A & B are equal partners in a partnership firm. They admit C & D as partners with 1/5th and 1/6th share respectively. What will be the new profit-sharing ratio?

19:19:12:10

The correct answer is option 2- 19:19:12:10.

OLD RATIO IS 1:1 (A&B)
C share is 1/5
D share is 1/6
Total share of C & D = 1/5 +1/6
                                 = (6+5)/30
                                 = 11/30

Let total share of the firm = 1
Remaining share after C & D = 1-11/30
                                             = 19/30

This 19/30 share is distributed between old partners in their old ratio i.e. equally.
A's NEW SHARE = 19/30 X 1/2
                         = 19/60

B's  NEW SHARE = 19/30 X 1/2
                          = 19/60

So, the new ratio = 19/60:19/60:1/5:1/6
                            = 19/60 : 19/60 :12/60:10/60
                            = 19:19:12:10