New Profit Sharing Ratio

A's sacrifice is (5/6-2/3=1/6) and total sacrifice is also (1/6). So B's sacrifice is zero and sacrificing ratio is (1:0).

In the new profit-sharing ratio, the shares of A, B and C must total 1. Therefore, B’s new share is \(1-\frac{1}{3}-\frac{2}{9}=\frac{9-3-2}{9}=\frac{4}{9}\). \(\frac{2}{9}\) is C’s allotted share, while \(\frac{1}{3}\) is A’s new share. Exam tip: Always check that the new shares of all partners add up to 1.

Answer: option A, 1:1. Sacrificing ratio is calculated partner by partner as old share minus new share. The old ratio 4:5 has total 9 parts, so A’s old share was 4/9. A’s new share is 1/3=3/9. Thus A sacrifices 4/9−3/9=1/9. C receives a total share of 2/9. The remaining part of C’s share must be sacrificed by B, so B’s sacrifice=2/9−1/9=1/9. Therefore the sacrificing ratio A:B is (1/9):(1/9)=1:1. Option B and option C represent unequal sacrifices and do not satisfy the given information. Option D is merely the old profit-sharing ratio, not the sacrificing ratio. The total sacrifice 1/9+1/9=2/9 also checks exactly with C’s admitted share.

A sacrifices (2/15) and B sacrifices (1/15). New shares are (3/5) (1/5) and (1/5) so the ratio can be written as (9:3:3).

The governing concept is that a new partner’s share is obtained by reducing the shares of the sacrificing partners, while the non-sacrificing partners retain their old shares. The old ratio 9:6:5 totals 20, so the old shares are 9/20, 6/20 and 5/20. The incoming partner receives 1/10, which is equal to 2/20, and this entire amount is sacrificed by the third partner. Therefore, the first partner remains at 9/20, the second remains at 6/20, and the third becomes 5/20 − 2/20 = 3/20. The incoming partner has 2/20. Hence the new ratio is 9:6:3:2, so option A is correct. The other options either deduct from the wrong partner or fail to preserve the stated total share.

The governing rule is that the total sacrifice made by the old partners must equal the incoming partner’s share. The old ratio 3:5 gives Neeraj 3/8 and Gopal 5/8. Neeraj sacrifices 1/6 of his own old share, not 1/6 of the total profit; therefore his sacrifice is (1/6) × (3/8) = 1/16. The required total sacrifice is 1/4, so Gopal’s sacrifice is 1/4 − 1/16 = 4/16 − 1/16 = 3/16. Neeraj’s new share is 3/8 − 1/16 = 5/16, and Gopal’s is 5/8 − 3/16 = 7/16. The new partner receives 1/4 = 4/16. Thus the ratio is 5:7:4, equivalent to 15:21:12. Since option B gives that equivalent ratio, B is correct; option C is the unreduced form.

The governing concept is sacrificing ratio: sacrifice by an old partner equals the old share minus the new share. The old ratio 2:1 gives old shares of 2/3 and 1/3. For the first partner, sacrifice is 2/3 − 3/8. Using denominator 24, this is 16/24 − 9/24 = 7/24. For the second partner, sacrifice is 1/3 − 1/4 = 4/12 − 3/12 = 1/12 = 2/24. Therefore the sacrificing ratio is 7/24:2/24, or 7:2. The sacrifices together equal 9/24 = 3/8, exactly the incoming partner’s share, which confirms the calculation. Option A is correct. The other options confuse the old ratio with the sacrificing ratio or fail to use the stated new shares.

The relevant principle is equal sacrifice: when the incoming partner’s share is taken equally from two old partners, each sacrifices half of that share. The old ratio 5:5:2 totals 12, so the first two partners each have 5/12 and the third has 2/12. The new partner receives 1/4, and each of the first two sacrifices 1/8. Thus each retained share is 5/12 − 1/8. With denominator 24, this is 10/24 − 3/24 = 7/24. The third partner is unaffected and retains 2/12 = 4/24. The new partner receives 1/4 = 6/24. Hence the new ratio is 7:7:4:6, option A. Option B ignores sacrifice, while C is not the resulting ratio and D changes the third partner incorrectly.

The governing concept is that all new profit shares together must equal one whole, while the stated condition determines how the remaining share is distributed. The new partner receives 1/3, so the three old partners together retain 1 − 1/3 = 2/3. Since their new shares are equal, each old partner receives (2/3) ÷ 3 = 2/9. The incoming partner’s 1/3 is 3/9. Therefore the four new shares are 2/9, 2/9, 2/9 and 3/9, giving the ratio 2:2:2:3. Option B is correct. The original ratio 1:2:3 does not determine the final proportions once the question explicitly states that the old partners’ new shares are equal. Option A incorrectly makes the incoming share equal to each old share.

