New Profit Sharing Ratio

After Tina receives \(1/7\) of the profit, the remaining share for the old partners is \(1-1/7=6/7\). Seema’s share among the old partners is \(4/(4+3)=4/7\). Therefore, Seema’s new share is \(6/7\times4/7=24/49\). The value \(4/7\) is Seema’s old share, not her new share. Exam tip: When the new partner’s share is sacrificed in the old ratio, distribute the remaining profit among the old partners in that ratio.

The remaining share is (4/5) and Yogesh's old ratio part is (3/5). So his new share is (4/5\times3/5=12/25).

The total profit share is taken as 1. Therefore, the collective share remaining for the old partners is 1 − 1/3 = 2/3. Hence, option A is correct. Option B is the new partner’s share, while option D represents the entire profit share without deducting the new partner’s share. Exam tip: To find the old partners’ remaining share, subtract the new partner’s share from 1.

Old partners' total share is (7/8) and it is in (4:3). Taking denominator (56) gives C's share (1/8=7/56).

The new partner receives \(1/5\), so the profit remaining for the old partners is \(4/5\). Under the old ratio 7:3, the first partner receives \(\frac{4}{5}\times\frac{7}{10}=\frac{14}{25}\), and the second partner receives \(\frac{4}{5}\times\frac{3}{10}=\frac{6}{25}\). The new partner’s share is \(\frac{1}{5}=\frac{5}{25}\). Therefore, the new ratio is 14:6:5. Option B is incorrect because it does not reduce the old partners’ shares to account for the new partner’s share. Exam tip: When the remaining profit is shared in the old ratio, calculate each old partner’s new share as remaining profit × old fraction.

New profit sharing ratio is used to divide profit among all partners after admission. Do not limit it only to the new partner.

In the old ratio of 5:1, Raj’s share is 5/6 and Taj’s share is 1/6. Dev’s entire 1/6 share is taken from Taj, so Raj retains 5/6, Taj’s new share becomes zero, and Dev receives 1/6. Therefore, the new ratio is 5/6:0:1/6 = 5:0:1. Exam tip: When a new partner’s entire share is sacrificed by only one old partner, the shares of the other partners remain unchanged.

Since the old ratio is 3:2, Anil’s old share is 3/5 and Sunil’s old share is 2/5. Anil’s new share = 3/5 − 1/8 = 19/40, while Sunil’s new share = 2/5 − 1/8 = 11/40. Kajal’s share, 1/4, equals 10/40. Therefore, the new ratio is 19/40 : 11/40 : 10/40 = 19:11:10. Exam tip: The incoming partner’s share should equal the total sacrifice made by the old partners; here, 1/8 + 1/8 = 1/4.

The direct answer is 2:1:1, so option A is correct. To convert fractional shares into a whole-number ratio, multiply all fractions by their least common denominator. The denominators are 2, 4, and 4, whose least common multiple is 4. Multiplying each share by 4 gives (1/2)×4=2, (1/4)×4=1, and (1/4)×4=1. Therefore the new profit-sharing ratio is 2:1:1. Check the result by adding the ratio parts: 2+1+1=4. The corresponding fractions are 2/4, 1/4, and 1/4, exactly the given shares. Option B changes the order of the partners, so it assigns the half share to the wrong person. Option C also changes the order. Option D does not preserve the given fractions because 4:2:1 has total 7 and represents 4/7, 2/7, and 1/7. The memory cue is: use a common denominator, then remove the denominator.

All the fractions have the same denominator, 8, so their profit-sharing ratio is determined directly by the numerators: 3:3:2. Options B and C change the given order, while 8:8:8 incorrectly uses the common denominator as the ratio. Exam tip: When fractions have the same denominator, compare their numerators directly.

Direct answer: The new ratio is Vikas:Nikhil:Pooja = 9:15:8, so option A is correct. Pooja receives \(1/4\), so the old partners together retain \(3/4\). This remainder is divided in the old ratio 3:5. Vikas receives \(3/4×3/8=9/32\), and Nikhil receives \(3/4×5/8=15/32\). Pooja's share is \(1/4=8/32\). Hence the ratio is 9:15:8. Option A matches these shares. Option B incorrectly treats the old ratio as unchanged and does not reduce it for Pooja. Option C is not in the required simplest proportional result and gives the wrong total scaling. Option D gives Nikhil the wrong share. The safe method is remainder times each old partner's fractional share.

The whole profit is taken as \(1\). Therefore, the combined remaining share of the old partners is \(1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{3}{5}\), so option A is correct. \(\frac{2}{5}\) is the new partner’s share, not the remaining combined share of the old partners. Exam tip: subtract the incoming partner’s share from the total share \(1\) to find the old partners’ combined share.

