New Profit Sharing Ratio

Correct answer: A. (1:1)

A's sacrifice is (6/10-5/10=1/10) and B's sacrifice is (4/10-3/10=1/10). So C's share came in (1:1).

Correct answer: A. Both assertion and reason are true and the reason is the correct explanation

If old shares reduce proportionately, sacrifice is in the old ratio. Equal percentage sacrifice correctly explains this.

Correct answer: A. Arun (15/32), Bala (9/32), Chetan (8/32)

The remaining share is (3/4) and dividing it in (5:3) gives (15/32) and (9/32). In exams find the remaining share first.

Correct answer: B. (5:5:2)

The first partner's old share was (7/12) and (1/6) is deducted from it. The shares become (5/12,5/12,2/12).

Correct answer: A. (16:12:8:9)

The old partners' remaining share is (4/5) and it is divided in (4:3:2). So the new shares are (16/45,12/45,8/45,9/45).

Correct answer: A. 4:3:3:2

The total of the old ratio 5:4:3 is 12, so Raj, Seema and Mohan originally have 5/12, 4/12 and 3/12, respectively. Raj’s new share is 5/12 − 1/12 = 4/12, and Seema’s new share is 4/12 − 1/12 = 3/12. Mohan’s share remains 3/12, while Neel receives 1/6 = 2/12. Therefore, the new ratio is 4:3:3:2. Exam tip: Subtract each sacrificing partner’s share from the old share, and leave the shares of non-sacrificing partners unchanged.

Correct answer: B. (48:30:17)

The sacrifices are (3/25) and (1/10). The new shares are (12/25,3/10,11/50), so the ratio is (24:15:11).

Correct answer: A. 2:1:1

Karan’s old share was 2/3, so his new share is 2/3 − 1/6 = 1/2. Tarun’s old share was 1/3, so his new share is 1/3 − 1/12 = 1/4. Varun receives 1/4. Therefore, the new ratio is 1/2 : 1/4 : 1/4 = 2:1:1. Exam tip: The incoming partner’s share must equal the total sacrifice made by the old partners; here, 1/6 + 1/12 = 1/4.

Correct answer: B. (99:81:40)

The remaining share is (9/11). Dividing it in (11:9) gives (99/220) and (81/220), and the new partner has (40/220).

Correct answer: A. (5:5:4:2)

The new partner gets (1/8), so each of the first two partners sacrifices (1/16). The shares are (5/16,5/16,4/16,2/16).

Correct answer: A. Aarav : Divya : Esha)

Under the old ratio 4:1, Aarav’s share was 4/5 and Divya’s share was 1/5. Aarav’s new share is 4/5 − 1/10 = 7/10, while Divya’s new share is 1/5 − 1/10 = 1/10. Esha receives 1/5 = 2/10. Therefore, Aarav : Divya : Esha = 7/10 : 1/10 : 2/10 = 7:1:2. Option B incorrectly calculates Aarav’s revised share. Exam tip: To find the new ratio, subtract each existing partner’s sacrifice from the old share and then include the incoming partner’s share.

Correct answer: D. (19:13:6)

The sacrifices are (1/10) and (1/20). The new shares are (21/40,13/40,6/40), so the ratio is (21:13:6).

Correct answer: A. (24:16:16:8:9)

The old partners' remaining share is (8/9) and it is divided in (3:2:2:1). The shares are (24:16:16:8:9).

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

The old partners' total new share is (2/3). Dividing it in (2:3) gives (4/15) and (6/15), while Priya has (5/15).

Correct answer: A. 3/10

The sum of all partners’ new shares must equal 1. Therefore, the second old partner’s share = 1 − 1/2 − 1/5 = 10/10 − 5/10 − 2/10 = 3/10. Hence, option A is correct. The old ratio 8:7 is not required for this direct balancing calculation. Exam tip: To find an unknown new share, subtract all known shares from the total share of 1.

Correct answer: B. (10:7:4:6)

Total sacrifice is (1/5). Maya's sacrifice is (1/30), so the shares are (1/3,7/30,7/30,1/5), giving (10:7:7:6).

Correct answer: A. (9:5:4:6)

The first two partners sacrifice (1/8) each. The new shares are (3/8,5/24,1/6,1/4), giving (9:5:4:6).

Correct answer: B. 0:0:1

The sacrificing ratio is the ratio of the profit shares surrendered by the old partners. Here, the first and second partners surrender nothing, while the third partner gives the entire 1/10 share to the incoming partner. Hence, the sacrificing ratio is 0:0:1. Remember that 1/10 is the incoming partner’s acquired share, not the sacrificing ratio.

Correct answer: A. (1:0:0)

The old shares were (5/10,3/10,2/10), and the new shares are (4/10,3/10,2/10). Only the first partner sacrificed (1/10).

Correct answer: C. 4/16

In the new ratio 7:5:4, the new partner is represented by the third term, 4. The total parts are 7+5+4=16, so the new partner’s share is 4/16, or 1/4. The values 7/16 and 5/16 represent the shares of the first and second old partners, respectively. Exam tip: divide the new partner’s ratio part by the sum of all new-ratio parts; the old ratio is not needed for this direct calculation.

Correct answer: D. (7:3)

Old shares are (5/9,4/9), and new shares are (3/8,3/8). Sacrifices are (13/72) and (5/72), giving (13:5).

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

The old partners' total new share is (4/5). Dividing it in (2:1) gives (8/15) and (4/15), while Raman has (3/15).

Correct answer: A. (7:6:1:2)

The new partner gets (1/8), so first and third sacrifice (1/16) each. The new shares are (7/16,6/16,1/16,2/16).

Correct answer: A. (9:6:3:6)

The correct answer is option A: (9:6:3:6), which is equivalent to (3:2:1:2). The new partner receives 1/4, so the old partners together retain 1 − 1/4 = 3/4. Their stated ratio 3:2:1 has 6 total parts. Therefore their shares are 3/4 × 3/6 = 3/8, 3/4 × 2/6 = 1/4, and 3/4 × 1/6 = 1/8. The new partner has 1/4. Converting all to denominator 8 gives 3:2:1:2. Option A, 9:6:3:6, reduces by 3 to this same ratio, so it is correct. Option B, 3:2:1:4, gives the new partner too large a share. Option C, 3:2:1:1, gives only 1/8 to the new partner. Option D, 6:4:2:3, does not preserve the required 1/4 share. Remember: first find the old partners’ remaining share, then divide it in their ratio.

Correct answer: A. (11:10:6:3)

The total sacrifice (1/6) is divided as (1/18) and (1/9). The new shares are (31/90,26/90,18/90,15/90), giving (31:26:18:15).