New Ratios

The new ratio is the ratio of the partners’ new shares: \(\frac{3}{8}:\frac{5}{8}\). Since the denominators are equal, they cancel, giving \(3:5\). Option B reverses the order of the partners’ shares. Exam tip: For fractions with the same denominator, compare their numerators to obtain the ratio.

After retirement future profits belong to remaining partners. Therefore new ratio is made only among remaining partners.

From the date of death, the partner ceases to be a member of the firm. Therefore, future profits are shared by the surviving partners in their new profit-sharing ratio. The deceased partner’s heirs receive the amount due up to the date of death, not a share in future profits. Exam tip: Distinguish profit up to the date of death from profit earned after that date.

In the absence of a new agreement, the continuing partners, B and C, share profits in their old relative ratio. Thus, their ratio is 6:3. Dividing both terms by their highest common factor, 3, gives the simplified ratio 2:1. Option B is the same ratio in unsimplified form. Exam tip: Always reduce a ratio to its lowest terms when the question asks for the simplified ratio.

When there is no new agreement, the continuing partners acquire the deceased partner’s share in their old mutual ratio. A and C had an old ratio of 9:5, so B’s 4 shares are adjusted between them in the same proportion, leaving their new ratio as 9:5. Exam tip: In the absence of a new agreement, retain the old mutual ratio of the continuing partners.

C’s original share is 2/9. A and B acquire it in the ratio 2:1, so A gets 4/27 and B gets 2/27. A’s new share is 3/9 + 4/27 = 13/27, while B’s new share is 4/9 + 2/27 = 14/27. Therefore, the new ratio is 13:14. Exam tip: Add the acquired share to each partner’s old share; the acquisition ratio alone is not the new ratio.

A’s share is 6 out of the total 10 parts, i.e. \(6/10\). B acquires \(1/6\) of A’s share, which is \(1/10\), while C acquires \(5/6\), which is \(5/10\). Thus, B’s new share is \(1/10+1/10=2/10\), and C’s new share is \(3/10+5/10=8/10\). Therefore, the new ratio is \(2:8=1:4\). The ratio 1:5 is only the gaining ratio, not the new profit-sharing ratio. Exam tip: first convert the old ratio into fractional shares, then distribute the retiring partner’s share.

A’s profit share was 2. Since B and C acquire it equally, each receives an additional share of 1. Therefore, B’s new share is 4+1=5 and C’s new share is 4+1=5. Hence, the new ratio is 5:5, or 1:1. Exam tip: When the outgoing partner’s share is acquired equally, add half of that share to each acquiring partner’s original share.

After C retires, C’s share is removed, leaving A:B = 12:8. Divide both terms by their greatest common divisor, 4: 12÷4 : 8÷4 = 3:2. Therefore, 3:2 is correct. Remember that 12:8 represents the same ratio but is not in its simplest form.

After A retires, only B and C remain, and their old mutual ratio was 5:10. Dividing both terms by their highest common factor, 5, gives the simplified ratio 1:2. Therefore, option A is correct. Exam tip: when finding a new ratio, reduce the remaining partners’ mutual ratio to its simplest form.

The direct answer is A, gaining ratio. In partnership reconstitution, a partner’s old share is compared with the new share. If the new share is larger, the increase is called gain. Step by step, write the old fraction, write the new fraction, and subtract old share from new share: gain = new share − old share. The ratio of the gains of partners is the gaining ratio. Option A is correct because it deals exactly with the extra profit share received by continuing partners. Option B, cash ratio, concerns cash or liquid assets, not profit-sharing changes. Option C, loan ratio, concerns borrowed money and is not used for this calculation. Option D, stock ratio, concerns inventory and is also unrelated. Remember: after retirement, compare new shares with old shares; the increase gives gain.

In a gaining ratio, the first and second terms represent the gains of the first and second partners, respectively. In 3:4, the second partner’s share is 4, which is greater than the first partner’s share of 3; therefore, the second partner gains more. In exams, compare the terms in the same order as the partners are given.

