ramesh’s share is 3/5 and Suresh’s share is 2/5. The new share equals the old share minus the sacrifice: Ramesh = 3/5 − 1/20 = 11/20, and Suresh = 2/5 − 1/20 = 7/20. Dinesh receives 1/10 = 2/20. Therefore, the new ratio is 11/20 : 7/20 : 2/20 = 11:7:2. Exam tip: Convert all shares to a common denominator before forming the ratio.

When sacrifice is in the old ratio the mutual ratio of old partners does not change. This is an easy check point.

Only the old partner who gives the share loses it. The other old partner's share remains unchanged.

Since Arun and Varun originally shared profits in the ratio 5:5, each had a share of 1/2. Arun’s new share = 1/2 − 3/20 = 7/20, while Varun’s new share = 1/2 − 1/20 = 9/20. Tarun’s share is 1/5 = 4/20. Therefore, the new ratio is 7/20 : 9/20 : 4/20 = 7:9:4. Option C is incorrect because Arun and Varun have surrendered different portions, so their new shares cannot remain equal. Exam tip: Subtract each partner’s surrendered share from the old share and express all resulting shares with a common denominator.

Shiv’s and Mohan’s old shares are 1/3 and 2/3, respectively. Since Rakesh’s 1/3 share is taken entirely from Mohan, Mohan’s new share is 2/3 − 1/3 = 1/3. Thus, Shiv, Mohan and Rakesh have shares of 1/3, 1/3 and 1/3, giving the new ratio 1:1:1. Exam tip: only the partner who sacrifices the share experiences a reduction in the new ratio.

The direct answer is option A, 19/60. Before Maya joins, Kiran’s share is 3/5 and Lata’s share is 2/5. Maya receives 1/4 of the total profit. Her share is sacrificed by Kiran and Lata in the ratio 2:1, so Lata sacrifices 1/3 of Maya’s share: 1/3 × 1/4 = 1/12. Lata’s new share is therefore 2/5 − 1/12. Taking denominator 60, 2/5 = 24/60 and 1/12 = 5/60, so the result is 19/60. Option A is correct. Option B, 2/5, is Lata’s old share and ignores her sacrifice. Option C, 1/4, is Maya’s share, not Lata’s new share. Option D, 17/60, does not follow from the stated sacrifice ratio. A useful check is that the new shares are Kiran 3/5 − 1/6 = 13/30, Lata 19/60, and Maya 1/4; together they equal 1.

The governing concept is sacrifice on admission. When a new partner receives a share of future profits, the old partners generally surrender part of their former shares. For any old partner, the new share is therefore calculated as: old share minus that partner's sacrifice. For example, if an old partner had 3/5 and sacrificed 1/10, the new share would be 3/5 - 1/10 = 6/10 - 1/10 = 5/10, or 1/2. Hence option A is correct. Adding sacrifice would increase the partner's share, contrary to the meaning of sacrifice; the other options mix profit-sharing with capital accounting.