A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for 1/4th share. Afterwards, D enters for 20 paisa in the rupee. The new profit sharing ratio after D's admission will be :

9:6:5:5

The correct answer is option 1- 9:6:5:5.

Old ratio between A & B = 3:2
C admitted = 1/4

Total share = 1
After C share, remaining share = 1-1/4
                                                 = 3/4
This 3/4 share is divided between old partners in their old ratio (3:2).

A's New Share after admission of C = 3/5 x 3/4
                                                        = 9/20
B's New Share after admission of C = 2/5 x 3/4
                                                        = 6/20
New ratio after admission of C = 9/20 : 6/20 : 1/4
                                                 = 9/20 : 6/20 : 5/20
                                                 = 9:6:5

Share of D = 20 paisa means 20/100 or 1/5
Total share = 1
Remaining share after D' share = 1 - 1/5
                                                  = 4/5
This 4/5 is divided between old partners i.e. A, B & C in their old ratio means 9:6:5.

A's New share after D's Admission = 9/20 x 4/5
                                                       = 36/100
B's Share after D's Admission = 6/20 x 4/5
                                               = 24/100
C's New Share after admission of D = 5/20 x 4/5
                                                        = 20/100
D 's Share = 1/5 or 20/100

New ratio = 36/100:24/100:20/100:20/100
                  = 36:24:20:20 i.e. 9:6:5:5