The governing idea is that the incoming partner’s share is divided among old partners according to the specified sacrifices. The old ratio 11:4 totals 15, so the first partner has 11/15 and the second has 4/15. The new partner needs 1/5 = 3/15. The second partner sacrifices 1/15, so the first partner must sacrifice the balance, 3/15 − 1/15 = 2/15. The first partner’s new share is 11/15 − 2/15 = 9/15. The second partner’s new share is 4/15 − 1/15 = 3/15, and the incoming partner receives 3/15. Therefore the new ratio is 9:3:3, which is option A. It may be simplified to 3:1:1, but option A is the equivalent ratio presented.

The governing concept is conservation of the whole profit share: the new shares of every old partner and the incoming partner must add to 1. The first partner has 1/5, the second has 1/4, and the new partner has 1/4. Therefore the third partner receives the residual share, calculated as 1 − 1/5 − 1/4 − 1/4. Taking denominator 20 gives 20/20 − 4/20 − 5/20 − 5/20 = 6/20, which simplifies to 3/10. Thus option A is correct. The old ratio 2:3:5 is not required for this residual calculation because the question already supplies the relevant new shares. Options B, C and D would make the total of all four shares different from one.

The governing rule is that each old partner’s new share equals the old share minus the amount sacrificed, and the incoming partner’s share equals the total sacrifice. From the old ratio 3:2, the first partner’s old share is 3/5 and the second partner’s old share is 2/5. The first retains 3/5 − 1/10 = 6/10 − 1/10 = 1/2. The second retains 2/5 − 1/5 = 1/5. The new partner receives 1/10 + 1/5 = 1/10 + 2/10 = 3/10. Therefore the new shares are 1/2, 1/5 and 3/10. Multiplying each by 10 gives 5:2:3, so option A is correct. Their total is 10/10, confirming that no share has been omitted.

The governing concept is sole sacrifice: when the incoming partner obtains the entire share from one existing partner, only that partner's share is reduced. In the old ratio 4:3:2, the partners' shares are 4/9, 3/9 and 2/9. The third partner sacrifices 1/9, so the third partner retains 2/9 − 1/9 = 1/9. The first and second partners remain at 4/9 and 3/9, while the new partner receives 1/9. Therefore the new ratio is 4/9:3/9:1/9:1/9, or 4:3:1:1 after removing the common denominator. Hence option A is correct.

The key concept is that a fraction of an old partner’s share is calculated from that partner’s actual old share. The old ratio 2:3 gives Seema 2/5 and Geeta 3/5. Seema sacrifices 1/8 of her old share, so her sacrifice is (1/8) × (2/5) = 1/20. Radha’s total share is 1/4, therefore Geeta’s balance sacrifice is 1/4 − 1/20 = 5/20 − 1/20 = 1/5. Seema retains 2/5 − 1/20 = 8/20 − 1/20 = 7/20. Geeta retains 3/5 − 1/5 = 2/5 = 8/20. Radha receives 1/4 = 5/20. Consequently, the new ratio is 7:8:5, which is option B. The other choices do not reflect both the fractional sacrifice and the balance sacrifice.

The governing concept is that the incoming partner’s share equals the combined sacrifice of the old partners. The old ratio 6:5:4 totals 15, so the old shares are 6/15, 5/15 and 4/15. The first and second partners each sacrifice 1/15. The new partner’s total share is 1/5 = 3/15, so the third partner sacrifices the balance: 3/15 − 1/15 − 1/15 = 1/15. The retained shares are therefore 6/15 − 1/15 = 5/15, 5/15 − 1/15 = 4/15 and 4/15 − 1/15 = 3/15. The incoming partner receives 3/15. Thus the new ratio is 5:4:3:3, making option A correct. The other options fail to deduct the specified sacrifices consistently.

The governing concept is that a fraction stated as being taken from a partner applies to that partner’s old profit share, not to the whole profit. In the old ratio 2:1, the first partner’s share is 2/3 and the second partner’s share is 1/3. The first partner sacrifices (1/4) × (2/3) = 1/6, so the retained share is 2/3 − 1/6 = 1/2. The second sacrifices (1/3) × (1/3) = 1/9, so the retained share is 1/3 − 1/9 = 2/9. The incoming partner receives 1/6 + 1/9 = 5/18. Expressing all shares in eighteenths gives 9/18:4/18:5/18, or 9:4:5. Therefore, option A is correct; the other options result from applying the fractions incorrectly or failing to reduce the shares to a common denominator.

The governing concept is that the incoming partner’s share is first deducted from the total profit, and the balance is distributed among the old partners in their specified new inter se ratio. The new partner receives 1/4, so the old partners together retain 3/4. Their ratio 3:2:1 has a total of 6. Therefore, their individual shares are (3/4)(3/6) = 3/8, (3/4)(2/6) = 1/4, and (3/4)(1/6) = 1/8. The incoming partner receives 1/4. Thus the complete ratio is 3/8:1/4:1/8:1/4. Multiplying by 8 gives 3:2:1:2, and multiplying by 3 gives the equivalent ratio 9:6:3:6. Hence option A is correct. Option B omits the scaling for the retained 3/4, while the other alternatives do not preserve the stated shares.

