New Profit Sharing Ratio

Manu’s old share is 3/5 and Tanu’s is 2/5. Converting them to twentieths gives 12/20 and 8/20. Therefore, Manu’s new share is 12/20 − 1/20 = 11/20, while Tanu’s new share is 8/20 − 1/20 = 7/20. Janu receives 1/10 = 2/20. Hence, the new ratio is 11:7:2. Option B does not correctly adjust the old ratio for the sacrifices. Exam tip: always verify that the new shares add up to the whole profit, here 20/20.

The governing concept is the sacrificing ratio: the new partner’s share is supplied by old partners in the stated proportion. The total share sacrificed is 1/8. The old partners sacrifice in the ratio 3:1, whose total is 4 parts; therefore the first partner contributes 3/4 of the total sacrifice. Calculation: first partner’s sacrifice = 1/8 × 3/4 = 3/32. The second partner would contribute 1/8 × 1/4 = 1/32, and together they contribute 4/32 = 1/8, confirming the result. Thus option A is correct. Option C gives the entire sacrifice rather than the first partner’s share, while B belongs to the second partner and D uses the ratio incorrectly.

The old partners share the new partner’s portion in the ratio \(3:1\). Therefore, the second partner’s fraction of the sacrifice is \(1/(3+1)=1/4\). His sacrificing share is \(1/8 \times 1/4=1/32\). The amount \(3/32\) would be the first partner’s sacrifice. Exam tip: When the new partner’s share is sacrificed in the old ratio, multiply it by each partner’s fraction of that ratio.

Old partners' remaining share is (5/6). Dividing it in (5:1) gives (25/36) and (5/36) while the new partner is (6/36).

Because all three fractions have the same denominator, their ratio is 6:4:2. Dividing each term by 2, their greatest common divisor, gives the simplified ratio 3:2:1. Therefore, option A is correct.

Since all three profit shares have the same denominator, the ratio is obtained by comparing their numerators: \(\frac{9}{20}:\frac{7}{20}:\frac{4}{20}=9:7:4\). Therefore, the new profit-sharing ratio is 9:7:4. Exam tip: when the denominators are equal, use the numerators directly to form the ratio.

All the given shares have the common denominator 5. Therefore, 2/5 : 2/5 : 1/5 becomes 2:2:1 after comparing their numerators. Option D is incorrect because 5:5:5 represents equal shares, whereas the given shares are not equal. Exam tip: verify the ratio by checking the sum of its terms; here, 2+2+1=5.

Mohit receives 1/9 of the total profit, leaving 8/9 for Ajay and Vikas. Ajay’s old share is 7/(7+2) = 7/9. Since Mohit’s share is acquired in the old ratio, Ajay’s new share is (8/9) × (7/9) = 56/81. Therefore, option A is correct.

Raj’s old share was \(\frac{4}{5}\), and Taj’s old share was \(\frac{1}{5}\). Since Dev’s entire \(\frac{1}{5}\) share is taken from Taj, Taj’s new share becomes \(\frac{1}{5}-\frac{1}{5}=0\). Raj’s share remains unchanged. Therefore, the new ratio is \(\frac{4}{5}:0:\frac{1}{5}=4:0:1\). Exam tip: When a new partner’s share is taken entirely from one existing partner, deduct it fully from that partner’s old share.

Taking the total profit as 1, the combined share of the old partners is \(1-\frac{3}{10}=\frac{7}{10}\). Therefore, \(\frac{7}{10}\) is correct. \(\frac{3}{10}\) is the new partner’s share, not the old partners’ remaining share. Exam tip: Subtract the new partner’s share from 1 to find the share left for the old partners.

The sum of all fractions in the new profit-sharing ratio must be 1, or the whole share. Therefore, adding all the new fractions is the primary check of the ratio. Capital or cash alone does not determine the profit-sharing ratio. In an exam, always verify the sum of the fractions after calculating the ratio.

Harsh’s new share = 2/5 − 1/10 = 4/10 − 1/10 = 3/10. Tarun’s new share = 3/5 − 1/10 = 6/10 − 1/10 = 5/10. Isha’s share is 1/5 = 2/10. Therefore, the new ratio is 3/10 : 5/10 : 2/10 = 3:5:2. Remember that each sacrificing partner’s sacrifice is deducted from their old share, while the incoming partner’s share is added directly.

The governing concept is that the sacrificing ratio records the relative portions of the incoming partner’s share surrendered by the old partners. If the question states that the old partners give this share equally, each partner sacrifices an identical fraction. Equal quantities have a ratio of 1:1, regardless of the old profit-sharing ratio or the final new ratio. For example, if the incoming partner receives 1/5 and two old partners contribute equally, each gives 1/10; their sacrifice ratio is 1/10:1/10, which simplifies to 1:1. Therefore option A is correct. Option B implies unequal sacrifice, while options C and D refer to profit-sharing ratios and cannot be selected without additional information.

