New Profit Sharing Ratio

The governing concept is sacrificing ratio on admission of a partner. A partner’s sacrifice is calculated as Old Share − New Share. A’s old share is 3/(3+2) = 3/5. Under the new ratio 2:2:1, the total parts are 5 and A receives 2/5. Therefore, A’s sacrifice is 3/5 − 2/5 = 1/5. Option A is correct. Option C is A’s new-share denominator error or old share rather than the sacrifice; option B results from an incorrect subtraction; and option D would be possible only if A’s share remained unchanged. Since A’s share falls by one-fifth, that amount is surrendered for the new arrangement.

The governing rule is sacrificing ratio = old share − new share for each old partner. A’s old share is 4/7 and his new share is 3/8. Thus A sacrifices 4/7 − 3/8 = 32/56 − 21/56 = 11/56. B’s old share is 3/7 and his new share is 3/8, so B sacrifices 3/7 − 3/8 = 24/56 − 21/56 = 3/56. Comparing the sacrifices gives 11/56 : 3/56 = 11:3. Therefore option A is correct. Option B reverses the order, option C incorrectly excludes B even though B also sacrifices, and option D assumes equal sacrifice despite the different old shares. The new partner’s share is represented by the combined sacrifice of A and B.

To find sacrifice, compare each old partner’s old share with the new share. A’s old share is 5/9 and his new share is 4/9, so A sacrifices 1/9. B’s old share is 4/9 and his new share is 3/9, so B also sacrifices 1/9. Consequently, the sacrificing ratio is 1/9:1/9, or 1:1. Option A is therefore correct. Options B, C and D are inconsistent with the calculation because both A and B lose an equal portion of their original shares. C’s new share is 2/9, which equals the total sacrifice of 2/9, confirming that the comparison is internally consistent.

C receives one-third of the total profit, so A and B together retain two-thirds. Since this retained portion remains in their old ratio 5:4, A’s new share is (2/3)×(5/9) = 10/27 and B’s new share is (2/3)×(4/9) = 8/27. C’s share is 1/3 = 9/27. Putting all shares over the common denominator 27 gives the new ratio 10:8:9. Hence option A is correct. Option B simply adds C’s fraction without reducing the old partners’ shares. Option C incorrectly treats the old numerators as unchanged and gives C three parts, while option D reverses the relative positions of A and B. The ratios also sum to 27, representing the whole profit.

C's (1/6) share is sacrificed in (2:1) so A gives (1/9) and B gives (1/18). The new shares are (37/72) (23/72) and (12/72).

The governing principle is that the incoming partner’s share is deducted from the specified sacrificing partner only. The old ratio 4:3:2 totals 9, so A, B and C originally receive 4/9, 3/9 and 2/9. D is admitted for 1/6, and the entire amount is surrendered by A. A’s new share is therefore 4/9 − 1/6. Using denominator 18, this is 8/18 − 3/18 = 5/18. B remains at 3/9 = 6/18, and C remains at 2/9 = 4/18. D receives 1/6 = 3/18. Hence the new ratio is 5:6:4:3, making option A correct. The other options either fail to subtract D’s share from A or simply retain the old ratio without adjustment.

The remaining share for old partners is (3/4) and it is shared in (3:2). So the shares are (9/20) (6/20) and (5/20).

C's total share is (1/5) and B gives (1/5-1/8=3/40). A B and C get (11/40) (19/40) and (10/40).

The governing concept is that the share surrendered by a partner equals the partner’s old profit share multiplied by the fraction of that old share surrendered. K’s old share is 3/5, so K gives G (3/5) × (1/5) = 3/25. Kh’s old share is 2/5, so Kh gives G (2/5) × (1/10) = 2/50 = 1/25. G’s final share is the sum of both contributions: 3/25 + 1/25 = 4/25. Therefore option A is correct. Option B incorrectly treats the stated fractions as direct shares rather than fractions of the old shares. Options C and D arise from incomplete multiplication or incorrect addition. The calculation also confirms that G’s share is less than one-fourth, as expected.

A’s old share is \(\frac{5}{5+4}=\frac{5}{9}\). A sacrifices three-fourths of C’s share, so A’s sacrifice is \(\frac{2}{9}\times\frac{3}{4}=\frac{1}{6}\). Therefore, A’s new share is \(\frac{5}{9}-\frac{1}{6}=\frac{7}{18}\).

