A, B and C are partners sharing profits in the ratio of 3 : 2 : 1. D is admitted into firm for $\frac{1}{4}$th share of profit, which he gets $\frac{1}{8}$ from A and $\frac{1}{8}$ from B. Calculate new profit sharing ratio of all the partners.

9 : 5 : 4 : 6

The correct answer is Option (2) - 9 : 5 : 4 : 6.

A, B and C = 3 : 2 : 1.

D is admitted into firm for $\frac{1}{4}$th share of profit, which he gets $\frac{1}{8}$ from A and $\frac{1}{8}$ from B.

A's new share = 3/6 -1/8
                     = (12-3)/24
                     = 9/24

B's new share = 2/6 - 1/8
                     = (8-3)/24
                     = 5/24

C's share will be as old share = 1/6 or 4/24

D's share = 1/4 or 6/24

New ratio = 9/24 : 5/24 : 4/24 : 6/24
               = 9:5:4:6