New Profit Sharing Ratio

If old partners sacrifice in the old ratio their mutual ratio remains the same. This is a quick rule for new ratio.

Manu’s new share = 2/5 − 1/10 = 4/10 − 1/10 = 3/10. Tanu’s new share = 3/5 − 1/10 = 6/10 − 1/10 = 5/10. Janu’s share is 1/5 = 2/10. Therefore, the new ratio is 3/10 : 5/10 : 2/10 = 3:5:2. Option B is not an equivalent form of this ratio; 4:6:2 has a different proportion. Exam tip: subtract the sacrifice made by each existing partner from their old share, add the new partner’s share, and then simplify the ratio.

The new profit-sharing ratio is based on the profit shares mutually agreed by all partners, including the incoming partner. Capital contributed or goodwill brought does not automatically fix the ratio. Exam tip: look for mutual agreement.

The second old partner's fraction of the total sacrifice is 2/(1+2) = 2/3. Their sacrificing share is therefore 1/6 × 2/3 = 2/18 = 1/9, so option B is correct.

Old partners retain (8/9). Dividing it in (4:5) gives (32/81) and (40/81) and the new partner has (9/81).

To convert fractional shares into a ratio, first remove the common denominator 10, giving 4:4:2. All three terms have a common factor of 2, so divide each by 2: 4÷2 : 4÷2 : 2÷2 = 2:2:1. Thus option B is the simplest equivalent ratio. Option A is equivalent but not fully simplified; options C and D do not preserve the given proportions.

All three fractions have the common denominator 15, so the new profit-sharing ratio is obtained by taking their numerators in the given order: \(6:5:4\). Option C reverses the order and is therefore incorrect. Exam tip: for fractions with the same denominator, the ratio is directly the ratio of their numerators.

The new profit-sharing ratio is the ratio of the partners’ given profit shares. Here, \(\frac{1}{3}:\frac{1}{3}:\frac{1}{3}\) simplifies to \(1:1:1\) by multiplying all three terms by 3. Therefore, option D is correct. Options A, B, and C show unequal shares, whereas all three partners have equal shares here. Exam tip: To convert fractional shares into a ratio, multiply all terms by their common denominator.

Mohit receives \(1/9\), so the share left for the old partners is \(1-1/9=8/9\). Ajay’s old proportionate share was \(5/9\). Therefore, Ajay’s new share is \(8/9\times5/9=40/81\). The option \(5/9\) represents Ajay’s old share, not his share after admission. Exam tip: When the incoming partner’s entire share is given in the old ratio, calculate each old partner’s new share as remaining profit × old proportionate share.

Sonu’s old share is 7/8 and Monu’s old share is 1/8. Dolly’s entire 1/8 share is taken from Monu, so Monu’s new share is 1/8 − 1/8 = 0. Sonu retains 7/8 and Dolly receives 1/8. Therefore, the new ratio is 7/8 : 0 : 1/8 = 7:0:1. Exam tip: If an incoming partner takes an old partner’s entire share, that old partner’s new share becomes zero.

Taking the total profit as \(1\), the combined share of the old partners is \(1-\frac{2}{9}=\frac{7}{9}\). Therefore, option A is correct. Option B represents the new partner’s share, not the old partners’ combined share. Exam tip: subtract the incoming partner’s share from 1 to find the remaining share of the old partners.

The shares of all partners in a new profit-sharing ratio must add up to 1 or 100%, because the entire profit is distributed among these partners. Therefore, adding the shares is the simplest way to verify the ratio. Capital and cash balances do not determine the total of the profit-sharing ratio. In an examination, check that fractions total 1 and percentages total 100%.

Under the old ratio of 3:1, Harsh’s share is 3/4 and Tarun’s share is 1/4. Harsh’s new share is 3/4 − 1/8 = 5/8, while Tarun’s new share is 1/4 − 1/8 = 1/8. Isha receives 1/4 = 2/8. Therefore, the new ratio is 5/8 : 1/8 : 2/8 = 5:1:2. Exam tip: subtract each sacrificing partner’s share from that partner’s old share, not from the total profit.

The sacrificing ratio represents the proportion of profit surrendered by the old partners. When the new partner’s share is taken equally from the old partners, each old partner makes an equal sacrifice; therefore, the sacrificing ratio is 1:1. Exam tip: equal sacrifice always gives a 1:1 sacrificing ratio.

