New Ratios

Correct answer: A. In their old ratio

If there is no new agreement remaining partners share in their old ratio. In exams remove the retiring partner share and check.

Correct answer: A. The new share

The governing formula for a continuing partner's gain is: Gain = New Share - Old Share. Thus, the old share is subtracted from the new share, not from capital, cash, or the retiring partner's share as a direct operation. For example, if a partner's old share is 2/5 and the new share is 3/5, the gain is 3/5 - 2/5 = 1/5. This increase represents the portion acquired from the retiring or deceased partner. Capital and cash may be involved in separate accounting adjustments, but they do not determine the gaining ratio. Therefore, option A states the correct relationship.

Correct answer: A. 4:3

C’s profit share was 2/9. Since there is no new agreement, A and B acquire C’s share in their old ratio of 4:3. Thus, A’s new share is 4/9 + (4/7 × 2/9) = 4/7, and B’s new share is 3/9 + (3/7 × 2/9) = 3/7. Therefore, the new ratio is 4:3. Exam tip: In the absence of a new agreement, the remaining partners acquire the retiring partner’s share in their old ratio.

Correct answer: A. 5:3

After A’s death, only B and C will share the profit. Their respective shares in the original ratio were 5 and 3, so their old mutual ratio was 5:3. Therefore, their new profit-sharing ratio is 5:3. Exam tip: When a partner leaves, use the remaining partners’ old mutual ratio unless the question specifies a change.

Correct answer: A. 1:3

When there is no new agreement, the retiring partner’s share is acquired by the continuing partners in their old profit-sharing ratio. A and C were sharing in the ratio 1:3, so their new profit-sharing ratio remains 1:3. Exam tip: In the absence of a new agreement, use the continuing partners’ old ratio for the gain.

Correct answer: A. 11:9

C’s old profit share is 5/10. Since A and B acquire it equally, each receives half of 5/10, which is 5/20. Therefore, A’s new share is 3/10 + 5/20 = 11/20, while B’s new share is 2/10 + 5/20 = 9/20. Hence, the new ratio is 11:9. Option 3:2 is only A and B’s old ratio and ignores the redistribution of C’s share. Exam tip: Add each acquiring partner’s gain from the retiring partner’s share to their original share.

Correct answer: A. 9:1

The total of the original ratio 4:1:5 is 10. A’s original share is 4/10 and C’s share is 5/10. Since A acquires C’s entire share, A’s new share becomes 4/10 + 5/10 = 9/10, while B’s share remains 1/10. Therefore, the new ratio of A and B is 9:1. Exam tip: Add the retiring partner’s acquired share to the existing share of the gaining partner.

Correct answer: A. 3:2

B’s profit share is 2, and C acquires it entirely. Therefore, A’s share remains 6, while C’s new share becomes 2 + 2 = 4. The new ratio is 6:4, which simplifies to 3:2. Hence, option A is correct. Exam tip: Add the retiring partner’s share to the old share of the gaining partner.

Correct answer: A. 31:19

Direct answer: Option A, 31:19. The old total ratio is 5+3+2=10, so A has 5/10, B has 3/10 and C has 2/10. C’s retiring share is divided between A and B in 3:2, whose total is 5. Therefore A receives (2/10)×(3/5)=3/25, and B receives (2/10)×(2/5)=2/25. A’s new share is 5/10+3/25=25/50+6/50=31/50. B’s new share is 3/10+2/25=15/50+4/50=19/50. The new ratio is therefore 31:19. Option A is correct. Option B, 5:3, ignores the extra share received from C. Option C, 8:5, does not result from the stated fractions. Option D, 3:2, is only the ratio in which C’s share is gained, not the complete new ratio. Memory cue: add each continuing partner’s gain to the old share.

Correct answer: A. 2:3

A’s profit share is 7 parts. B and C acquire it in the ratio 2:5, so B receives \(7 \times \frac{2}{7}=2\) parts and C receives \(7 \times \frac{5}{7}=5\) parts. Thus, B’s new share is \(2+2=4\), and C’s new share is \(1+5=6\). The new ratio is \(4:6=2:3\). Exam tip: Add the acquired share to each partner’s old share and simplify the resulting ratio.

Correct answer: A. 2:3

B's profit share was 4 parts. When it is divided equally, A and C each receive 2 additional parts. Thus, A's new share is \(2+2=4\) and C's new share is \(4+2=6\). The new ratio is \(4:6=2:3\). In exams, always reduce the ratio to its simplest form, so 2:3 is preferred over 4:6.

