New Ratios

B’s old share was 5/10. Under the new ratio 2:3, B’s new share is 3/5 = 6/10. Therefore, B’s gaining share = new share − old share = 6/10 − 5/10 = 1/10. The option 3/5 represents B’s new share, not the gain. Exam tip: For a retiring partner’s reconstitution, calculate a gaining share as new share minus old share.

Under the old ratio, A’s share was 3/10 and B’s share was 5/10. Under the new ratio of 2:3, A’s share becomes 2/5 = 4/10 and B’s share becomes 3/5 = 6/10. Therefore, A’s gain is 4/10 − 3/10 = 1/10 and B’s gain is 6/10 − 5/10 = 1/10. Hence, the gaining ratio is 1/10:1/10 = 1:1. Exam tip: Gaining ratio = New share − Old share.

The sum of the terms in the new ratio 7:3 is 10. Therefore, the first partner’s share is 7/10 and the second partner’s share is 3/10. Option B incorrectly uses reciprocal-like values instead of dividing each ratio term by the total. Exam tip: Convert a ratio into shares by dividing each term by the sum of all ratio terms.

The denominators of both new shares are the same, i.e., 9. Therefore, the ratio of the shares is the ratio of their numerators: 4/9 : 5/9 = 4:5. Hence, option A is correct. Option B reverses the order of the partners’ shares. Exam tip: When fractions have the same denominator, compare their numerators directly to obtain the ratio.

When the denominators of two partners’ shares are the same, their ratio is obtained directly from the numerators. Thus, \(\frac{2}{7}:\frac{5}{7}=2:5\), so option A is correct. Option B reverses the order of the partners. Exam tip: For fractions with a common denominator, compare the numerators directly to form the ratio.

Retiring partner does not share future profit. The whole profit is shared among remaining partners in new ratio.

After death future profit is shared among surviving partners. Therefore new ratio is calculated among them.

In the absence of a new agreement, the surviving partners, B and C, continue to share profits in their old relative ratio. Their old ratio was 3:3, which simplifies to 1:1. Therefore, option A is correct. Exam tip: When a partner retires or dies and there is no new agreement, the surviving partners retain their old mutual ratio.

In the absence of a new agreement, the continuing partners share profits in their old ratio. Therefore, after B’s death, A and C will share profits in the ratio of their old shares, 6:5. The ratio 4:5 is the old ratio of B and C, not the new ratio of the continuing partners. Exam tip: When a partner retires or dies and no new agreement is made, use the old ratio of the remaining partners.

The direct answer is 10:17, so option A is correct. The old total ratio is 2+3+4=9. Therefore A has 2/9, B has 3/9, and C has 4/9. C’s share is taken by A and B in the ratio 1:2. Divide 4/9 into three equal parts: each part is 4/27. A receives one part, 4/27, and B receives two parts, 8/27. Convert the old shares to denominator 27: A’s old share is 2/9=6/27, and B’s old share is 3/9=9/27. New A share = 6/27+4/27=10/27. New B share = 9/27+8/27=17/27. Hence the new ratio is 10:17. Option A is correct. Options B, 3:5, and C, 2:3, merely repeat or alter the old relationship and do not include C’s transferred share. Option D, 1:2, is only the takeover ratio, not the final ratio. Remember: first calculate the deceased partner’s share, then distribute it.

A’s share is 5 out of the total 10 parts. B receives \(5 \times \frac{2}{5}=2\) parts and C receives \(5 \times \frac{3}{5}=3\) parts from A’s share. Thus, B’s new share is \(1+2=3\) and C’s new share is \(4+3=7\). Therefore, the new ratio is 3:7. Exam tip: Apply the gaining ratio only to the retiring partner’s share, not to the entire original ratio.