Old partners retain (3/4) and A gets (1/3) of it which is (1/4). A's sacrifice is (3/8-1/4=1/8).

Old partners retain (4/5) and in (3:1) B gets (1/5). B's old share was also (1/5) so sacrifice is zero.

D's (1/5) share is sacrificed in (2:2:1) so sacrifices are (2/25) (2/25) and (1/25). New shares are (21/50) (11/50) (8/50) and (10/50).

Out of Reena's (1/6) Meera gives (1/9) so Neera gives (1/18). The new shares are (17/36) (13/36) and (6/36).

The first old partner's new share is (3/4\times5/6=5/8) while old was (2/3) so he did not gain. The second new share is (1/8) so there is no gaining partner.

B’s old profit share was \(\frac{1}{3}\). After giving C \(\frac{1}{4}\), the remaining profit is \(\frac{3}{4}\). B’s new share is therefore \(\frac{3}{4}\times\frac{1}{6}=\frac{1}{8}\), since A and B divide the balance in the ratio \(5:1\). Thus, B’s sacrifice is \(\frac{1}{3}-\frac{1}{8}=\frac{5}{24}\). Remember: sacrifice = old share − new share; \(\frac{1}{8}\) is B’s new share, not the sacrificed share.

Total profit is (1) so B's share is (1-1/2-1/5=3/10). Use the total (1) rule to find the missing share.

A’s old share was 5/8 and his new share is 1/2. Therefore, A’s sacrifice is 5/8 − 1/2 = 1/8. Since C receives 1/4 of the profits, the total sacrifice of A and B is 1/4. Hence, B’s sacrifice = 1/4 − 1/8 = 1/8. Option B is incorrect because 1/4 is the combined sacrifice of A and B, not B’s individual sacrifice. Exam tip: The new partner’s share equals the total sacrifice made by the old partners.

A and B together give (1/12+1/18=5/36) so C gives the balance (1/36). C's new share should be (1/6-1/36=5/36).

D's (1/6=6/36) and A plus B give (5/36). C gives the balance (1/36) so C remains (6/36-1/36=5/36).

After giving C a \(\frac{1}{3}\) share, \(\frac{2}{3}\) of the profits remains for A and B. This remaining share is divided between them in their new mutual ratio of 4:3. Thus, A’s share is \(\frac{2}{3} \times \frac{4}{7}=\frac{8}{21}\), and B’s share is \(\frac{2}{3} \times \frac{3}{7}=\frac{6}{21}\). C’s share is \(\frac{1}{3}=\frac{7}{21}\). Therefore, the new profit-sharing ratio is 8:6:7. Exam tip: Use the new mutual ratio to divide the remaining profit; the old 7:5 ratio is not used at this stage.

A sacrifices (9/16\times1/6=3/32) and B sacrifices (7/16\times1/14=1/32). New shares are (63/144) (65/144) and (16/144).

C’s share of 2/9 must equal the total sacrifice made by A and B. Since A sacrifices 1/18, B’s sacrifice = 2/9 − 1/18 = 4/18 − 1/18 = 3/18 = 1/6. Option B is only A’s sacrifice, not B’s. Exam tip: In the admission of a partner, the incoming partner’s share equals the total sacrifice of the old partners.

Assume the total profit is 1. C’s new share is 1/4 and A’s new share is 1/2. Therefore, B’s new share is 1 − 1/2 − 1/4 = 1/4. Thus, the new ratio is 1/2 : 1/4 : 1/4, which becomes 2:1:1 after multiplying by 4. Exam tip: calculate the remaining partner’s share from the total before forming the ratio.

The old shares are A = 2/5, B = 2/5 and C = 1/5. D receives 1/5, which is sacrificed equally by A and B; therefore, each sacrifices 1/10. The new shares are A = 2/5 − 1/10 = 3/10, B = 3/10, C = 1/5 = 2/10 and D = 1/5 = 2/10. Hence, the new ratio is 3:3:2:2. Option B incorrectly retains A’s and B’s old shares without deducting their sacrifice. Exam tip: Deduct the incoming partner’s share only from the partners who actually sacrifice it.