New Profit Sharing Ratio

After C receives 1/4 of the profit, 3/4 remains for A and B. This remainder is divided in their old ratio of 3:2. Thus, A’s new share is 3/4 × 3/5 = 9/20, B’s new share is 3/4 × 2/5 = 6/20, and C’s share is 1/4 = 5/20. Therefore, the new ratio is 9:6:5. Exam tip: Subtract the incoming partner’s share from 1, then distribute the remainder in the old ratio.

Mohan’s old share was 5/8 and Sohan’s was 3/8. Rohan receives 1/4 = 2/8 entirely from Mohan, so Mohan’s new share becomes 5/8 − 2/8 = 3/8. The new shares are therefore 3/8, 3/8 and 2/8, giving the ratio 3:3:2. Exam tip: If the incoming partner’s share is taken from only one old partner, reduce only that partner’s share.

Tina's (1/6) share is given equally so each sacrifices (1/12). The old partners' new shares are (5/12) and (5/12).

After admitting Kamal for a 1/9 share, the old partners retain 8/9 of the profits. This remaining share is divided between Deepak and Bhavesh in their old ratio of 4:5. Thus, Deepak’s share is 8/9 × 4/9 = 32/81, and Bhavesh’s share is 8/9 × 5/9 = 40/81. Kamal’s share, 1/9, equals 9/81. Therefore, the new ratio is 32:40:9. Option B is incorrect because it does not reduce the old partners’ shares. Exam tip: When the incoming partner’s share is surrendered in the old ratio, distribute the remaining profit in that same ratio.

Under the old ratio \(2:3\), Kiran’s share is \(\frac{2}{5}\) and Varun’s share is \(\frac{3}{5}\). Since Naman’s \(\frac{1}{5}\) share is taken entirely from Varun, Varun’s new share becomes \(\frac{3}{5}-\frac{1}{5}=\frac{2}{5}\). Therefore, the new ratio is \(\frac{2}{5}:\frac{2}{5}:\frac{1}{5}=2:2:1\). Exam tip: reduce the share only of the partner who sacrifices it; the other existing partner’s share remains unchanged.

After giving Geeta a \(1/10\) share, the remaining profit for the old partners is \(1-1/10=9/10\). Pooja’s old share was \(7/10\), and she receives the same proportion of the remaining profit. Therefore, her new share is \(9/10\times7/10=63/100\). The option \(7/10\) represents her old share, not her new share. Exam tip: first calculate the profit left for the old partners, then distribute it in their old ratio.

Ansh makes no sacrifice so his share remains (1/5). When sacrifice is from one partner the other share does not change.

Ravi’s new share is 3/4 − 1/16 = 11/16, and Kavi’s new share is 1/4 − 1/16 = 3/16. Lavi’s share, 1/8, is 2/16. Thus, their new shares are 11/16 : 3/16 : 2/16, giving the ratio 11 : 3 : 2. The two sacrifices total 2/16 = 1/8, equal to Lavi’s share.

The total profit is taken as 1. After allocating 1/10 to the new partner, the share remaining for the old partners is 1 − 1/10 = 9/10. Therefore, option A is correct. Exam tip: subtract the incoming partner’s share from the total share of 1 to find the old partners’ combined share.

Direct answer: An old partner's new share is old share minus sacrifice, so option A is correct. When a new partner is admitted, the new partner must receive a share of future profits. That share is usually given up by the old partners. Therefore each old partner's new share becomes: old share − the portion sacrificed by that partner. For example, if an old partner had \(1/2\) and sacrificed \(1/12\), the new share is \(1/2−1/12=5/12\). Option A states this correct rule. Option B is wrong because adding sacrifice would increase the old partner's share, whereas sacrifice means giving up profit. Option C reverses the subtraction and can produce a meaningless negative or wrong result. Option D concerns capital and drawings, not profit-sharing ratios. Exam cue: admission means sacrifice; new share = old share − sacrifice.

All three fractions have the same denominator, 15. When fractions have a common denominator, their ratio is obtained directly from their numerators: 8:4:3. The numerators already have no common factor greater than 1, so this ratio is also in its simplest form. Options C and D rearrange the partners' shares, while option B ignores the actual numerators and is therefore incorrect.

The governing concept is that admission of a partner changes the profit-sharing arrangement from the date of admission. Therefore, the new profit-sharing ratio is used for profits earned after the incoming partner is admitted. Profits relating to the period before admission belong to the old partners and are normally divided in their old ratio, unless a specific adjustment is required for an exceptional situation. The ratio is not restricted to cash profit, because accounting profit may include credit transactions and non-cash items. It also has no direct connection with the amount of capital contributed. Hence option A is correct; options B, C and D confuse the effective date or the basis of profit sharing.