Correct answer: A. 4:1

The gaining ratio is the ratio in which the remaining partners acquire the retiring partner’s share of profit. Since the share is acquired in the ratio 4:1, the gaining ratio is 4:1. The new ratio and old ratio are different concepts and cannot be determined from this information alone. Exam tip: In retirement questions, gaining ratio equals the ratio of the share gained by the remaining partners.

Correct answer: A. 1:1

The gaining ratio shows the proportion in which the remaining partners acquire the retiring partner’s share. Since both partners acquire equal shares, their gains are equal, so the gaining ratio is 1:1. Remember that the gaining ratio is generally calculated from the difference between the new ratio and the old ratio.

Correct answer: A. 1/5

Under the new ratio 3:2, A’s new share is \(3/(3+2)=3/5\). A’s old share was \(2/5\). Therefore, A’s gaining share = new share − old share = \(3/5-2/5=1/5\). Option B is A’s old share, not the gain. Exam tip: Calculate a partner’s gain by subtracting the old share from the new share.

Correct answer: A. Zero

The new ratio 3:2 represents shares of 3/5 for A and 2/5 for B because the total parts are five. B's old share was already 3/5, but his new share is only 2/5. Using the gaining-ratio rule, B's change is New Share - Old Share = 2/5 - 3/5 = -1/5. A negative result means that B has sacrificed or lost 1/5; it does not mean that B has gained. Since gaining share is recorded only when the new share exceeds the old share, B's gaining share is zero. Therefore, option A is correct; the fractional options confuse B's old or new share with his gain.

Correct answer: A. \(\frac{1}{4}\)

Gaining share = New share − Old share. Therefore, \(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\), so option A is correct. Option B, \(\frac{1}{8}\), results from an incorrect subtraction. Exam tip: Always calculate a partner’s gaining share as the difference between the new share and the old share.

Correct answer: A. \(\frac{1}{6}\)

Gaining share = new profit share − old profit share. Therefore, B’s gaining share is \(\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}=\frac{1}{6}\). Option B is only the old share, not the gain. Exam tip: for a gaining partner, always subtract the old share from the new share.

Correct answer: A. No

A gainer is the one whose share increases. If share decreases he is not included in gaining ratio.

Correct answer: A. For goodwill adjustment

Remaining partners bear retiring or deceased partner goodwill share in gaining ratio. So it is important in goodwill adjustment.

Correct answer: A. 3/5

After C’s retirement, A and B share profits in the new ratio 3:2. The total of the ratio is 3+2=5, so A’s share is 3/5. The old ratio 5:4:1 is not needed because the new ratio is already given. Exam tip: To find a partner’s share from a ratio, divide that partner’s ratio number by the sum of all ratio numbers.

Correct answer: A. 2/5

After C’s retirement, the new ratio of A:B is 3:2. The total number of parts is 3 + 2 = 5, so B’s new share is 2/5. The fraction 3/5 represents A’s share, not B’s. Exam tip: To find a partner’s share from a ratio, divide that partner’s ratio number by the sum of all ratio numbers.

Correct answer: A. 1/10

A’s old share was 5/(5+4+1) = 5/10. Under the new ratio 3:2, A’s share is 3/5 = 6/10. Therefore, A’s gaining ratio = new share − old share = 6/10 − 5/10 = 1/10. The option 1/5 results from an incorrect calculation of the change in share. Exam tip: Gaining ratio is calculated as new share minus old share.

Correct answer: A. Zero

B’s old share was 4/(5+4+1) = 4/10 = 2/5. In the new ratio 3:2, B’s new share is 2/(3+2) = 2/5. Therefore, B’s gaining share = new share − old share = 2/5 − 2/5 = zero. The value 1/5 is a distractor, not B’s gain. Exam tip: Always calculate gain as the new share minus the old share.

Correct answer: A. 1:0

Under the old ratio 5:4:1, A and B had shares of 5/10 and 4/10 respectively. The new ratio 3:2 gives them shares of 6/10 and 4/10. Therefore, A gains 6/10 − 5/10 = 1/10, while B gains nothing. Hence, the gaining ratio is 1:0. Exam tip: Gaining ratio = New share − Old share.

Correct answer: A. 1/10

A’s old profit share was \(3/(3+5+2)=3/10\). After C’s retirement, A’s new share is \(2/(2+3)=2/5=4/10\). Therefore, A’s gaining share = new share − old share = \(4/10-3/10=1/10\). Option B is A’s new share, not the gain. Exam tip: Always calculate gaining share by subtracting the old share from the new share.