New Profit Sharing Ratio

C’s 1/10 share is sacrificed by A and B in the ratio 4:1. Thus, A’s sacrifice is 1/10 × 4/5 = 4/50, and B’s sacrifice is 1/10 × 1/5 = 1/50. Their old shares were 45/50 and 5/50, respectively. Therefore, the new shares are A = 41/50, B = 4/50, and C = 5/50, giving the new ratio 41:4:5. Exam tip: Subtract each existing partner’s sacrifice from their old share, then include the incoming partner’s share.

Since the old ratio is 6:5, A and B originally held 6/11 and 5/11, respectively. C’s 1/11 share is sacrificed in the ratio 5:6, so A sacrifices 5/121 and B sacrifices 6/121. Therefore, A’s new share is 66/121 − 5/121 = 61/121, B’s new share is 55/121 − 6/121 = 49/121, and C’s share is 11/121. Hence, the new ratio is 61:49:11. Exam tip: subtract each existing partner’s sacrifice from the old share and then express all shares with a common denominator.

C receives \(1/5\) of the total profit, and A and B sacrifice it in the ratio 1:4. Thus, A sacrifices \(1/25\) and B sacrifices \(4/25\). A’s new share is \(7/10-1/25=33/50\), B’s new share is \(3/10-4/25=7/50\), and C’s share is \(1/5=10/50\). Therefore, the new ratio is \(33:7:10\). Option B incorrectly retains the old ratio without accounting for the sacrifice. Exam tip: Divide the incoming partner’s share according to the sacrificing ratio and subtract those amounts from the old shares.

A’s old share was 5/11 and B’s was 6/11. To provide C’s 2/11 share, A sacrifices 3/4 × 2/11 = 3/22 and B sacrifices 1/4 × 2/11 = 1/22. Thus, A’s new share is 5/11 − 3/22 = 7/22, B’s is 6/11 − 1/22 = 11/22, and C’s share is 2/11 = 4/22. Therefore, the new ratio is 7:11:4. Exam tip: Convert the old shares to a common denominator before subtracting the sacrificing shares.

A’s old share is 2/5 and B’s is 3/5. Of C’s 1/4 share, A sacrifices 1/16 and B sacrifices 3/16, because the sacrifice is divided in the ratio 1:3. Therefore, A’s new share is 2/5 − 1/16 = 27/80, B’s is 3/5 − 3/16 = 33/80, and C’s is 1/4 = 20/80. The new profit-sharing ratio is 27:33:20.

Under the old ratio, A's and B's shares are 4/9 and 5/9 respectively. Since C receives 1/6 of the total profit equally from A and B, each partner sacrifices 1/12. Thus, A's new share is 4/9 − 1/12 = 13/36, B's new share is 5/9 − 1/12 = 17/36, and C's share is 1/6 = 6/36. Therefore, the new ratio is 13:17:6. Exam tip: When the sacrifice is equal, subtract the same amount from each existing partner's share.

The sum of the terms in the new ratio 6:5:4 is 6 + 5 + 4 = 15. C's term is 4, so C's share is 4/15. The option 4/11 is incorrect because the denominator must be the sum of all three ratio terms, not just two of them. Exam tip: calculate a partner's share as that partner's ratio term divided by the total of the ratio terms.

In the new ratio, A and B have 9 and 7 parts respectively, so their combined parts are 9 + 7 = 16. The total number of parts is 9 + 7 + 4 = 20. Therefore, their combined share is \(\frac{16}{20}=\frac{4}{5}\). The distractor \(\frac{3}{5}\) represents 12 out of 20 parts, not the combined share of A and B. Exam tip: Add the shares of the specified partners and divide by the total of all ratio terms.

A’s new share is found by subtracting B’s and C’s shares from the total profit: 1 - 2/5 - 1/4 = 20/20 - 8/20 - 5/20 = 7/20. Therefore, option A is correct. The old ratio 7:5 is not needed directly because B’s and C’s new shares are already specified. In such questions, remember that the sum of all partners’ new shares must equal 1.

The total profit share is 1. Therefore, C's share = 1 − 1/2 − 1/3 = 1/6. Converting 1/2:1/3:1/6 into whole numbers by multiplying by 6 gives 3:2:1. Hence, option A is correct. Exam tip: Multiply fractional shares by the LCM of their denominators to obtain the simplest whole-number ratio. Option C is incorrect because 1/2 + 1/3 + 1/4 exceeds 1.

