New Profit Sharing Ratio

The old ratio of Saral and Taral is 6:4, or 3:2. Garima receives 1/5 of the total profit, so the old partners retain 4/5. Since the sacrificed share is taken in the old ratio, Saral receives 3/5 of the retained 4/5 = 12/25, while Taral receives 2/5 of 4/5 = 8/25. Garima receives 1/5 = 5/25. Thus the new ratio is 12:8:5, which sums to 25 and represents the whole profit. Therefore option A is correct. Option B fails to reduce the old partners' shares, while C and D do not preserve the required old-ratio sacrifice.

The ratio of profit portions given up by existing partners in favour of the incoming partner is the sacrificing ratio. Use: sacrifice = old share − new share. Exam tip: do not confuse it with gaining ratio.

C receives \(\frac{2}{7}\), so the remaining profit for A and B is \(1-\frac{2}{7}=\frac{5}{7}\). Dividing this remainder in the old ratio 2:5 gives A’s share as \(\frac{5}{7}\times\frac{2}{7}=\frac{10}{49}\) and B’s share as \(\frac{5}{7}\times\frac{5}{7}=\frac{25}{49}\). C’s share is \(\frac{2}{7}=\frac{14}{49}\). Therefore, the new ratio is 10:25:14. Option B incorrectly retains the old ratio without applying the reduced remainder. Exam tip: First calculate the share left for the old partners, then distribute it in their old ratio.

C receives \(1/3=9/27\) of the total profit, leaving \(2/3\) for A and B. A receives \(\frac{2}{3}\times\frac{7}{9}=\frac{14}{27}\), while B receives \(\frac{2}{3}\times\frac{2}{9}=\frac{4}{27}\). Therefore, the new ratio A:B:C is 14:4:9. Exam tip: Subtract the incoming partner’s share from 1, then distribute the remainder among the old partners in their old ratio.

C receives \(3/11\) of the profit, so the remaining share for A and B is \(1-3/11=8/11\). Distributing this in the old ratio 4:7 gives A \(8/11\times4/11=32/121\) and B \(8/11\times7/11=56/121\). C’s share is \(3/11=33/121\). Therefore, the new ratio is \(32:56:33\). Exam tip: Find the remaining share first, then distribute it among the old partners in their old ratio.

The new profit-sharing ratio shows each partner’s share in the firm’s future profits after admission. The sacrificing ratio concerns only the profit given up by old partners. Exam tip: look for the phrase “future profits”.

C receives 1/5 of the profits, so the remaining share for A and B is 4/5. A’s new share is \((4/5)\times(1/5)=4/25\), and B’s new share is \((4/5)\times(4/5)=16/25\). C’s share is \(1/5=5/25\). Therefore, the new ratio is 4:16:5. Option B is incorrect because it does not reduce the old partners’ shares proportionately. Exam tip: First find the remaining profit, then distribute it among the old partners in their old ratio.

C receives \(1/7\) of the total profit, so the profit left for A and B is \(1-1/7=6/7\). Sharing this remainder in the old ratio 6:1 gives A \(6/7\times6/7=36/49\) and B \(6/7 imes1/7=6/49\). C’s share is \(1/7=7/49\). Hence, the new ratio is 36:6:7. Exam tip: When the remaining profit is divided in the old ratio, multiply each old ratio fraction by the remaining-profit fraction.

The old ratio of A and B is 3:8, whose total is 11. After C receives 2/11, the remaining profit is 9/11. Therefore, A receives 9/11 × 3/11 = 27/121 and B receives 9/11 × 8/11 = 72/121. C’s share, 2/11, is equal to 22/121. Hence, the new ratio is 27:72:22. Exam tip: First find the profit left after giving the new partner’s share, then distribute that balance among the old partners in their old ratio. Option B is incorrect because it combines the old ratio with C’s share without adjusting A’s and B’s shares.

C receives 1/7 of the total profit, so 6/7 remains for A and B. This remainder is divided in their old ratio of 9:5. Therefore, A’s share is (6/7) × (9/14) = 27/49, and B’s share is (6/7) × (5/14) = 15/49. C’s share is 1/7 = 7/49. Hence, the new ratio is 27:15:7. Exam tip: When the incoming partner receives a specified share and the remainder is divided in the old ratio, multiply each old share by the remaining fraction.

The governing principle is that after C receives 3/11, the remaining profit is 1 − 3/11 = 8/11. This balance is divided between A and B in their old ratio 5:6. Hence A receives (8/11) × (5/11) = 40/121, and B receives (8/11) × (6/11) = 48/121. C’s share is 3/11 = 33/121. Placing all three shares over the common denominator 121 gives the new ratio 40:48:33. Their total is 121 parts, confirming that the shares sum to one whole. Therefore option A is correct; the other choices fail to apply the remaining-profit factor or use the old figures unchanged.

A’s and B’s old shares are 5/9 and 4/9, respectively. Since C’s 1/9 share is taken entirely from A, A’s new share becomes 5/9 − 1/9 = 4/9. B continues to have 4/9, while C receives 1/9. Therefore, the new ratio is 4/9 : 4/9 : 1/9 = 4:4:1. Option B is incorrect because it does not deduct C’s share from A. Exam tip: Reduce the share only of the partner from whom the new partner’s share is taken.

