New Profit Sharing Ratio

The old shares of A and B are \(\frac{3}{11}=\frac{15}{55}\) and \(\frac{8}{11}=\frac{40}{55}\), respectively. C receives \(\frac{2}{11}=\frac{10}{55}\). Since A and B sacrifice in the ratio 2:3, A sacrifices \(\frac{4}{55}\) and B sacrifices \(\frac{6}{55}\). Therefore, A’s new share is \(\frac{11}{55}\), B’s is \(\frac{34}{55}\), and C’s is \(\frac{10}{55}\). Hence, the new ratio is 11:34:10. The ratio 3:8:2 is incorrect because it does not deduct the sacrificing shares from A and B. Exam tip: Convert the old ratio into fractional shares before subtracting the sacrifice.

A’s old share is \(10/13=50/65\), and B’s old share is \(3/13=15/65\). C receives \(1/13=5/65\). Since the sacrificing ratio is 3:2, A sacrifices \(3/65\) and B sacrifices \(2/65\). Thus, A’s new share is \(47/65\), B’s is \(13/65\), and C’s is \(5/65\). Therefore, the new ratio is 47:13:5. Exam tip: Subtract each old partner’s sacrifice from the old share, then assign the new partner’s share.

The old total ratio of A and B is 5+11=16, so their old shares are 5/16 and 11/16. To give C a 1/4 share, A sacrifices 1/20 and B sacrifices 1/5 because the sacrificing ratio is 1:4. Thus, A’s new share is 5/16−1/20=21/80, and B’s new share is 11/16−1/5=39/80. C’s share is 1/4=20/80. Therefore, the new ratio is 21:39:20. Option C incorrectly distributes the sacrificed share; the sacrifice must be deducted from the old shares in the stated ratio. Exam tip: subtract each old partner’s sacrifice from their old share before forming the new ratio.

C’s 2/15 share is sacrificed by A and B in the ratio 5:1. Therefore, A’s sacrifice is 2/15 × 5/6 = 1/9, and B’s sacrifice is 2/15 × 1/6 = 1/45. Expressing the old shares with denominator 45, A has 33/45 and B has 12/45. Their new shares are A = 33/45 − 5/45 = 28/45, B = 12/45 − 1/45 = 11/45, while C receives 6/45. Hence, the new ratio is 28:11:6. Exam tip: subtract each old partner’s sacrificing share from the old share and then include the incoming partner’s share.

A and B originally receive \(2/11=4/22\) and \(9/11=18/22\), respectively. C’s share is \(3/11=6/22\). Since A and B sacrifice in the ratio 1:5, A sacrifices \(1/22\) and B sacrifices \(5/22\). Thus, A’s new share is \(4/22-1/22=3/22\), B’s is \(18/22-5/22=13/22\), and C’s is \(6/22\). Therefore, the new ratio is \(3:13:6\). Exam tip: subtract each existing partner’s sacrifice from their old share and then include the admitted partner’s share.

A and B’s old shares are 7/15 and 8/15. Since C receives 1/5 of the total profit equally from A and B, each old partner sacrifices 1/10. Thus, A’s new share is 7/15 − 1/10 = 11/30, B’s new share is 8/15 − 1/10 = 13/30, and C’s share is 1/5 = 6/30. Therefore, the new ratio is 11:13:6. Exam tip: When the sacrifice is equal, subtract the same amount from each old partner’s share.

Direct answer: Option A, 3:4:2, is correct. A and B originally share profits in 4:5, so their shares are 4/9 and 5/9. C receives 2/9, and this is taken equally from A and B. Equal sacrifice means each gives up half of 2/9, namely 1/9. Therefore A’s new share is 4/9 − 1/9 = 3/9, and B’s new share is 5/9 − 1/9 = 4/9. C keeps 2/9. The resulting ratio is 3:4:2. Option A exactly matches. Option B, 4:5:2, fails to subtract the sacrificed amounts from A and B. Option C, 8:10:4, is numerically equivalent to 4:5:2, so it has the same error and is not the final ratio. Option D, 2:5:2, wrongly reduces A by two parts instead of one. Exam method: divide the incoming partner’s share according to the sacrifice condition, subtract each sacrifice from the relevant old share, and retain the incoming share unchanged.

A and B’s old shares are 6/17 and 11/17, respectively. Since C receives 3/17 equally, A and B each sacrifice 3/34. Thus, A’s new share is 12/34 − 3/34 = 9/34, B’s new share is 22/34 − 3/34 = 19/34, and C’s share is 6/34. Therefore, the new ratio is 9:19:6. Exam tip: When the sacrifice is equal, subtract half of the incoming partner’s share from each existing partner’s share.

The total number of ratio parts is 8+7+5=20. C has 5 parts, so C’s share is \(\frac{5}{20}=\frac{1}{4}\). Options B and C represent the shares of the second and first partners, respectively, while option D uses an incorrect total of 15 parts. Exam tip: A partner’s share equals that partner’s ratio part divided by the sum of all ratio parts.

The total parts in the new ratio are \(6+9+5=20\). The old partners A and B receive 6 and 9 parts respectively, so their combined share is \(6+9=15\) parts. Therefore, their combined profit share is \(\frac{15}{20}=\frac{3}{4}\). Exam tip: Add the ratio terms of the partners whose combined share is required, then divide by the total of all ratio terms. Option C represents only B’s individual share, \(\frac{9}{20}\).

