New Profit Sharing Ratio

Correct answer: A. (12:8:5)

The remaining profit is (4/5) and sharing it in (3:2) gives A (12/25) and B (8/25). In exams first find the remaining share.

Correct answer: A. (7:3:2)

A and B sacrifice (1/8) each. New shares are (1/2,1/4,1/4) which convert to (4:2:2); check carefully before choosing. This row has an error.

Correct answer: A. (10:5:3)

The remaining share is (5/6). Dividing it in (2:1) gives (5/9,5/18,1/6) so the ratio is (10:5:3).

Correct answer: A. त्याग अनुपात

The ratio in which existing partners surrender their profit shares to admit a new partner is called the sacrificing ratio. Gaining ratio is generally relevant on retirement or death. Exam tip: sacrifice = old share − new share.

Correct answer: A. (2:1:1)

A's new share is (3/4-1/4=1/2) and B's share remains (1/4). So the ratio is (1/2:1/4:1/4=2:1:1).

Correct answer: A. 4:1:2

The old ratio of 4:3 gives A a share of 4/7 and B a share of 3/7. Since C receives 2/7 entirely from B, B’s new share becomes 3/7 − 2/7 = 1/7, while A’s share remains 4/7. Therefore, A:B:C = 4/7:1/7:2/7 = 4:1:2. Exam tip: when the incoming partner’s share is acquired from only one existing partner, reduce only that partner’s share.

Correct answer: A. (13:11:3)

C's (1/9) share is taken in (2:1) so A sacrifices (2/27) and B sacrifices (1/27). New shares are (13/27,11/27,3/27).

Correct answer: A. 3:5:2

The mathematically correct new ratio is 3:5:2, so option A is correct after correcting the original option text. C receives 1/5, and the sacrifice is equal, so A and B each give up half of 1/5, which is 1/10. A’s old share is 2/5=4/10; after sacrifice it becomes 4/10−1/10=3/10. B’s old share is 3/5=6/10; after sacrifice it becomes 6/10−1/10=5/10. C receives 1/5=2/10. Therefore the new shares are 3/10, 5/10, and 2/10, giving 3:5:2. Their total is 3+5+2=10, so the shares add to the whole profit. Option B leaves the old shares unchanged and gives C an incorrectly scaled share. Option C does not subtract equal sacrifices correctly, and option D reverses the old partners’ relative shares. The key warning is that an equal sacrifice means equal fractions are subtracted, not equal proportions of the old shares.

Correct answer: A. (13:5:2)

A's new share is (7/10-1/20=13/20) and B's is (3/10-1/20=5/20). C's share is (2/20) so the ratio is (13:5:2).

Correct answer: A. 5:3:2

A’s old share is 3/5 and B’s is 2/5. After giving up 1/10 each, their new shares are A = 3/5 − 1/10 = 1/2 and B = 2/5 − 1/10 = 3/10. C receives 1/10 + 1/10 = 1/5. Thus, the new ratio is 1/2 : 3/10 : 1/5 = 5:3:2.

Correct answer: A. 12/25

After C receives 1/5 of the profit, the remaining profit is 1 − 1/5 = 4/5. A’s old share was 6/(6+4) = 3/5. Therefore, A’s new share is \(\frac{4}{5}\times\frac{3}{5}=\frac{12}{25}\). Option B is only A’s old share and does not account for the reduction due to C’s admission. Exam tip: When the remaining profit is shared in the old ratio, each old partner’s new share equals the remaining profit multiplied by that partner’s old fraction.

Correct answer: A. \(\frac{28}{75}\)

C receives \(1/5\) of the total profit, so the portion left for A and B is \(1-1/5=4/5\). B’s old share was \(7/(8+7)=7/15\). Therefore, B’s new share is \(\frac{4}{5}\times\frac{7}{15}=\frac{28}{75}\). The value \(7/15\) represents B’s old share before C’s admission, not the new share. Exam tip: First calculate the profit left for the old partners, then multiply it by the concerned partner’s old fraction.

Correct answer: A. 36:9:5

C receives 1/10 of the total profit, so the balance available to A and B is 9/10. This balance is divided in the old ratio 4:1: A receives 9/10 × 4/5 = 18/25 = 36/50, while B receives 9/10 × 1/5 = 9/50. C’s share is 1/10 = 5/50. Therefore, the new ratio is 36:9:5. Exam tip: first calculate the balance left for the old partners, then distribute it in their old ratio.

Correct answer: A. (6:4:5)

Direct answer: Option A, 6:4:5, is correct. The old ratio of A and B is 9:6, which simplifies to 3:2. C receives 1/3, so only 2/3 remains for A and B. That remaining 2/3 must be divided in the old ratio 3:2. A receives (2/3)×(3/5)=2/5, and B receives (2/3)×(2/5)=4/15. C receives 1/3 = 5/15. Expressing every share with denominator 15 gives A 6/15, B 4/15 and C 5/15, hence 6:4:5. Option A is therefore correct. Option B, 9:6:3, treats the original figures as if they could simply be joined with C’s share; their total does not represent the required normalized distribution. Option C gives C three parts instead of five in the common denominator. Option D does not preserve the correct remaining-profit calculation. Exam cue: when the new partner gets a stated share and the remainder follows the old ratio, multiply the remainder by each old partner’s fraction.