The governing concept is sole sacrifice: when the incoming partner obtains the entire share from one old partner, only that partner’s share decreases. The old ratio 9:7:4 totals 20, so the original shares are 9/20, 7/20 and 4/20. The first partner gives 1/5, which equals 4/20, to the incoming partner. Consequently, the first partner retains 9/20 − 4/20 = 5/20. The second and third partners make no sacrifice and retain 7/20 and 4/20. The new partner receives 1/5 = 4/20. Therefore, the complete new ratio is 5/20:7/20:4/20:4/20, which reduces to 5:7:4:4. Option A is correct. Option B fails to reduce the first partner’s share, while C and D change partners who were not stated to sacrifice.

The governing concept is that the incoming partner's share is sacrificed by old partners in the stated sacrifice ratio, while the old ratio determines their original shares. The old shares are 5/9 and 4/9. The total sacrifice is 2/9 in the ratio 2:3, so the first sacrifices (2/5)(2/9) = 4/45 and the second sacrifices (3/5)(2/9) = 2/15 = 6/45. The first retains 25/45 − 4/45 = 21/45, and the second retains 20/45 − 6/45 = 14/45. The new partner has 2/9 = 10/45. Thus the new ratio is 21:14:10, option A.

The governing concept is that the specified sacrifice is taken first, and the balance of the incoming partner’s share is taken from the other named partner. The old ratio 8:5:2 totals 15, so the old shares are 8/15, 5/15 and 2/15. The first partner sacrifices 1/15. The new partner’s total share is 1/5 = 3/15, so the second partner sacrifices the balance, 3/15 − 1/15 = 2/15. The retained shares are therefore 8/15 − 1/15 = 7/15 for the first partner, 5/15 − 2/15 = 3/15 for the second, and 2/15 for the third. The incoming partner gets 3/15. Hence the new ratio is 7:3:2:3. Option A is correct; the other options either deduct the wrong amount from the second partner or alter the unaffected third partner.

The governing rule is Sacrifice = Old Share − New Share. In the old ratio 3:2, the first partner originally held 3/5 and the second held 2/5. The first partner’s sacrifice is 3/5 − 1/2 = 6/10 − 5/10 = 1/10. The second partner’s sacrifice is 2/5 − 1/4 = 8/20 − 5/20 = 3/20. To compare them, convert 1/10 into twentieths: 1/10 = 2/20. Thus the sacrificing ratio is 2/20:3/20, or 2:3. Option A is correct. Option B reverses the two sacrifices. Options C and D cannot be obtained from the required old-share-minus-new-share calculation. The sacrifices also total 1/4, exactly matching the incoming partner’s share.

The governing concept is that the old partners’ stated new ratio is an inter se ratio, not the complete ratio including the incoming partner. Since the new partner receives 1/5, the old partners together retain 4/5. Their inter se ratio 4:3:1 totals 8, so their individual shares are (4/5)(4/8) = 2/5, (4/5)(3/8) = 3/10, and (4/5)(1/8) = 1/10. The incoming partner’s share is 1/5. Thus the complete shares are 2/5:3/10:1/10:1/5. Multiplying by 40 gives 16:12:4:8. Therefore option A is correct. Option B incorrectly treats the inter se ratio as the complete ratio, while C and D do not preserve the total 4/5 share of the old partners.

The correct answer is A. Sacrifice equals an old partner’s old share minus the partner’s new share. Before admission, A’s share is 5/8 and B’s share is 3/8. The new ratio 7:5:4 has total 16 parts, so A’s new share is 7/16 and B’s new share is 5/16. A sacrifices 5/8 − 7/16 = 10/16 − 7/16 = 3/16. B sacrifices 3/8 − 5/16 = 6/16 − 5/16 = 1/16. Thus the sacrificing ratio is 3/16:1/16 = 3:1. B reverses the ratio; C is the old ratio; D is part of the new ratio, not the sacrifice. Always subtract new share from old share.

The relevant rule is that each old partner’s sacrifice equals old share minus new share. The old ratio 7:5 gives A an old share of 7/12 and B an old share of 5/12. The new ratio 4:3:1 totals eight parts, so A receives 4/8 = 1/2 and B receives 3/8. A’s sacrifice is therefore 7/12 − 1/2 = 7/12 − 6/12 = 1/12. B’s sacrifice is 5/12 − 3/8 = 10/24 − 9/24 = 1/24. Thus the ratio is 1/12 : 1/24 = 2:1, so option A is correct. The old ratio 7:5 and the new ratio 4:3:1 describe allocations, not the amount surrendered by each partner.

The governing concept is goodwill under the capitalization of average profit method. Capitalized value of the business is calculated by dividing average profit by the normal rate and expressing the rate as a percentage: Capitalized Value = ₹2,80,000 × 100/14 = ₹20,00,000. Goodwill is the excess of this capitalized value over the actual capital employed. Therefore, Goodwill = ₹20,00,000 − ₹16,50,000 = ₹3,50,000. Option C is correct. Option A can result from using an incorrect capitalized figure; option B does not equal the calculated excess, and option D also ignores the required subtraction of actual capital. The rate must be treated as 14 percent, not as an absolute amount of ₹14.