Khushi’s 1/5 share is sacrificed by Om and Prem in their old ratio of 1:4. Thus, Om sacrifices 1/25 and Prem sacrifices 4/25. Om’s new share is 1/5 − 1/25 = 4/25, while Prem’s new share is 4/5 − 4/25 = 16/25. Khushi receives 1/5 = 5/25. Therefore, the new ratio is 4:16:5. Exam tip: Divide the incoming partner’s share in the old ratio and subtract each partner’s sacrifice from their old share.

Ankit's original share is 2/5, or 4/10, and Rachit's is 3/5, or 6/10. Since Mansi's 1/10 share comes entirely from Rachit, Rachit's new share is 6/10 − 1/10 = 5/10. The new ratio is therefore 4/10 : 5/10 : 1/10, or 4:5:1.

Old partners' total share is (5/6). Dividing it in (2:3) gives (10/30) and (15/30) while the new partner is (5/30).

The governing rule is that, when an incoming partner takes a share in the old ratio, each old partner sacrifices the incoming share in proportion to that partner’s old share. The total old ratio is 3+2=5, so the first partner’s proportion is 3/5. The new partner receives 1/5, and the first partner’s sacrifice is therefore 1/5 × 3/5 = 3/25. Hence option A is correct. Option B uses the second partner’s proportion, 2/5, rather than the first partner’s 3/5. Option C treats the entire incoming share as the first partner’s sacrifice, while option D states the first partner’s old share instead of the amount surrendered.

The second old partner’s share in the old ratio is \(1/5\). Since the new partner takes \(1/10\) in the old ratio, the second partner’s sacrifice is \(1/10 \times 1/5 = 1/50\). Option B represents the first partner’s sacrifice because that partner’s old share is \(4/5\). Exam tip: Multiply the incoming partner’s share by each old partner’s share in the old ratio.

All three fractions have the same denominator, 12. Therefore, their profit-sharing ratio is given directly by the numerators: 5:4:3. Option B reverses the order, while option D incorrectly treats the partners as having equal shares. Exam tip: when fractions have a common denominator, compare their numerators to obtain the ratio.

The new ratio shows the profit shares of all partners of the firm. After admission the new partner is also included.

The governing concept is that the incoming partner’s share is deducted from the whole profit first, and the remainder is distributed among the old partners in their old ratio. Radha receives 1/5, so 4/5 remains for Mona and Sona. Their old ratio is 3:7, whose total is 10. Mona receives (4/5) × (3/10) = 12/50, and Sona receives (4/5) × (7/10) = 28/50. Radha’s 1/5 equals 10/50. Thus the new ratio is 12:28:10, so option A is correct. Option B fails to reduce the old shares, while C and D do not distribute the remaining 4/5 in the ratio 3:7.

Bala’s old share was 1/3 because Abhay and Bala shared profits in the ratio 2:1. Bala sacrifices 1/8 of his share. Therefore, his new share = 1/3 − 1/8 = 8/24 − 3/24 = 5/24. Option B is only Bala’s old share and does not account for the sacrifice. Exam tip: On admission of a partner, a sacrificing partner’s new share is calculated as old share minus the share sacrificed.

The sacrificing ratio is the ratio of the profit shares surrendered by the old partners. When the new partner’s share is taken equally from both old partners, their sacrifices are equal; hence, the sacrificing ratio is 1:1. Exam tip: Sacrifice = Old Profit-Sharing Ratio − New Profit-Sharing Ratio.

First know how much share the new partner gets and from whom it comes. This keeps the calculation in the right direction.

Since the old ratio is 5:3, Ishan's share is 5/8 and Dhruv's share is 3/8. Nayan receives 1/8 = 2/16. Therefore, Ishan's new share is 5/8 − 1/16 = 9/16, while Dhruv's new share is 3/8 − 1/16 = 5/16. Hence, the new ratio is 9/16 : 5/16 : 2/16 = 9:5:2. Option B merely scales up the old ratio and does not account for the shares sacrificed by Ishan and Dhruv. Exam tip: When the incoming partner acquires a share equally from existing partners, subtract the acquired portion from each of their old shares.

A profit-sharing ratio represents the fraction of the firm’s total profit assigned to all partners. Since the whole profit is one complete unit, all the new fractions must together equal 1, or 100 percent. This is a basic checking rule after a partner is admitted or the ratio is changed. It does not depend on the amount of profit, cash, or capital.

To verify the result, add every new partner’s share using a common denominator if necessary. If the total is less than or greater than 1, at least one share has been calculated, copied, or simplified incorrectly. Therefore, the suitable conclusion is that there is an error in calculation, which is option A. The other choices describe unrelated financial conditions.