New Profit Sharing Ratio

The direct answer is A:B:C=24:18:7, so option A is correct. C receives 1/7 of the total profit, leaving 6/7 for A and B together. The statement says that A and B sacrifice in their old ratio 4:3, so the remaining 6/7 must be divided between them in the fractions 4/7 and 3/7. A’s new share is (6/7)×(4/7)=24/49. B’s new share is (6/7)×(3/7)=18/49. C’s share is 1/7=7/49. Removing the common denominator 49 gives the ratio 24:18:7. The parts add to 24+18+7=49, confirming that the complete profit is distributed. Option B fails to reduce A and B’s shares after C enters. Option C uses an incorrect reduction, and option D simply scales the old ratio without correctly allocating C’s share. A useful warning is to distinguish the old ratio from the new ratio: the old ratio determines how the remaining profit is shared, but it is not itself the final ratio.

The governing concept is that a new partner’s share must be deducted from the partner or partners who sacrifice it. The old ratio 5:2 represents total parts of 7, so Mohan’s old share is 5/7 and Sohan’s is 2/7. Rohan’s 1/7 share is taken entirely from Mohan. Therefore, Mohan’s new share is 5/7 − 1/7 = 4/7, Sohan’s share remains 2/7, and Rohan receives 1/7. With the common denominator 7 removed, the new ratio is 4:2:1. Option A is correct. Option B ignores Mohan’s sacrifice, while C and D alter Sohan’s share without any stated reason.

Tina's (1/5) is sacrificed equally so each gives (1/10). The old partners' new shares are (2/5) and (2/5).

Kamal's (1/10) share is sacrificed in (2:3) so sacrifices are (1/25) and (3/50). New shares are (28/50) (17/50) and (5/50) so the ratio should be (28:17:5).

For C's (1/10) share A gives (1/25) and B gives (3/50). The new shares are (28/50) (17/50) and (5/50).

Naman receives \(\frac{1}{5}\), so the profit left for the old partners is \(1-\frac{1}{5}=\frac{4}{5}\). Varun’s old share was \(\frac{3}{10}\); therefore, his new share is \(\frac{4}{5}\times\frac{3}{10}=\frac{6}{25}\). Option C represents Kiran’s new share, while option D is Naman’s share. Exam tip: multiply an old partner’s old fraction by the fraction of profit remaining for the old partners.

The initial ratio of Pooja and Neha is 2:5, so their shares are \(\frac{2}{7}\) and \(\frac{5}{7}\), respectively. Since Geeta’s \(\frac{1}{7}\) share is taken entirely from Neha, Pooja makes no sacrifice and her share remains \(\frac{2}{7}\). The new ratio is Pooja : Neha : Geeta = \(\frac{2}{7}:\frac{4}{7}:\frac{1}{7}\), or 2:4:1. Therefore, option C is correct. Exam tip: when a new partner’s share is sacrificed by only one existing partner, the other partners’ shares remain unchanged.

After giving Reshma \(\frac{1}{5}\) of the profit, the remaining share for the old partners is \(1-\frac{1}{5}=\frac{4}{5}\). Ansh’s old share was \(\frac{4}{5}\) of the total old-partner share, so his new share is \(\frac{4}{5}\times\frac{4}{5}=\frac{16}{25}\). Option B is the total share left for both old partners, not Ansh’s individual share. Exam tip: subtract the new partner’s share first, then distribute the remainder in the old ratio.

The total profit is taken as \(1\). Therefore, the combined remaining share of the old partners is \(1-\frac{1}{8}=\frac{7}{8}\). Hence, \(\frac{7}{8}\) is correct. Exam tip: this question asks for the old partners’ combined remaining share, not their individual profit-sharing ratios.

On admission old partners give up share for the new partner. Therefore sacrifice is deducted from the old share.

Direct answer: The new ratio is Ravi:Kavi:Lavi = 27:18:5, so option A is correct. Lavi receives \(1/10\), leaving \(9/10\) for Ravi and Kavi. Their old ratio 6:4 simplifies to 3:2, so Ravi's old fraction is \(3/5\) and Kavi's is \(2/5\). Ravi's new share is \(9/10×3/5=27/50\); Kavi's is \(9/10×2/5=18/50\); Lavi's is \(1/10=5/50\). Thus the ratio is 27:18:5. Option A exactly matches. Option B fails because it uses 6:4:1 without adjusting the old partners' shares. Option C has the wrong scaling and gives Lavi 5 while retaining too large a total. Option D gives incorrect old-partner shares. Always reduce the old ratio before distributing the remainder.

Since all three fractions have the same denominator, their numerators directly give the ratio: \(7:3:2\). Also, \(\frac{7}{12}+\frac{3}{12}+\frac{2}{12}=1\), confirming that the shares represent the whole profit. Options C and D change the order of the partners. Exam tip: When denominators are equal, compare the numerators to obtain the ratio.

The governing concept is that admission changes the partnership agreement and therefore changes the proportions in which future profits and losses are shared. The new profit-sharing ratio applies from the date on which the new partner is admitted, subject to the terms of the agreement. Profits belonging to the period before admission are divided according to the old ratio because the incoming partner was not yet a partner. Thus option A is correct. Options C and D concern unrelated accounting activities, and option B incorrectly applies the new arrangement retrospectively to earlier profits.

