New Ratios

Correct answer: A. A sacrificed and B gained

A decreased from 7/10 to 3/5 or 6/10 and B increased from 1/10 to 2/5 or 4/10. So A sacrificed and B gained.

Correct answer: A. \(\frac{3}{10}\)

B’s old share was \(\frac{1}{10}\). Under the new ratio 3:2, B’s new share is \(\frac{2}{5}=\frac{4}{10}\). Therefore, B’s gain = new share − old share = \(\frac{4}{10}-\frac{1}{10}=\frac{3}{10}\). The value \(\frac{2}{5}\) is B’s new share, not the gain. Exam tip: calculate gain by subtracting the old share from the new share.

Correct answer: A. 3:7:10

D’s old share was 2 out of 10, i.e. 2/10. When this share is acquired in the ratio 1:1:2, A, B and C receive 1/20, 1/20 and 2/20 respectively. Their new shares become 2/20+1/20=3/20, 6/20+1/20=7/20 and 8/20+2/20=10/20. Therefore, the new ratio is 3:7:10. Remember that 1:1:2 is only the ratio for acquiring D’s share, not the final profit-sharing ratio.

Correct answer: A. When one continuing partner share increases and another decreases

On comparing new share with old share one may gain and another may sacrifice. So identify the signs separately.

Correct answer: A. 1:1

The direct answer is A, 1:1. The old ratio is A:B:C=2:2:6. A and B’s old mutual ratio is 2:2, which simplifies to 1:1. C’s share is 6/10. When A and B acquire this share in their old mutual ratio, they divide it equally. A therefore receives 3/10 extra and B also receives 3/10 extra. Their new shares are A=2/10+3/10=5/10 and B=2/10+3/10=5/10. Thus the new ratio is 5:5, or 1:1. Option A is correct. Option B is an unsimplified form of the old mutual ratio, not the usual simplest answer. Option C includes the retiring partner and is not the new ratio. Option D is equivalent to 1:1 but is not the standard simplest expression offered by the question. Reduce ratios to lowest terms.

Correct answer: A. 1:1

A and B originally had shares of 2/10 each. Under the new ratio of 1:1, each receives 1/2, or 5/10. Therefore, each partner’s gain is 5/10 − 2/10 = 3/10. Since both gains are equal, the gaining ratio is 3/10:3/10 = 1:1. Exam tip: Calculate gaining ratio as new share minus old share, then reduce it to the simplest form.

Correct answer: A. 16:21:13

The governing method is to add each partner’s acquired portion of C’s share to that partner’s original share. The original total is 10, so C’s share is 3/10. A, B and D acquire it in 2:2:1, whose total is 5; their additions are 3/25, 3/25 and 3/50 respectively. In fiftieths, A’s old 2/10 is 10/50, so A becomes 16/50. B’s old 3/10 is 15/50, so B becomes 21/50. D’s old 2/10 is 10/50, so D becomes 13/50. Therefore the new ratio is 16:21:13. Option A is correct; the other options confuse the acquisition ratio or old ratio with the final shares.

Correct answer: A. 4:6

C share 1/10 goes to A so A becomes 4/10 and B remains 6/10. New ratio is 4:6 which may also be written as 2:3.

Correct answer: A. 2:3

C’s share is 1/10. Since A takes over C’s entire share, A’s new share becomes 3/10 + 1/10 = 4/10, while B’s share remains 6/10. Thus, the new ratio is 4:6, which simplifies to 2:3. Exam tip: First add the retiring partner’s share to the gaining partner’s old share, and then reduce the resulting ratio to its simplest form.

Correct answer: A. 0:1

C’s share is 2/10. Since B alone takes over C’s entire share, B’s gain is 2/10 while A’s gain is zero. Therefore, the gaining ratio of A:B is 0:2, which simplifies to 0:1. Exam tip: calculate the gain of each continuing partner separately before simplifying the ratio.

Correct answer: A. 1:1

Under the old ratio 2:5:3, B’s share was 5/10 and C’s share was 3/10. Under the new ratio 6:4, B’s share becomes 6/10 and C’s share becomes 4/10. Therefore, B gains 6/10 − 5/10 = 1/10 and C gains 4/10 − 3/10 = 1/10. Hence, their gaining ratio is 1:1. Exam tip: Gaining ratio = New share − Old share; the retiring partner’s share is not included in this ratio.

Correct answer: A. B and C gained equally

Under the old ratio of 6:2:2, both B and C had a share of 2/10. Under the new ratio of 5:5, each receives 5/10. Therefore, B's gain is 5/10 − 2/10 = 3/10, and C's gain is also 3/10. Hence, both partners gained equally. Exam tip: In retirement questions, calculate each continuing partner's gain as new share minus old share.

Correct answer: A. New share minus old share

To find gained share subtract old share from new share. Positive result shows gain and negative result shows sacrifice.

Correct answer: A. 4:9:7

The total of the old ratio is 10, so C’s share is 2/10. This share is acquired by A, B and D in the ratio 2:1:1, giving them increments of 1/10, 1/20 and 1/20 respectively. Their new shares are A = 1/10 + 1/10 = 4/20, B = 4/10 + 1/20 = 9/20, and D = 3/10 + 1/20 = 7/20. Hence, the new ratio is 4:9:7. Exam tip: distribute the outgoing partner’s share according to the acquiring ratio, not according to the old ratio.