The total parts in the new ratio are \(12+9+4=25\). C receives 4 parts, so C's share is \(\frac{4}{25}\). Option B incorrectly uses 21 as the total; the sum of all ratio terms is 25. Exam tip: divide the partner's ratio term by the sum of all terms in the new ratio.

The governing concept is sacrificing ratio, which is calculated by subtracting each old partner’s new share from the corresponding old share. The old ratio totals 8, so A’s old share is 5/8 and B’s old share is 3/8. The new ratio totals 16, so A’s new share is 7/16 and B’s new share is 4/16. A’s sacrifice is 5/8 − 7/16 = 10/16 − 7/16 = 3/16. B’s sacrifice is 3/8 − 4/16 = 6/16 − 4/16 = 2/16. Therefore, the sacrificing ratio is 3/16:2/16 = 3:2, making option A correct. Options B and C are old or new ratio figures, while D reverses the calculated sacrifices.

A's old and new share is (2/3) so A made no sacrifice. B's share fell from (1/3) to (1/6) so B sacrificed.

The direct answer is A, (1:1). First convert the old ratio 3:7 into fractions: A had 3/10 and B had 7/10. The new ratio 2:6:2 has total 10, so A now has 2/10 and B has 6/10. A’s sacrifice is 3/10 − 2/10 = 1/10. B’s sacrifice is 7/10 − 6/10 = 1/10. Therefore their sacrifices are equal, or 1:1. Option A is correct. Option B, 3:7, is merely the old ratio, not the calculated sacrifice. Option C, 2:6, gives the new shares of A and B, not their sacrifices. Option D, 1:2, does not follow because both calculated sacrifices are equal. Exam cue: always subtract each partner’s new share from the old share before forming the ratio.

B’s old profit share was \(1/5\), and its share in the new ratio is also \(1/5\). Thus, B’s share did not decrease, so B made no sacrifice. In contrast, A’s share fell from \(4/5\) to \(3/5\), meaning A sacrificed \(1/5\). For exams, compare each old partner’s old and new share; equal shares indicate zero sacrifice.

Under the old ratio, A’s share was 7/10 and B’s share was 3/10. Under the new ratio, A’s share is 6/10 and B’s share is 2/10. Therefore, A’s sacrifice is 7/10 − 6/10 = 1/10, and B’s sacrifice is 3/10 − 2/10 = 1/10. Since both partners sacrificed equally, C’s 2/10 share was obtained through equal sacrifice. Exam tip: Subtract each old partner’s new share from the old share to find the sacrifice ratio.

Under the old ratio, A’s share was 5/9 and B’s share was 4/9. Under the new ratio, A’s share is 4/9 and B’s share is 3/9. Therefore, A’s sacrifice = 5/9 − 4/9 = 1/9 and B’s sacrifice = 4/9 − 3/9 = 1/9. Hence, the sacrificing ratio is 1:1. Exam tip: Calculate each old partner’s sacrifice as old share minus new share.

In such a case the usual exam rule is that the balance profit is shared in the old ratio. If the question gives another basis follow it.

The new profit sharing ratio shows sharing of future profits and losses after admission. Do not confuse it with capital ratio.

An old partner's new share is found by subtracting sacrifice from old share. First calculate the sacrifice correctly.

The governing accounting principle is that all distributable profit represents one complete whole. Consequently, after a new partner is admitted, the fractional shares of every partner together must add to 1, or 100 percent. For example, if the shares are 1/2, 1/3 and 1/6, their total is 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1. This check confirms that no profit has been omitted or allocated twice. The old ratio’s total is relevant only to the old arrangement, and the new partner’s share alone is not the total. Therefore option A is correct; zero would mean that no profit is allocated.

When only A sacrifices, B's old share remains B's new share. Read the source of share carefully.

Taking the share in old ratio means the sacrificing ratio will also be the old ratio. This is a common rule in admission.

The total parts in the new ratio 3:2:1 are 3+2+1=6. Therefore, the partners’ profit shares are 3/6, 2/6 and 1/6 respectively, which can also be written as 1/2, 1/3 and 1/6. Option B is incorrect because each ratio part must be divided by the sum of all parts, not by the largest part. Exam tip: To convert any ratio into fractions, divide each part by the total of the ratio parts.

After admission the new partner shares future profits. Therefore the new profit sharing ratio includes all partners.