New Profit Sharing Ratio

Correct answer: A. (6:3:1:3)

The old ratio 6:4:3 has a total of 13, so the old shares are 6/13 for the first partner, 4/13 for the second, and 3/13 for the third. The new partner receives 1/13 from the second partner and 2/13 from the third partner. The first partner gives nothing and therefore remains at 6/13. The second partner gives 1/13, so the new share is 4/13 − 1/13 = 3/13. The third gives 2/13, so the new share is 3/13 − 2/13 = 1/13. The incoming partner receives 1/13 + 2/13 = 3/13. Therefore the new ratio, in the order first, second, third, and new partner, is 6:3:1:3, so option A is correct.

A useful check is that the new parts add to 6 + 3 + 1 + 3 = 13, matching the whole profit. The first partner’s share is unchanged, even though the total number of partners increases. The new partner’s share must be taken from the existing partners, and the stated contributions show exactly who gives up the shares. Hence choices that leave old shares unchanged or subtract from the wrong partners cannot be correct.

Correct answer: A. (14:13:8)

The total sacrifice is (2/9). Sacrifices are (1/6) and (1/18), so new shares are (7/18,7/18,2/9), giving (7:7:4).

Correct answer: C. (5/24)

The first partner's sacrifice is (1/8). Total sacrifice is (1/3), so the second sacrifices (1/3-1/8=5/24).

Correct answer: B. Second partner

Old shares were (5/10,3/10,2/10), and new shares are (2/6,2/6,1/6). The second partner increased from (3/10) to (1/3).

Correct answer: B. Directly deducting (1/5) from total profit

"One-fifth of share" means multiplying the old partner's share by (1/5). Treating it as (1/5) of total profit is wrong.

Correct answer: A. (13:25:18:15)

Total sacrifice is (1/5). The first sacrifices (1/20) and the third sacrifices (3/20). The new shares are (13/60,20/60,9/60,12/60), giving (13:20:9:12).

Correct answer: C. Only second sacrifices

Old shares are (2/7,5/7), and new shares are (3/10,5/10). The first partner gains, so only the second is sacrificing.

Correct answer: A. 11/20

The new profit shares of all partners must add up to 1. Therefore, Bindu’s new share = 1 − 1/5 − 1/4 = 20/20 − 4/20 − 5/20 = 11/20. Option C (7/10) is Bindu’s old share, so it does not represent the revised ratio. Exam tip: subtract the new partner’s share and the specified new shares from 1 to find the remaining partner’s share.

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

The old partners' remaining total share is (4/5), and they divide it equally. Each old partner has (2/5), and the new partner has (1/5).

Correct answer: A. (16)

The old ratio total is (16) and the new partner's share is (3/16). The shares directly become (4/16,5/16,4/16,3/16).

Correct answer: A. (13:18:35:14)

The total sacrifice (1/6) is divided in (3:4), giving (1/14) and (2/21). The new shares are (5/28,5/21,5/12,1/6).

Correct answer: B. (15:20:14)

Old partners' total share is (5/7). Dividing it in (3:4) gives (15/49) and (20/49), while the new partner has (14/49).

Correct answer: A. (4:8:12:3)

Total sacrifice is (1/9). The first sacrifices (2/27), and the second sacrifices (1/27). The new shares are (4/27,8/27,12/27,3/27).

Correct answer: A. (221:119:60)

Old partners' remaining share is (17/20). Dividing it in (13:7) gives (221/400) and (119/400), while the new partner has (60/400).

Correct answer: A. \(\frac{3}{14}\)

Under the old ratio 5:2, the second partner’s share was \(\frac{2}{7}\). The incoming partner receives a total share of \(\frac{1}{7}\). Since the first partner sacrifices \(\frac{1}{14}\), the second partner must sacrifice the remaining \(\frac{1}{14}\). Therefore, the second partner’s new share is \(\frac{2}{7}-\frac{1}{14}=\frac{4}{14}-\frac{1}{14}=\frac{3}{14}\). Exam tip: the incoming partner’s share must equal the total sacrifice made by the old partners.

Correct answer: A. Total (3/20), ratio (10:5:2:3)

The new partner's total share is (3/20). Old partners' new shares are (1/2,1/4,1/10), giving (10:5:2:3).

Correct answer: C. (1/6)

The second partner's old share was (2/5) and new share is (1/3), so his sacrifice is (1/15). The first sacrifices (1/4-1/15=11/60).

Correct answer: A. (7:1:2)

Old partners' total share is (4/5). Dividing it in (7:1) gives (7/10) and (1/10), and the new partner has (2/10).

Correct answer: A. Sacrifice (1:1), new (3:1:2)

Each old partner sacrifices (1/8). The new shares are (1/2,1/4,1/4), giving (2:1:1); none of the listed ratios matches exactly.

Correct answer: A. (19:19:9:15)

The third remains (1/5) and the new partner gets (1/6). The balance for the first two is (19/30), so each gets (19/60).

Correct answer: A. (25:20:9)

The direct answer is A, 25:20:9. Chetan receives 1/6, so the old partners together retain 5/6. Their old ratio is 5:4, whose total is 9. Ajay’s new share is (5/6) × (5/9) = 25/54. Bhavesh’s new share is (5/6) × (4/9) = 20/54. Chetan’s share is 1/6 = 9/54. Hence the new ratio is 25:20:9. Option A is correct. Option B, 5:4:1, does not correctly reduce the remaining 5/6 and also does not represent the exact common denominator. Option C, 20:16:9, wrongly uses a different scaling for the old partners. Option D, 15:12:6, reduces to 5:4:2, so Chetan’s share is not 1/6. Memory cue: multiply the remaining share by each old-ratio fraction.

Correct answer: A. 28:20:12:15

Mohit receives 1/5 of the profits, leaving 4/5 for the old partners. They divide this remainder in their old ratio, 7:5:3: its 15 total parts give Rahul 28/75, Sameer 20/75 and Tanay 12/75. Mohit's share is 1/5, or 15/75. Thus, the new ratio is 28:20:12:15.

Correct answer: A. (7:8:3:6)

The total sacrifice is (1/5). The first sacrifices (3/20) and the third sacrifices (1/20). The new shares are (7/20,1/3,7/60,1/5) giving (21:20:7:12).

Correct answer: B. (6:3:4)

The old partners' total new share is (3/4). Dividing it in (2:1) gives (1/2) and (1/4), and the new partner has (1/4).

Correct answer: C. Third partner

The third partner's old share was (1/10) and the new share is (2/10). Therefore the third partner has gained.