Alia and Deepika are partners in a firm. They admitted Priyanka into partnership giving her $\frac{1}{5}th$ share which she acquired from Alia and Deepika in the ratio of 1 : 2. What will be the new profit sharing ratio?

13 : 11 : 6

The correct answer is Option (3) → 13 : 11 : 6.

Alia and Deepika = 1:1 (Old ratio as no ratio is given so it should be equal)

Priyanka into partnership giving her 1/5th share which she acquired from Alia and Deepika in the ratio of 1 : 2.

Priyanka admitted with 1/5th share

Sacrificing ratio = 1:2

Sacrificed share of Alia = 1/5 x 1/3
                                  = 1/15

Sacrificed share of Deepika = 1/5 x 2/3
                                        = 2/15

New share = Old Share - Sacrificed share

New share of Alia = 1/2 - 1/15
                          = (15-2)/30
                          = 13/30

New share of Deepika = 1/2 - 2/15
                                = (15-4)/30
                                = 11/30

Share of Priyanka = 1/5

New ratio = 13/30 :11/30 :1/5
               = 13/30 :11/30 : 6/30
               = 13:11:6