New Ratios

Correct answer: A. 3:2

B’s share consists of 7 parts, which A and C acquire in the ratio 3:4. Thus, A receives 3 parts and C receives 4 parts from B’s share. A’s new share is 6+3=9, while C’s new share is 2+4=6. Therefore, the new ratio is 9:6, which simplifies to 3:2. The option 9:4 is incorrect because C’s original share of 2 parts must also be included. Exam tip: Divide the outgoing partner’s share in the stated acquisition ratio and add each acquired portion to the respective partner’s original share.

Correct answer: A. 2:2

Gaining ratio = New share − Old share. The first partner’s gain is \(7/12-5/12=2/12\). The second partner’s old share is \(1/4=3/12\), so the gain is \(5/12-3/12=2/12\). Therefore, the gaining ratio is \(2/12:2/12=2:2\), which is also expressible in simplified form as \(1:1\). In an exam, calculate each partner’s gain separately; using the ratio of new shares alone would be incorrect.

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

Gaining share = New share − Old share. Convert the old share to a common denominator: \(\frac{4}{9}=\frac{8}{18}\). Therefore, A's gaining share is \(\frac{11}{18}-\frac{8}{18}=\frac{3}{18}=\frac{1}{6}\). The value \(\frac{11}{18}\) is the new share itself, not the gain. Exam tip: Always subtract the old share from the new share to find a partner's gaining share.

Correct answer: A. \(1/10\)

Gaining ratio = New ratio − Old ratio = \(9/20 - 7/20 = 2/20 = 1/10\). Therefore, B’s gaining ratio is \(1/10\). The value \(9/20\) represents B’s new ratio, not the gain. Exam tip: calculate a partner’s gain by subtracting the old ratio from the new ratio.

Correct answer: A. 1:4

The new ratio 8:7 has a total of 15, so the new shares are 8/15 and 7/15. The first partner’s gain is 8/15 − 1/2 = 1/30, while the second partner’s gain is 7/15 − 1/3 = 4/30. Therefore, the gaining ratio is 1/30 : 4/30 = 1:4. Option B reverses the ratio, while 8:7 is the new ratio, not the gaining ratio. Exam tip: Calculate new share − old share for each partner and then simplify the gains.

Correct answer: A. 2:0

The direct answer is A, 2:0. The old total is 5+5+2=12. Thus A and B each originally had 5/12. After C retires, A:B is 7:5, whose total is 12, so A’s new share is 7/12 and B’s new share is 5/12. A’s gain is 7/12−5/12=2/12; B’s gain is 5/12−5/12=0. Therefore the gaining ratio is 2:0, equivalently 1:0. Option A is correct. Option B is the new profit-sharing ratio, not the gaining ratio. Option C is the old A:B ratio, not the gains. Option D incorrectly says both gained equally; only A received an increase. A zero gain is written in the ratio because B’s share did not change. Remember: gaining ratio uses increases, not simply the final ratio.

Correct answer: A. A

Before C's retirement, A's share was 7/10 and B's share was 1/10. Under the new ratio of 3:2, A's share becomes 3/5, or 6/10, while B's share becomes 2/5, or 4/10. Thus, A's share decreases from 7/10 to 6/10, whereas B's share increases. Exam tip: Convert the old and new ratios into fractions with a common denominator before comparing them.

Correct answer: A. 3/10

B’s old profit share was \(1/10\). Under the new ratio of 3:2, B’s new share is \(2/5=4/10\). Therefore, B’s gaining ratio = new share − old share = \(4/10-1/10=3/10\). Option B, \(2/5\), represents B’s new share, not the gain. In such questions, calculate gaining ratio as ‘new share − old share’.

Correct answer: A. 0:1

Under the old ratio, A’s share was \(7/10\) and B’s share was \(1/10\). Under the new ratio 3:2, A’s share is \(3/5=6/10\) and B’s share is \(2/5=4/10\). Thus, A’s share decreases by \(1/10\), while B’s share increases by \(3/10\). Therefore, A gains nothing and B gains \(3/10\), giving a gaining ratio of \(0:3=0:1\). Exam tip: The gaining ratio includes only the increases in the shares of the continuing partners who actually gain.

Correct answer: A. 1/3

A’s old profit share was 4/(4+7+4) = 4/15. Under the new ratio 3:2, A’s new share is 3/5 = 9/15. Therefore, A’s gaining share = new share − old share = 9/15 − 4/15 = 5/15 = 1/3. Option B is A’s new share, not the gain. Exam tip: Always calculate gaining share as the new share minus the old share.

Correct answer: A. 2/15

C’s old profit share was \(4/(4+7+4)=4/15\). Under the new ratio 3:2, C’s new share is \(2/(3+2)=2/5=6/15\). Therefore, C’s gaining share = new share − old share = \(6/15-4/15=2/15\). Exam tip: do not confuse the new share \(2/5\) with the gaining share; gaining share is always calculated as new share minus old share.

Correct answer: A. 5:2

Under the old ratio, A and C each had a share of 4/15. Under the new ratio of 3:2, A’s share is 3/5 = 9/15 and C’s share is 2/5 = 6/15. Therefore, A’s gain is 9/15 − 4/15 = 5/15, while C’s gain is 6/15 − 4/15 = 2/15. Hence, the gaining ratio is 5:2. Exam tip: Gaining share = new share − old share.