The total profit share is taken as \(1\). Therefore, C's new share is \(1-\frac{2}{5}-\frac{7}{20}=\frac{20-8-7}{20}=\frac{5}{20}=\frac{1}{4}\). Thus, \(\frac{2}{5}:\frac{7}{20}:\frac{1}{4}\), after multiplying each term by 20, becomes \(8:7:5\). Option C incorrectly calculates C's share as \(\frac{3}{20}\). Exam tip: Convert all fractional shares to a common denominator before forming the new ratio.

When a new partner receives a profit share, the old partners give up part of their existing shares; this is the sacrificing ratio. The new profit-sharing ratio is a different concept. Exam tip: sacrifice is always identified for old partners.

The correct answer is option C, 1:1. Sacrificing share means old share minus new share, because it shows how much of an existing partner's share is given up for the incoming partner. The old ratio A:B=5:4 has total 9, so A's old share is 5/9 and B's old share is 4/9. The new ratio A:B:partner=7:5:6 has total 18, so A's new share is 7/18 and B's new share is 5/18. A's sacrifice is 5/9−7/18=10/18−7/18=3/18. B's sacrifice is 4/9−5/18=8/18−5/18=3/18. Thus the ratio is 3/18:3/18=1:1. Option A is the old ratio, not the sacrifice. Option B is part of the new ratio and ignores the amounts surrendered. Option C correctly compares equal sacrifices. Option D would mean A sacrificed twice as much as B, which the calculation disproves.

B’s old profit share was \(2/9\), since the old ratio was \(7:2\). In the new ratio \(5:2:2\), B’s share remains \(2/9\), so B made no sacrifice. In contrast, A’s share decreased from \(7/9\) to \(5/9\), so A sacrificed a part of his share. Exam tip: Compare each old partner’s old and new shares; equal shares indicate zero sacrifice.

The governing concept is sacrificing ratio, calculated as old share minus new share for each existing partner. The old ratio 3:5 has a total of 8, so A’s old share is 3/8 and B’s old share is 5/8. The new ratio 2:4:2 also totals 8, so A’s new share is 2/8 and B’s new share is 4/8. Therefore, A’s sacrifice is 3/8 − 2/8 = 1/8, while B’s sacrifice is 5/8 − 4/8 = 1/8. Their sacrifices are equal, so the sacrificing ratio is 1/8:1/8, which simplifies to 1:1. Hence option C is correct. Option A repeats the old ratio, option B repeats the new partners’ ratio terms, and option D incorrectly indicates unequal sacrifice.

Under the old ratio, A’s share was 5/12 and B’s share was 7/12. In the new ratio, A receives 4/12 and B receives 6/12. Thus, A sacrifices 1/12 and B also sacrifices 1/12. Since both sacrifices are equal, C’s 2/12 share was acquired through equal sacrifice. Exam tip: Calculate sacrifice as old share minus new share and then compare the partners’ sacrifices.

The governing concept is comparison of each existing partner’s old share with the corresponding share in the new ratio. The old ratio 4:5 totals 9, so A originally had 4/9 and B had 5/9. The new ratio 3:5:1 also totals 9; therefore A now has 3/9, B has 5/9, and C receives 1/9. A’s reduction is 4/9 − 3/9 = 1/9, exactly equal to C’s share. B’s reduction is 5/9 − 5/9 = 0, meaning B has sacrificed nothing. Thus the whole of C’s share has come only from A, so option A is correct. Option B wrongly identifies B as the sacrificing partner, option C assumes equal sacrifice despite B’s unchanged share, and option D does not answer the source of C’s share.

When only B sacrifices, A's old share remains A's new share. Always check from whom the share is taken.

The new profit sharing ratio is used to share future profits and losses among all partners after admission. Do not confuse it with capital ratio.

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

An old partner's new share is found by subtracting sacrifice from old share. First convert the sacrifice to a common denominator.

The governing concept is the completeness check for a profit-sharing ratio. The entire divisible profit is treated as one unit, so the shares allotted to all partners must collectively equal 1, or 100 percent. This remains true whether there are two, three or more partners and whether the ratio is written as fractions or as whole-number terms. For instance, shares 2/8, 4/8 and 2/8 total 8/8 = 1. If the total is less than 1, some profit is unallocated; if it exceeds 1, some profit has been counted twice. Thus option B is correct. Option A means no profit is distributed, while C and D are not the required total of all current shares.

The total parts in the ratio are 5 + 4 + 3 = 12. Since C is represented by the third term, C’s share is 3/12, which equals 1/4. The option 4/12 is a close distractor, but it represents the second partner’s share. Exam tip: Divide the partner’s ratio term by the sum of all ratio terms.

A's old share was (2/5=6/15) and new share is (7/15). So A's share increased while B sacrificed.

Both the assertion and the reason are true, and the reason correctly explains the assertion. Since C’s share is deducted only from B’s old share, A’s share does not decrease; therefore, A’s new ratio remains equal to A’s old ratio. Exam tip: The sacrificing ratio is determined only among the old partners from whose shares the new partner’s share is obtained.