A, B and C were partners sharing profits and losses in the ratio of 5 : 3 : 2. They admitted D into partnership for 1/6^th share in profits, half (1/2) of which was given by A and the remaining half was given by B and C in the ratio 3 : 2. The new profit sharing ratio wil be :

5 : 3 : 2 : 2

The correct answer is Option (1) → 5 : 3 : 2 : 2

Old ratio of A, B and C = 5 : 3 : 2.
D admitted with 1/6th share

A sacrifice = 1/2 x 1/6
               = 1/12

Remaining share of D = 1/6 -1/12
                                = 1/12
1/12 is shared by B and C in the ratio 3 : 2.
B sacrifice = 1/12 x 3/5
                = 3/60

C sacrifice = 1/12 x 2/5
                = 2/60

A's new share = 5/10 - 1/12
                     = (30-5)/60
                     = 25/60

B's new share = 3/10 - 3/60
                     = (18-3)/60
                     = 15/60

C's new share = 2/10 - 2/60
                     = (12-2)/60
                     = 10/60

New ratio between A, B, C & D = 25/60 : 15/60 : 10/60 : 1/6
                                             = 25/60 : 15/60 : 10/60 : 10/60
                                             = 25:15:10:10
                                             = 5:3:2:2