Q.A and B share profits and losses in the ratio 3:2. They admit C, giving him a 1/5th share of future profits, which he acquires equally from A and B. Calculate

Since C's share is taken equally from both old partners, each of A and B gives up exactly the same amount — half of C's new share each.

C's share of 1/5 is split equally, so each of A and B sacrifices 1/10. A's new share = 3/5 − 1/10 = 1/2; B's new share = 2/5 − 1/10 = 3/10; C = 1/5 = 2/10. Expressed together, A:B:C = 5:3:2, and since both partners gave up the identical 1/10 each, the sacrificing ratio is 1:1.

1. New profit-sharing ratio Old ratio A:B = 3:2, so A's share = 3/5 and B's share = 2/5. C is given a 1/5th share, acquired EQUALLY from A and B, so each of them sacrifices half of C's share, i.e. 1/2 × 1/5 = 1/10 each. A's new share = 3/5 − 1/10 = 6/10 − 1/10 = 5/10 = 1/2. B's new share = 2/5 − 1/10 = 4/10 − 1/10 = 3/10. C's share = 1/5 = 2/10. Expressing all three over the common denominator 10: A : B : C = 5/10 : 3/10 : 2/10 = 5 : 3 : 2 (check: 5 + 3 + 2 = 10, the full whole — correct).
2. Sacrificing ratio Sacrifice = Old Share − New Share, for each old partner. A's sacrifice = 3/5 − 1/2 = 6/10 − 5/10 = 1/10. B's sacrifice = 2/5 − 3/10 = 4/10 − 3/10 = 1/10. Sacrificing ratio of A : B = 1/10 : 1/10 = 1 : 1, confirming that both partners have indeed sacrificed equally, exactly as the question stated.
   ✓Final answer

   New profit-sharing ratio of A, B and C = 5 : 3 : 2. Sacrificing ratio of A and B = 1 : 1 (equal).