Correct answer: A. Extra shares were acquired in 2:1

The correct answer is Option A, Extra shares were acquired in 2:1. The new ratio 4:3 tells how the continuing partners will divide the entire future profit after reconstitution. The gaining ratio 2:1 tells only the proportion in which the partners acquired the retiring partner's surrendered share. These two ratios answer different questions and need not be equal. Option A is correct because a gaining ratio of 2:1 directly means that the extra shares were obtained in the proportion 2:1. Option B is wrong because the total future profit is divided in the new ratio 4:3, not in the gaining ratio 2:1. Option C is wrong because new ratio and gaining ratio are not always the same; they may happen to look similar in some examples, but their meanings differ. Option D is wrong because a retiring partner does give up a share, and the gaining partners acquire it. A common mistake is to treat every ratio in the question as a profit-sharing ratio. Exam cue: “new” means total future shares; “gaining” means only the additional shares.

Correct answer: A. 1/20

In the new ratio 11:9, A’s new share is 11/(11+9) = 11/20. A’s old share, 1/2, is equal to 10/20. Therefore, A’s gaining share = new share − old share = 11/20 − 10/20 = 1/20. Remember that the gaining share is found by subtracting the old share from the new share; 11/20 is only the new share.

Correct answer: A. \(\frac{1}{20}\)

B’s new share is \(\frac{9}{11+9}=\frac{9}{20}\). B’s old share, \(\frac{2}{5}\), is equal to \(\frac{8}{20}\). Therefore, B’s gaining share = new share − old share = \(\frac{9}{20}-\frac{8}{20}=\frac{1}{20}\). Option C is only B’s old share, not the gain. Exam tip: For a gaining partner, subtract the old share from the new share.

Correct answer: A. 4:3:2

After D’s retirement, the old mutual ratio of A, B and C remains 4:3:2. Therefore, their new ratio is 4:3:2. D’s 1/10 share is not redistributed among them because the question states that they continue in their old mutual ratio. Exam tip: When continuing partners share profits in their old mutual ratio, simply omit the retiring partner’s term from the original ratio.

Correct answer: A. 6:5:3

C’s old share is 3 out of a total of 14 parts, i.e. 3/14. Since this share is acquired equally by A, B and D, each receives 1/14. Therefore, A’s new share is 5/14+1/14=6/14, B’s is 4/14+1/14=5/14, and D’s is 2/14+1/14=3/14. Hence, the new ratio is 6:5:3. Exam tip: Express the retiring partner’s share in terms of the total old parts before distributing it according to the acquisition ratio.

Correct answer: A. 4:3:2

The total of the old ratio is 18, so B’s share is 5/18. This share is acquired by A, C and D in the ratio 2:2:1; therefore, A receives 2/18, C receives 2/18 and D receives 1/18. Their new shares are A = 6/18 + 2/18 = 8/18, C = 4/18 + 2/18 = 6/18 and D = 3/18 + 1/18 = 4/18. Thus, the new ratio is 8:6:4, which simplifies to 4:3:2. In an examination, always express the final ratio in its simplest form.

Correct answer: A. 6:6:2

A’s original share was 3 out of the total 14 parts, or 3/14. This share is acquired by B, C and D in the ratio 2:1:0. Thus, B gains 2/14, C gains 1/14 and D gains nothing. Their new shares are B = 4/14 + 2/14 = 6/14, C = 5/14 + 1/14 = 6/14 and D = 2/14. Therefore, the new ratio is 6:6:2. Exam tip: Add the retiring partner’s share to each continuing partner’s old share according to the gaining ratio.

Correct answer: A. 24:11:7

D’s share is 2/14 of the total profit. This share is acquired by A, B and C in the ratio 3:2:1, so their respective gains are 1/14, 1/21 and 1/42. Their new shares are A = 7/14 + 1/14 = 24/42, B = 3/14 + 1/21 = 11/42, and C = 2/14 + 1/42 = 7/42. Therefore, the simplified new ratio is 24:11:7. Exam tip: First calculate the retiring partner’s share, distribute it in the gaining ratio, and add each gain to the partner’s old share.

Correct answer: A. 20:16:11

The governing concept is the calculation of a new profit-sharing ratio after retirement. The total of the old ratio is 16, so A’s share is 8/16 = 1/2. This retiring share is acquired equally by three continuing partners; therefore each receives 1/2 × 1/3 = 1/6. B’s new share is 4/16 + 1/6 = 5/12, C’s is 3/16 + 1/6 = 25/48, and D’s is 1/16 + 1/6 = 11/48. Expressing all shares over 48 gives B = 20/48, C = 16/48 and D = 11/48. Hence the new ratio is 20:16:11, so option A is correct. The other options either ignore equal acquisition or use incorrect additions.

Correct answer: A. 5:11:11

D share of 3 parts is divided in 1:2:3. A gets 0.5 B gets 1 and C gets 1.5 so the ratio is 5:12:11.

Correct answer: A. There is a calculation error

After retirement or death total future profit must equal one whole share. If total is more than one the calculation is wrong.

Correct answer: A. 47/75 and 28/75

The sum of the terms in the new ratio 47:28 is 47 + 28 = 75. Therefore, the first partner’s new share is 47/75 and the second partner’s new share is 28/75. Option C reverses the partners’ shares, while option B does not convert the ratio into proper fractions. Exam tip: To convert a ratio into shares, divide each term by the sum of all the terms.

Correct answer: A. 29:16

The new profit-sharing ratio is obtained by comparing the partners’ shares: 29/50 : 16/50. Since both fractions have the same denominator, the denominator cancels, giving the ratio 29:16. Therefore, option A is correct. Exam tip: when the denominators are equal, compare the numerators directly.