Charu receives 1/9, leaving 8/9 of the profits for Rachna and Bhavna. They divide this remainder in their old ratio of 2:7: Rachna receives (8/9) × (2/9) = 16/81, and Bhavna receives (8/9) × (7/9) = 56/81. Charu’s share, 1/9, equals 9/81. Therefore, the new ratio is 16:56:9.

The old ratio 4:5 has a total of 9 parts, so Ashish’s old share is 4/9 and Bablu’s is 5/9. Chanchal’s 1/9 share is taken entirely from Ashish; therefore, Ashish’s new share is 4/9 − 1/9 = 3/9. Bablu’s share remains 5/9, while Chanchal receives 1/9. Hence, the new ratio is 3:5:1. Option B is incorrect because it adds Chanchal’s share without reducing Ashish’s share. Exam tip: When a new partner’s share is surrendered entirely by one old partner, reduce only that partner’s share.

The new partner’s total share is \(\frac{1}{5}\), and it is sacrificed by the old partners in the ratio 2:3. The first partner’s share in the old ratio is \(\frac{2}{5}\). Therefore, his sacrifice is \(\frac{1}{5}\times\frac{2}{5}=\frac{2}{25}\). Option C represents the new partner’s total share, not the first partner’s sacrifice. Exam tip: When sacrifice is in the old ratio, calculate each partner’s sacrifice as the new partner’s share multiplied by that partner’s share in the old ratio.

The total share given to the new partner, \(\frac{1}{5}\), is sacrificed by the old partners in their old ratio, \(2:3\). The second old partner’s proportion in this ratio is \(\frac{3}{2+3}=\frac{3}{5}\). Therefore, his sacrifice is \(\frac{1}{5}\times\frac{3}{5}=\frac{3}{25}\), so option B is correct. Exam tip: When sacrifice is made in the old ratio, multiply the new partner’s share by each old partner’s fractional share of the old ratio.

The first old partner receives \(\frac{2}{2+1}=\frac{2}{3}\) of the combined share. Therefore, the partner’s new profit share is \(\frac{3}{4}\times\frac{2}{3}=\frac{1}{2}\). The option \(\frac{2}{3}\) represents only the partner’s fraction of the old partners’ combined share, not the total profit share. Exam tip: add the ratio terms first, then multiply the combined share by the required ratio fraction.

In the ratio \(2:1\), the second old partner receives 1 part out of a total of 3 parts, so the fraction of the combined share is \(\frac{1}{3}\). Therefore, the partner’s new profit share is \(\frac{3}{4}\times\frac{1}{3}=\frac{1}{4}\). Option A is the first partner’s share, calculated as \(\frac{3}{4}\times\frac{2}{3}=\frac{1}{2}\). Exam tip: first convert the individual ratio part into a fraction of the total ratio, then multiply it by the combined share.

After giving Arpita a 1/6 share, the old partners retain a total of 5/6. Since this retained share is divided in the old ratio 1:2, Vinay’s new share is \(\frac{5}{6}\times\frac{1}{3}=\frac{5}{18}\), while Sanjay’s is \(\frac{5}{6}\times\frac{2}{3}=\frac{10}{18}\). Arpita’s share is \(\frac{1}{6}=\frac{3}{18}\). Thus, the new ratio is 5:10:3. Exam tip: If the incoming partner’s share is taken from the old partners in their old ratio, distribute the remaining share in that same ratio.

The new profit sharing ratio applies to all old and new partners after admission. Do not treat it as capital ratio.

Old partners' remaining share is (3/4) and in (2:1) the total denominator can be (12). New partner's share (1/4) equals (3/12).

The total ratio is 5 + 4 + 3 = 12. Since the new partner has the third share, his profit-sharing fraction is 3/12, which is equal to 1/4. The fractions 4/12 and 5/12 represent the second and first partners respectively, while 1/4 is less than 1/3. Exam tip: Divide a partner’s ratio term by the sum of all ratio terms to find that partner’s share.

The sum of all parts in the new ratio is 6 + 3 + 1 = 10. Since the first old partner has a ratio of 6, the partner’s share of profit is 6/10. 6/9 is incorrect because the total of all three partners’ shares is 10, not 9. Exam tip: Convert a ratio into a profit share by dividing the concerned partner’s part by the total of the ratio.