New Ratios

Correct answer: A. 5:4

If there is no new agreement remaining partners continue in their old ratio. So A and B new ratio will be 5:4.

Correct answer: A. 3 : 1

In the absence of a new agreement, the continuing partners, B and C, share profits in the same relative ratio as before. Their old shares were 3 and 1 respectively, so their new ratio is 3 : 1. A’s share of 2 ceases; it is not automatically divided equally between B and C. Exam tip: After a partner’s retirement or death, use the old ratio for the continuing partners when no new agreement is given.

Correct answer: A. 6:5

In the absence of a new agreement, the retiring partner’s share is acquired by the continuing partners in their old ratio. After removing B, A and C retain their old shares of 6 and 5 respectively, so their new ratio is 6:5. Exam tip: remove only the retiring partner’s share and compare the remaining partners’ original shares.

Correct answer: A. Increased share of remaining partners

Gaining ratio shows the extra profit share of remaining partners. Do not confuse it with new ratio.

Correct answer: A. New share − Old share

A continuing partner gains when the new profit-sharing share is greater than the old share. Therefore, gaining share = New share − Old share. Option B reverses the order and generally represents sacrifice or a decrease. Exam tip: remember New − Old for gain and Old − New for sacrifice.

Correct answer: A. 1:1

In the old ratio, A’s share is 4 and C’s share is 1. When A acquires C’s entire share, A’s new share becomes 4 + 1 = 5, while B’s share remains 5. Thus, the new ratio of A:B is 5:5, which simplifies to 1:1. Exam tip: Add the retiring partner’s acquired share to the gaining partner’s old share, then simplify the ratio.

Correct answer: A. 7:3

The old ratio is A:B:C = 7:1:2. After B’s retirement, B’s share of 1 is taken entirely by C. Therefore, A’s share remains 7, while C’s share becomes 2 + 1 = 3. Hence, the new ratio of A and C is 7:3. Exam tip: Keep the unchanged partner’s share the same and add the retiring partner’s full share to the gaining partner’s share.

Correct answer: A. 5:5

C’s old share was 4 parts, and it was acquired by A and B in the ratio 1:3. Thus, A receives 1 additional part and B receives 3 additional parts. The new ratio is A:B = (4+1):(2+3) = 5:5. The ratio 1:3 represents only the acquisition of C’s share, not the new profit-sharing ratio. Exam tip: Add each partner’s acquired share to their original share to find the new ratio.

Correct answer: A. 1:1

In the original ratio, A has 8 parts, which B and C acquire in the ratio 3:5. Thus, B receives 3 parts and C receives 5 parts. The new ratio of B:C is (3+3):(1+5) = 6:6 = 1:1. The ratio 3:5 is only the gain ratio for acquiring A’s share, not the new profit-sharing ratio. Exam tip: Add each continuing partner’s acquired share to their original share to find the new ratio.

Correct answer: A. 9:11

A, B and C originally have shares of 2/10, 5/10 and 3/10, respectively. B’s share of 5/10 is acquired equally by A and C, so each receives 5/20, or 1/4. Therefore, A’s new share is 2/10 + 1/4 = 9/20, while C’s new share is 3/10 + 1/4 = 11/20. Hence, the new ratio is 9:11. Exam tip: Divide the deceased partner’s share among the gaining partners first, then compare their revised shares.

Correct answer: A. 5:2

The governing concept is the gaining ratio, which records the relative proportions in which continuing partners acquire the outgoing partner's profit share. The question directly states that the acquisition takes place in the ratio 5:2. Therefore the first partner receives five parts of the gain for every two parts received by the second partner, and the gaining ratio is written as 5:2. It is not found by reversing the numbers, so 2:5 is incorrect. The old ratio is relevant for measuring changes but is not automatically the gaining ratio, and the new ratio describes final shares rather than the division of the acquired share. Thus option A is correct.

Correct answer: A. 1:1

The gaining ratio compares the additional share acquired by each remaining partner from the retiring partner. Since both partners acquire equal additional shares, their gaining ratio is 1:1. The old profit-sharing ratio represents their previous shares, not their gains. Exam tip: when the retiring partner’s share is acquired equally, write the gaining ratio as 1:1.

Correct answer: A. \(1/6\)

Under the new ratio \(1:1\), A’s new share is \(1/2\), while the old share was \(1/3\). Therefore, A’s gaining share = New share − Old share = \(1/2-1/3=1/6\). Option B is only A’s old share, not the gain. Exam tip: Gain = New share − Old share.