A’s original share was 1/10 of the profits. When this share is divided equally, B and C each receive an additional 1/20. Thus, B’s new share is 5/10 + 1/20 = 11/20, while C’s new share is 4/10 + 1/20 = 9/20. Therefore, the new ratio is 11:9. Option 5:4 is only the old ratio of B and C. Exam tip: When the retiring or deceased partner’s share is acquired equally, add half of that share to each acquiring partner’s original share.

After C retires, the mutual profit-sharing ratio of A and B remains their old ratio, 8:6. Dividing both terms by their greatest common divisor, 2, gives 4:3. Therefore, the correct answer is 4:3. Exam tip: When the remaining partners continue in their old ratio, simplify their original ratio directly.

After A retires, only B and C remain as partners. Since they continue in their old ratio, their shares remain 5:5. Simplifying 5:5 gives 1:1, so option A is correct. Exam tip: When the remaining partners continue in the old ratio, reduce their original shares directly to find the new ratio.

In partnership reconstitution, comparison of each continuing partner's new share with the old share identifies whether that partner has gained or sacrificed. The increase is calculated as New Share - Old Share. The positive increases of the continuing partners are then compared with one another to express the gaining ratio. For example, if two partners gain 1/10 and 2/10, their gaining ratio is 1:2. Cash balance, cost of goods, and bank interest are unrelated accounting items and cannot be obtained from a comparison of profit-sharing ratios. Therefore, the correct concept is the gaining ratio, represented by option A.

In 2:3 the second partner part is 3 which is greater than the first partner part 2. So the second gains more.

1:0 means the first partner got extra share and the second got no extra share. Read zero carefully in exams.

Gaining ratio is calculated as new profit share minus old profit share. In the ratio 0:1, the first partner gains nothing, while the second partner receives the entire gain. Therefore, it represents one-sided gaining. Exam tip: the partner with 0 in the ratio has no gain.

The total share acquired from the retiring partner is 1/5. Since it is divided equally between two partners, each partner’s gaining share is 1/5 ÷ 2 = 1/10. The fraction 1/5 represents the total share acquired by both partners, not the share of each one. Exam tip: When partners gain equally, divide the retiring partner’s share by the number of gaining partners.

The first partner receives \(\frac{2}{2+1}=\frac{2}{3}\) of the retiring partner’s share. Therefore, the additional share is \(\frac{3}{10}\times\frac{2}{3}=\frac{1}{5}\). The value \(\frac{2}{3}\) is only the first partner’s proportion of the gain, not the total additional share. In exams, multiply the retiring partner’s share by the relevant fraction of the gaining ratio.

The retiring partner’s \(3/10\) share is divided between the remaining partners in the ratio 2:1. The second partner receives 1 out of the 3 total parts, so the additional share is \(3/10 \times 1/3 = 1/10\). The first partner would receive \(2/10\). Exam tip: Additional share received = retiring partner’s share × the partner’s fraction of the gaining ratio.

Gaining ratio is the ratio in which the retiring share is acquired. Here A and B acquire it in 1:4.

A’s old profit share was \(4/10=2/5\), while the new share is \(3/5\). Therefore, A’s gaining ratio = new share − old share = \(3/5-2/5=1/5\). Option C represents A’s new share, not the gain. Exam tip: Calculate gain by subtracting the old share from the new share.

B’s old share was 4/10 = 2/5. In the new ratio of 3:2, B’s share is also 2/5. Therefore, B’s gaining share = new share − old share = 2/5 − 2/5 = zero. The fraction 1/5 is C’s old share, not B’s gain. Exam tip: Always calculate gaining share by subtracting the old share from the new share.

Under the old ratio 4:4:2, A and B have shares of 4/10 and 4/10. Under the new ratio 3:2, their shares become 3/5 = 6/10 and 2/5 = 4/10. Thus, A gains 6/10 − 4/10 = 2/10 = 1/5, while B gains nothing. Therefore, the gaining ratio is 1:0. Exam tip: Calculate each partner’s gain by subtracting the old share from the new share.