Correct answer: A. 33:27:20

C receives 1/4 of the total profit, so 3/4 remains for A and B. Since their old ratio is 11:9, its total is 20. Therefore, A’s new share is 3/4 × 11/20 = 33/80, B’s is 3/4 × 9/20 = 27/80, and C’s share is 1/4 = 20/80. Hence, the new ratio is 33:27:20. Option B is incorrect because it treats C’s share as though it could simply be added to the old ratio. Exam tip: Multiply each old partner’s fraction by the profit remaining after the new partner’s share is deducted.

Correct answer: A. (30:12:7)

When the new share is taken in old ratio the old partners share the balance in old ratio. Therefore the ratio is (30:12:7).

Correct answer: A. 3:3:2

Let the total profit be 1. C receives 1/4, so the amount left for A and B is 1 − 1/4 = 3/4. The question specifically states that A and B divide this remainder equally, so each receives (3/4) ÷ 2 = 3/8. C’s share, 1/4, is equal to 2/8. Thus the three shares are 3/8, 3/8 and 2/8, which produce the new ratio 3:3:2. Therefore option A is correct. The ratio sums to 8, confirming the shares total one whole. Option B would give C only one-third, while options C and D do not preserve C’s fixed one-fourth share together with equal distribution of the remainder.

Correct answer: A. (8:11:3)

A's new share is (3/5-1/15=8/15) and B's is (2/5-1/30=11/30). With common denominator the ratio is (16:11:3) not option A.

Correct answer: A. 9:15:8

C receives 1/4 of the total profit, leaving 3/4 for A and B. Dividing this remainder in the old ratio 3:5 gives A's share as (3/4) × (3/8) = 9/32 and B's share as (3/4) × (5/8) = 15/32. C's share is 1/4 = 8/32. Therefore, the new profit-sharing ratio is 9:15:8. Option B incorrectly keeps A and B's old ratio without adjusting it for the remaining profit. Exam tip: First find the profit left for the old partners, then distribute it in their old ratio.

Correct answer: A. 28:35:18

C receives 2/9 of the total profit, so the remaining share for A and B is 7/9. Since their old ratio 4:5 has a total of 9, A receives \(\frac{7}{9}\times\frac{4}{9}=\frac{28}{81}\) and B receives \(\frac{7}{9}\times\frac{5}{9}=\frac{35}{81}\). C’s share is \(\frac{2}{9}=\frac{18}{81}\). Therefore, the new ratio is 28:35:18. Exam tip: First calculate the remaining share, then distribute it among the old partners in their old ratio.

Correct answer: A. 3:7:2

Convert A and B's old ratio into fractions: A=5/12 and B=7/12. Since C takes 1/6=2/12 from A, A's remaining share is 5/12−2/12=3/12=1/4. B remains 7/12 and C receives 1/6=2/12. Expressing all shares over 12 gives 3:7:2. Therefore option A is correct; the other ratios either fail to deduct C's share correctly or use inconsistent proportions.

Correct answer: A. 6:3:2

The old ratio is 6:5, so A’s and B’s old shares are 6/11 and 5/11, respectively. Since C receives 2/11 entirely from B, B’s new share becomes 5/11 − 2/11 = 3/11, while A’s share remains 6/11. Therefore, A:B:C = 6/11:3/11:2/11 = 6:3:2. Exam tip: If the incoming partner acquires the share entirely from one existing partner, reduce only that partner’s share.

Correct answer: A. (17:31:12)

C's (1/5) share is taken in (3:1) so A sacrifices (3/20) and B sacrifices (1/20). New shares are (17/60,31/60,12/60).

Correct answer: A. (7:3:3)

Direct answer: Option A, 7:3:3, is correct. The old ratio A:B is 9:4, so their old shares are 9/13 and 4/13. C receives 3/13. The question says this is sacrificed by A and B in the ratio 2:1. Since the total sacrifice is 3/13, A sacrifices 2/13 and B sacrifices 1/13. A’s new share is 9/13 − 2/13 = 7/13. B’s new share is 4/13 − 1/13 = 3/13. C’s share remains 3/13. Removing the common denominator 13 gives 7:3:3. Option A matches this calculation. Option B simply repeats the old ratio and adds C without reducing A and B. Option C does not use either the old ratio or the stated sacrifice ratio. Option D doubles A’s and B’s old parts and is not a normalized ratio. Always divide a new partner’s share among sacrificing partners before subtracting.

Correct answer: A. 8/21

A’s old share is 3/(3+4) = 3/7. Since C’s 1/7 share is taken from A and B in the ratio 1:2, A’s sacrifice is 1/7 × 1/3 = 1/21. Therefore, A’s new share is 3/7 − 1/21 = 9/21 − 1/21 = 8/21. Exam tip: A partner’s new share equals the old share minus the share sacrificed. Option B is only A’s old share and ignores the sacrifice.