The old ratio 3:5 means that A's share is 3/8 and B's share is 5/8. Since C receives 1/8 entirely from B, A remains at 3/8, B's new share becomes 5/8 − 1/8 = 4/8, and C receives 1/8. Therefore, the new ratio is 3:4:1. Exam tip: When the incoming partner gets a share from only one existing partner, reduce the share of only that partner.

Direct answer: The new ratio is A:B:C = 5:5:2, so option A is correct. Initially A and B share in 7:5, whose total is 12. Therefore A's old share is \(7/12\), and B's is \(5/12\). C receives \(1/6=2/12\), entirely from A. A's new share is \(7/12−2/12=5/12\). B gives nothing, so B remains \(5/12\). C has \(2/12\). Removing the common denominator gives 5:5:2. Option A follows exactly. Option B forgets that A must surrender one-sixth. Option C gives A and C incorrect amounts. Option D reduces B even though C's share came only from A. The key phrase is “only from A”: subtract the new partner's share only from A.

The old ratio of 4:9 means that A and B have shares of 4/13 and 9/13, respectively. Since C receives 2/13 entirely from B, B’s new share becomes 9/13 − 2/13 = 7/13, while A’s share remains 4/13. Therefore, the new ratio of A, B and C is 4/13:7/13:2/13 = 4:7:2. Exam tip: When a new partner acquires the entire share from one old partner, only that partner’s share is reduced.

The old ratio of 11:4 gives A a share of 11/15 and B a share of 4/15. C’s share of 1/5 equals 3/15 and is taken entirely from A. Therefore, A’s new share is 11/15 − 3/15 = 8/15, while B remains at 4/15 and C receives 3/15. Hence, the new ratio is 8:4:3. Exam tip: Convert the old ratio into fractional shares first, then deduct the incoming partner’s share only from the sacrificing partner.

The old ratio 2:7 has a total of 9 parts, so A’s share is 2/9 and B’s share is 7/9. Since C receives 1/9 entirely from B, B’s new share becomes 7/9 − 1/9 = 6/9. Therefore, A:B:C = 2/9:6/9:1/9 = 2:6:1. Option B is incorrect because it adds C’s share without reducing B’s share. Exam tip: When the incoming partner’s share is taken from only one existing partner, reduce only that partner’s share.

When the entire share of the incoming partner is given by one partner, that partner alone sacrifices profit share. Hence, only that partner’s share falls; other old shares stay unchanged. Exam tip: verify that the new shares add up to \(1\).

Since C acquires the entire share only from B, A does not sacrifice any part of the old share. B’s share decreases by C’s acquired share. Exam tip: reduce only the sacrificing partner’s share.

The total of the old ratio 6:5 is 11, so A’s old share is 6/11 and B’s is 5/11. Since C’s 1/11 share is acquired entirely from A, A’s new share becomes 6/11 − 1/11 = 5/11. B’s share remains 5/11, while C receives 1/11. Hence, the new ratio is 5:5:1. Exam tip: If the incoming partner obtains the entire share from one existing partner, deduct that share only from that partner’s old share.

The old ratio 7:8 represents shares of 7/15 and 8/15 for A and B, respectively. Since C’s 2/15 share is given entirely by B, A’s share remains 7/15, while B’s new share becomes 8/15 − 2/15 = 6/15. Therefore, the new ratio A:B:C is 7/15:6/15:2/15 = 7:6:2. Option B is incorrect because it does not deduct C’s share from B. Exam tip: subtract the incoming partner’s share from the old partner who sacrifices it.

Since the old ratio is 4:3, A and B's old shares are 4/7 and 3/7 respectively. C's 1/7 share is acquired in the sacrificing ratio 3:4, so A sacrifices 3/49 and B sacrifices 4/49. Therefore, A's new share is 4/7 − 3/49 = 25/49, B's new share is 3/7 − 4/49 = 17/49, and C's share is 1/7 = 7/49. Hence, the new ratio is 25:17:7. Exam tip: Subtract each old partner's sacrifice from their old share, then include the incoming partner's share.

A’s old share is 5/7 and B’s old share is 2/7. Out of C’s 1/7 share, A sacrifices \(1/7 \times 2/7=2/49\) and B sacrifices \(1/7 \times 5/7=5/49\). Thus, A’s new share is \(35/49-2/49=33/49\), B’s is \(14/49-5/49=9/49\), and C’s is \(7/49\). Therefore, the new ratio is 33:9:7. Exam tip: divide the incoming partner’s share according to the sacrificing ratio and subtract those amounts from the old partners’ shares.

If the incoming partner takes the entire share from only one old partner, the other old partner makes no sacrifice; hence that partner’s new ratio remains unchanged. Exam tip: first identify the partner who sacrifices profit share.

A and B initially have shares \(3/7=15/35\) and \(4/7=20/35\), respectively. C receives \(2/7=10/35\). Since the sacrificing ratio is 2:3, A sacrifices \(4/35\) and B sacrifices \(6/35\). Thus, their new shares are \(11/35\) and \(14/35\), while C receives \(10/35\). Therefore, the new profit-sharing ratio is 11:14:10. Option B does not adjust the old partners’ shares for their sacrifice. Exam tip: subtract each partner’s sacrifice from the old share and then include the incoming partner’s share.