Q.A and B share profits and losses in the ratio 3:2. They admit C for a 1/5th share, which he acquires entirely from A. The new profit-sharing ratio of A, B and C will be:

Since C's whole share comes from A alone, only A's share needs to be reduced — B's share carries forward completely unchanged.

The correct option is (a) 2:2:1.

Old ratio of A:B = 3:2, so A's share = 3/5 and B's share = 2/5. C is admitted for a 1/5th share, acquired entirely from A, so B's share does not change at all.

A's new share = A's old share − C's share = 3/5 − 1/5 = 2/5.

B's new share = B's old share (unchanged) = 2/5.

C's share = 1/5.

New ratio, A : B : C = 2/5 : 2/5 : 1/5 = 2 : 2 : 1 (check: 2 + 2 + 1 = 5, matching the original whole, confirming the ratio is correctly worked out).

Why the other options are wrong:

• (b) 3:2:1 wrongly keeps A's OLD share (3/5) unreduced and simply appends C's share — this ignores that C's share must be carved OUT of an existing partner's share, not added on top of it. …