Charu receives 1/9 of the profit, so the remaining share for Rachna and Bhavna is 8/9. This remainder is divided in their old ratio of 5:4. Therefore, Rachna gets (8/9) × (5/9) = 40/81 and Bhavna gets (8/9) × (4/9) = 32/81. Charu’s share is 1/9 = 9/81. Hence, the new ratio is 40:32:9. Option B is incorrect because it does not reduce the old partners’ shares. Exam tip: When the incoming partner acquires a share in the old ratio, first calculate the remaining profit as 1 − the incoming partner’s share.

The total of the old ratio 5:4 is 9, so Ashish’s share is \(\frac{5}{9}\) and Bablu’s share is \(\frac{4}{9}\). Since Chanchal’s \(\frac{1}{9}\) share is taken entirely from Bablu, Bablu’s new share becomes \(\frac{4}{9}-\frac{1}{9}=\frac{3}{9}\). Therefore, the new ratio is \(\frac{5}{9}:\frac{3}{9}:\frac{1}{9}=5:3:1\). Exam tip: Reduce the share only from the partner who sacrifices it for the incoming partner.

The first partner’s old profit share is \(\frac{4}{5}\). Therefore, his portion of the new partner’s \(\frac{1}{5}\) share is \(\frac{1}{5}\times\frac{4}{5}=\frac{4}{25}\). Option C incorrectly treats the entire new partner’s share as the first partner’s sacrifice. Exam tip: when sacrifice is in the old ratio, multiply the incoming partner’s share by each old partner’s old fraction.

The new partner’s \(1/5\) share is sacrificed by the old partners in the ratio \(4:1\). The second partner’s fraction of the old ratio is \(1/(4+1)=1/5\). Therefore, his sacrifice is \(1/5\times1/5=1/25\), making option A correct. Exam tip: Multiply the incoming partner’s share by the concerned old partner’s fraction in the sacrifice ratio.

The first old partner’s proportional share is \(\frac{3}{3+1}=\frac{3}{4}\). Therefore, the partner’s new profit-sharing fraction is \(\frac{4}{5}\times\frac{3}{4}=\frac{3}{5}\). \(\frac{1}{5}\) is the second partner’s share, while \(\frac{3}{4}\) is only the first partner’s proportion of the combined share. Exam tip: To divide a combined fraction in a ratio, multiply it by the relevant ratio part divided by the total ratio.

The ratio \(3:1\) has a total of \(3+1=4\) parts. The second old partner receives 1 of these 4 parts, so the share is \(\frac{4}{5}\times\frac{1}{4}=\frac{1}{5}\). Option B represents the first partner's share, \(\frac{4}{5}\times\frac{3}{4}=\frac{3}{5}\). Exam tip: To divide a combined profit share in a ratio, multiply it by the required ratio part divided by the total ratio.

Arpita receives 1/7 of the total profit, so the old partners retain 6/7. This remainder is divided between Vinay and Sanjay in their old ratio of 2:5. Vinay’s share is 6/7 × 2/7 = 12/49, and Sanjay’s share is 6/7 × 5/7 = 30/49. Arpita’s share is 1/7 = 7/49. Therefore, the new ratio is 12:30:7. Exam tip: If the incoming partner’s share is acquired in the old ratio, multiply each old partner’s fraction by the remaining share.

Old partners' remaining share is (5/6) and the total of (2:3) is (5). Taking denominator (30) the new partner is (5/30).

The total parts in the ratio are 7 + 5 + 3 = 15. Since the new partner is in the third position, the partner’s share is 3/15, which is equal to 1/5. Option B represents the first partner’s share and option C represents the second partner’s share. Exam tip: Divide a partner’s ratio part by the sum of all ratio parts to find the profit share.

The total ratio is 8+3+1=12. Since the first old partner has a ratio of 8, the partner’s profit share is 8/12, which is also equal to 2/3. Option D is incorrect because it excludes the third partner’s ratio of 1 from the total. In exams, calculate a partner’s share by dividing that partner’s ratio by the total ratio.

C's (1/7) share is sacrificed in (2:1) so A gives (2/21) and B gives (1/21). The new shares are (7/21) (11/21) and (3/21).

A credit balance in the Profit and Loss Account represents accumulated profit earned by the firm. On dissolution, this undistributed profit is transferred to the partners’ capital accounts in their profit-sharing ratio, increasing the credit of each capital account. Hence option A is correct. A debit balance would represent accumulated loss, while expense and drawings are different accounting items.