Q.A and B are partners sharing profits in the ratio 3:2. They admit C for 1/5th share in future profits, which he acquires equally from A and B. Calculate the new profit-sharing ratio and the sacrificing ratio.

C's 1/5 share is taken equally (1/10 each) from A and B, so each of their old shares (converted to tenths) is reduced by 1/10.

A's old share 3/5 = 6/10, less 1/10 sacrificed = 5/10. B's old share 2/5 = 4/10, less 1/10 sacrificed = 3/10. C's share = 2/10.

C is admitted for 1/5 share, acquired EQUALLY from A and B — meaning each of A and B sacrifices half of C's share, i.e., (1/5) ÷ 2 = 1/10 each.

Converting A and B's old ratio (3:2, i.e., A = 3/5 and B = 2/5) to tenths so they can be combined with the 1/10 sacrifice: A = 3/5 = 6/10, B = 2/5 = 4/10.

A's new share = 6/10 − 1/10 = 5/10

B's new share = 4/10 − 1/10 = 3/10

C's share = 1/10 + 1/10 = 2/10

New ratio A : B : C = 5 : 3 : 2 (out of 10).

Check: 5/10 + 3/10 + 2/10 = 10/10 = 1, confirming the shares are correctly accounted for and none has been double-counted or omitted.

Sacrificing ratio: A's sacrifice = 6/10 − 5/10 = 1/10; B's sacrifice = 4/10 − 3/10 = 1/10. Sacrificing ratio of A and B = 1/10 : 1/10 = 1 : 1, which independently confirms the "equally" condition stated in the question.

A common slip is dividing C's 1/5 share equally as 1/5 each to A and B instead of 1/10 each — "acquired equally from A and B" means the 1/5 total is split into two EQUAL parts between them, not that each gives up the full 1/5.