XY, YZ & ZW are partners in ratio of 3:2:1. A joins the firm as a new partner for 1/6th share in profits. If ZW would retain his original share, then what will be the new profit-sharing ratio?

12:8:5:5

The correct answer is option 4- 12:8:5:5.

ZW Share will be the same i.e., 1/6
A share will be 1/6
Let total share = 1
Remaining share after ZW & A =  1- 1/6 - 1/6
                                                = 1 - 2/6
                                                = (6-2)6
                                                =  4/6

This 4/6 is distributed between XY & YZ in old ratio i.e., 3:2
So, XY new share = 3/5*4/6
                             = 12/30

YZ new share = 2/5*4/6
                      = 8/30

So, new profit-sharing ratio = 12/30:8/30:1/6:1/6
                                           = 12/30 : 8/30 : 5/30 : 5/30
                                           = 12:8:5:5