A gaining ratio expresses how the additional share is distributed among the continuing partners. In the ratio 0:1, the first term is zero, so the first partner receives no part of the additional share. The second term is one, so the second partner receives the entire gain. This is therefore a one-sided gain, not an absence of gain for everyone. Option B reverses the order of the partners, option C would require a ratio such as 1:1, and option D incorrectly interprets the zero as total gainlessness. The zero applies only to the first partner. Consequently, only the second partner is gaining, and option A is correct.

1:0 means the first partner's share increased and the second did not. So only first is the gainer.

The retiring partner’s share is \(\frac{2}{9}\). Dividing it equally between two remaining partners gives each an additional share of \(\frac{2}{9} \div 2 = \frac{1}{9}\). The full \(\frac{2}{9}\) is the combined gain of both partners, not the gain of each one, so option B is incorrect. Exam tip: Divide the retiring partner’s share by the number of partners who acquire it equally.

The first partner receives \(\frac{3}{3+1}=\frac{3}{4}\) of the retiring partner’s share. Therefore, the additional share is \(\frac{3}{4}\times\frac{4}{15}=\frac{3}{15}=\frac{1}{5}\). Option D represents the unsimplified value, but \(\frac{1}{5}\) is its simplest form. In exams, always reduce fractions to their lowest terms.

On retirement, continuing partners acquire the retiring partner’s share; the increase in their shares is called the gaining ratio. Sacrificing ratio applies on admission. Exam tip: calculate gain as New Ratio − Old Ratio.

Gaining ratio is the ratio in which the retiring partner share is acquired. Here acquisition is in 2:3.

A’s old profit share was \(3/(3+3+4)=3/10\). Under the new ratio of 2:1, A’s share is \(2/(2+1)=2/3\). Therefore, A’s gaining share = new share − old share = \(2/3-3/10=20/30-9/30=11/30\). The fraction 2/3 is A’s new share, not the gain. In exams, calculate the old and new shares first and then subtract the old share from the new share.

B’s old profit share was \(\frac{3}{10}\). Under the new ratio 2:1, B’s new share is \(\frac{1}{3}\). Therefore, B’s gaining ratio = new share − old share = \(\frac{1}{3}-\frac{3}{10}=\frac{10-9}{30}=\frac{1}{30}\). The value \(\frac{1}{3}\) is B’s new share, not the gaining ratio. Exam tip: Always calculate gaining ratio as the new share minus the old share.

Under the old ratio, A’s share was 3/10 and B’s share was 3/10. Under the new ratio of 2:1, A’s share is 2/3 and B’s share is 1/3. Thus, A’s gain = 2/3 − 3/10 = 11/30, while B’s gain = 1/3 − 3/10 = 1/30. Therefore, the gaining ratio is 11/30 : 1/30 = 11:1. Exam tip: calculate each continuing partner’s gain as new share minus old share.

A new ratio stated directly in a partnership question is the ratio in which the continuing partners will share future profits after the retirement or death of a partner. No further calculation is needed unless the question asks for a missing share, gain, or sacrifice. Here, the new ratio is explicitly given as 4:3.

Therefore, future profits will be divided between the remaining partners in the ratio 4:3, making option A correct. Reversing the numbers to 3:4 would change the stated entitlement. An equal ratio of 1:1 is also unjustified, and the old ratio applies only to matters belonging to the earlier period, such as past reserves or accumulated profits. The directly provided new ratio is the controlling basis for future profit sharing.

When continuing in old ratio the old shares of remaining partners become the new ratio. Write them in simplest form.

After retirement or death future profit is shared only among remaining partners. Therefore new ratio is calculated for them.

The governing concept is the gaining ratio in the retirement of a partner. When A retires, his former share of profit is no longer assigned to him. If the continuing partners, B and C, acquire that share in the proportion 3:2, this proportion shows how the continuing partners gain the retiring partner’s share. Therefore, option A is correct: 3:2 is the gaining ratio. A sacrificing ratio applies when a new partner is admitted and existing partners give up part of their shares. The old ratio refers to the partners’ ratio before reconstitution, while cash ratio is not the relevant partnership-accounting term for allocating a retiring partner’s profit share.