Correct answer: A. Zero

A partner has a gaining share only when the new share exceeds the old share. B's old share was 2/3, whereas the new ratio 1:1 gives B a share of 1/2. The difference is new share minus old share: 1/2 - 2/3 = 3/6 - 4/6 = -1/6. The negative result means B has sacrificed or lost 1/6, not gained it. In a gaining-share calculation, a partner whose share decreases is assigned zero gain; the decrease is considered a sacrifice. Therefore B's gaining share is zero. Option B incorrectly treats the loss as a gain, option C is merely the final share, and option D is the old share. Hence option A is correct.

Correct answer: A. \(\frac{2}{7}\)

Gaining share = New share − Old share. Therefore, \(\frac{4}{7}-\frac{2}{7}=\frac{2}{7}\). Option C represents only the new share, not the gain. Exam tip: Always subtract the old share from the new share to find the gaining share.

Correct answer: A. \(\frac{1}{5}\)

Gaining ratio = New ratio − Old ratio. Therefore, \(\frac{1}{2}-\frac{3}{10}=\frac{5}{10}-\frac{3}{10}=\frac{2}{10}=\frac{1}{5}\). Hence, option A is correct. Remember to express the fractions with a common denominator before subtracting; \(\frac{1}{10}\) is an incorrect difference.

Correct answer: A. Zero

Gaining share = New share − Old share. Since the new share and old share are equal, their difference is zero; therefore, the partner has no gain. Choosing the old or new share would be incorrect because the gaining ratio measures only the increase in the share. Exam tip: Always subtract the old ratio from the new ratio to calculate the gaining ratio.

Correct answer: A. Goodwill adjustment

Remaining partners bear retiring partner goodwill share in gaining ratio. Therefore it is useful in goodwill adjustment.

Correct answer: A. 5/9

After C’s retirement, only A and B share the profits. The sum of the new ratio 5:4 is 9, so A’s new share is \(\frac{5}{5+4}=\frac{5}{9}\). Option D, \(\frac{4}{9}\), represents B’s new share, not A’s. Exam tip: A partner’s share in a ratio is calculated as that partner’s ratio divided by the sum of all ratio terms.

Correct answer: A. 4/9

After C’s retirement, the given new ratio is A:B = 5:4. The total parts are 5 + 4 = 9, so B’s new share is 4/9. The old ratio is not needed because the new ratio is stated directly. Exam tip: divide the concerned partner’s part in the new ratio by the sum of all parts.

Correct answer: A. 7/45

A’s old profit share was 4/10 = 2/5. After C’s retirement, A’s new share under the ratio 5:4 is 5/9. Therefore, A’s gaining share = new share − old share = 5/9 − 2/5 = 25/45 − 18/45 = 7/45. The value 5/9 is A’s new share, not the gaining share. Exam tip: Always calculate gaining share by subtracting the old share from the new share.

Correct answer: A. 13/90

B’s old profit share was 3/(4+3+3) = 3/10. After C’s retirement, B’s new share is 4/(5+4) = 4/9. Therefore, B’s gaining share = new share − old share = 4/9 − 3/10 = 13/90. Option B is only B’s new share, not the gaining share. Exam tip: Calculate gaining share by subtracting the old share from the new share.

Correct answer: A. 14:13

Under the old ratio 4:3:3, A’s share was 4/10 and B’s share was 3/10. Under the new ratio 5:4, A’s share is 5/9 and B’s share is 4/9. Thus, A’s gain = 5/9 − 4/10 = 7/45, while B’s gain = 4/9 − 3/10 = 13/90. Therefore, the gaining ratio is 7/45 : 13/90 = 14:13. Remember that gaining ratio is calculated as new share minus old share.

Correct answer: A. 8/15 and 7/15

The sum of the terms of the new ratio is 8 + 7 = 15. Therefore, the first partner’s share is 8/15 and the second partner’s share is 7/15. Option C reverses the partners’ shares. Exam tip: Convert each ratio term into a share by dividing it by the sum of all ratio terms.

Correct answer: A. 6:5

Both new fractions have the same denominator, 11. Therefore, their ratio is the ratio of the numerators: \(6/11 : 5/11 = 6:5\). Option B reverses the order of the partners’ shares. Exam tip: When fractions have the same denominator, compare their numerators directly to find the ratio.