Direct answer: Option A, 2:1, is correct. Sacrificing ratio means the ratio in which the old partners give up their profit shares for the incoming partner. The question directly states that the new partner’s share is taken from the old partners in the ratio 2:1. Therefore the amount sacrificed by the first old partner is two parts and the amount sacrificed by the second is one part. No separate calculation is needed unless actual shares are requested. Option A repeats exactly this ratio. Option B reverses the order and would mean the first partner sacrifices one part while the second sacrifices two, which is not stated. Option C, old ratio, is not necessarily the sacrifice ratio; it is used only when the question says sacrifice follows the old ratio. Option D, new ratio, describes final profit distribution and is a different idea. Memory cue: sacrificing ratio tells “who gives up how much,” while new ratio tells “who finally receives how much.”

The governing rule is that a new partner’s share is deducted from the partner or partners who sacrifice it. The old ratio of Aditya and Neel is 5:1, so their fractional shares are 5/6 and 1/6. Kavya receives 1/6, and the question clearly states that this entire amount is taken only from Neel. Thus Aditya continues with 5/6, Neel’s revised share becomes 1/6 − 1/6 = 0, and Kavya receives 1/6. Expressing these shares with denominator 6 gives 5:0:1. Therefore option A is correct. Options B and D incorrectly transfer part of the share from Aditya, while C adds Kavya’s share without reducing Neel’s share.

After giving Dolly a \(\frac{1}{8}\) share, the old partners retain \(1-\frac{1}{8}=\frac{7}{8}\) of the profits. Monu's old share was \(\frac{5}{8}\), and he receives his proportionate share of the remaining profits. Therefore, his new share is \(\frac{5}{8}\times\frac{7}{8}=\frac{35}{64}\). The option \(\frac{5}{8}\) is Monu's old share, not his reduced share after admission. Exam tip: If the incoming partner's share is surrendered in the old ratio, multiply each old partner's share by the remaining share.

In a partnership, the entire profit is taken as 1. Therefore, after reconstitution or admission of a partner, the new profit-sharing ratios of all partners must always add up to 1. The values 0 and 1/2 do not represent the whole profit, while the old ratio is not necessarily the ratio under the new arrangement. Exam tip: Always verify that the sum of the new ratios is 1.

Riya's (1/10) share is taken equally so each sacrifices (1/20). The new shares are (15/20) (3/20) and (2/20).

The old partners share the remaining 1 − 1/4 = 3/4 of the profits. The first old partner receives 3/5 of that remainder, so the new share is (3/4) × (3/5) = 9/20. Therefore, option A is correct.

Khushi’s 1/3 share is sacrificed by Abhi and Ruchi in their old ratio of 2:1. Thus, Abhi sacrifices 1/3 × 2/3 = 2/9, while Ruchi sacrifices 1/3 × 1/3 = 1/9. Abhi’s new share is 2/3 − 2/9 = 4/9, Ruchi’s new share is 1/3 − 1/9 = 2/9, and Khushi receives 1/3 = 3/9. Therefore, the new ratio is 4:2:3. Exam tip: If the incoming partner’s share is given by the old partners in their old ratio, multiply that share by each partner’s old fraction to find the sacrifice.

The new partner receives 1/5, so the two old partners together receive 1 − 1/5 = 4/5. Dividing this 4/5 in the ratio 1:3 gives 1/5 to the first old partner and 3/5 to the second. Therefore, the new ratio is 1/5:3/5:1/5 = 1:3:1. Exam tip: First find the combined share of the old partners, divide it according to their mutual ratio, and then simplify the resulting ratio.

Suman’s old share is 5/7 and Kamal’s is 2/7. After each sacrifices 1/14, their new shares are 5/7 − 1/14 = 9/14 and 2/7 − 1/14 = 3/14, respectively. Aman’s share is 1/7 = 2/14. Thus, the new ratio is 9/14 : 3/14 : 2/14 = 9:3:2, so option A is correct.

On admission of a new partner, the old partner's new share equals the old share minus the share sacrificed. Thus, A's new share is \(\frac{3}{5}-\frac{1}{10}=\frac{6}{10}-\frac{1}{10}=\frac{5}{10}=\frac{1}{2}\). \(\frac{7}{10}\) results from addition, so it is incorrect. Exam tip: subtract the sacrificed share from the old share.

Sacrificing share = old share − new share. Therefore, B’s sacrificing share is \(\frac{4}{7}-\frac{3}{7}=\frac{1}{7}\). The value \(\frac{3}{7}\) is B’s new share, not the sacrificed share. Exam tip: In admission questions, calculate a partner’s sacrifice by subtracting the new share from the old share.

The old ratio 8 : 2 simplifies to 4 : 1. Sita’s 1/5 share is sacrificed in this old ratio, so Radha sacrifices 1/5 × 4/5 = 4/25 and Madhav sacrifices 1/5 × 1/5 = 1/25. Therefore, Radha’s new share is 4/5 − 4/25 = 16/25, Madhav’s is 1/5 − 1/25 = 4/25, and Sita’s share is 5/25. Hence, the new ratio is 16 : 4 : 5. Exam tip: When the new partner’s share is acquired from the old partners in their old ratio, divide that share according to the old ratio to calculate each partner’s sacrifice.

When sacrifice is in old ratio the mutual ratio of old partners does not change. This is a quick checking rule.