The direct answer is C, (3:1). Sacrificing ratio means the ratio in which the existing partners reduce their own profit shares to give a share to the incoming partner. The statement already says that the old partners give this share in 3:1, so their sacrifice is 3 parts by the first partner and 1 part by the second partner. Option A, (1:3), reverses the stated order and is therefore incorrect. Option B, old ratio, is not necessarily correct because the old profit-sharing ratio and the sacrifice ratio are different ideas. Option C, (3:1), exactly repeats the stated giving ratio and is correct. Option D, equal ratio, would apply only if both old partners surrendered equal amounts. Memory cue: “Sacrifice follows the way the new partner receives.”

Since the old ratio 5:3 has a total of 8 parts, Saral’s share is 5/8 and Taral’s share is 3/8. After deducting the sacrifice, Saral’s new share is 5/8 − 1/16 = 9/16 and Taral’s new share is 3/8 − 1/16 = 5/16. Garima’s share is 1/8 = 2/16. Therefore, the new ratio is 9/16 : 5/16 : 2/16 = 9:5:2. Exam tip: subtract each partner’s sacrifice from that partner’s old share, not from the ratio numbers directly.

The old total ratio is \(3+5=8\), so Neel’s old share was \(\frac{5}{8}\). Kavya’s share of \(\frac{1}{4}\) is equal to \(\frac{2}{8}\), and it is taken entirely from Neel. Therefore, Neel’s new share is \(\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\). Exam tip: When the incoming partner’s share is taken from only one old partner, deduct the entire share from that partner’s old share.

In the new profit-sharing ratio, the shares of all partners together represent the entire profit. The entire profit is taken as 1 or 100%, so the sum of all shares must be 1. The value 1/2 represents only half the profit, while 0 and 2 represent zero and more than the entire profit, respectively. In an exam, convert the ratio into fractions and check that their sum is 1.

Riya receives 1/6 of the profit, leaving 1 − 1/6 = 5/6 for the old partners. Mayank receives 2/3 of this remainder, or (5/6) × (2/3) = 5/9. Nayank receives 1/3 of the remainder, or (5/6) × (1/3) = 5/18. Expressing all shares with denominator 18 gives 10/18 : 5/18 : 3/18, so the new ratio is 10:5:3.

The new partner receives 1/3, leaving 1 − 1/3 = 2/3 of the profit for the old partners. The first old partner receives 4/(4+5) = 4/9 of that remainder. Thus, their share of the total profit is (2/3) × (4/9) = 8/27.

Khushi receives 1/4 of the profit, so the share remaining for the old partners is 3/4. Distributing this remainder in Abhi and Ruchi’s old ratio of 1:3 gives Abhi (3/4) × (1/4) = 3/16 and Ruchi (3/4) × (3/4) = 9/16. Khushi’s share is 1/4 = 4/16. Therefore, the new ratio is 3/16 : 9/16 : 4/16 = 3:9:4. Exam tip: When the new partner’s share is sacrificed by the old partners in their old ratio, first find the remaining share and distribute it in that ratio.

The new partner receives 1/4, so the old partners together retain 1 − 1/4 = 3/4. Dividing this 3/4 in the old mutual ratio of 5:1 gives shares of 5/8 and 1/8. Therefore, the new ratio is 5/8 : 1/8 : 1/4 = 15:3:6. Option B incorrectly keeps the old ratio as the complete new ratio and does not account for the new partner's share. Exam tip: First find the old partners' combined remaining share, then divide it according to their old mutual ratio.

Suman’s old share was \(\frac{3}{7}=\frac{6}{14}\). After sacrificing \(\frac{1}{14}\), her new share becomes \(\frac{5}{14}\). Kamal’s old share was \(\frac{4}{7}=\frac{8}{14}\), so his new share becomes \(\frac{7}{14}\). Aman receives \(\frac{1}{7}=\frac{2}{14}\). Therefore, the new ratio is \(5:7:2\). Exam tip: Convert the old ratio into fractions with a common denominator before subtracting the sacrificed shares.

A partner’s new profit-sharing share is calculated by subtracting the sacrificed share from the old share: \(\frac{2}{3}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6}=\frac{3}{6}=\frac{1}{2}\). Therefore, option A is correct. Option D is only the old share, not the revised share. Exam tip: In a sacrifice, new share = old share − sacrificed share.

A partner's sacrificing share is the old share minus the new share. For B, 3/5 − 1/2 = 6/10 − 5/10 = 1/10, so option B is correct.

Radha and Madhav originally share profits in the ratio 8:2, which simplifies to 4:1. Sita receives 1/10 of the total profit, and this share is sacrificed by Radha and Madhav in their old ratio. The remaining share for the old partners is therefore 1 − 1/10 = 9/10. Radha receives 4/5 of this remainder and Madhav receives 1/5. Hence their new shares are 36/50 and 9/50, while Sita receives 5/50. The new ratio is 36:9:5, so option A is correct.

The calculation is: Radha = 9/10 × 4/5 = 36/50; Madhav = 9/10 × 1/5 = 9/50; Sita = 1/10 = 5/50. All shares have the common denominator 50, making the ratio 36:9:5. Option 8:2:1 does not account for Sita’s admission correctly.