A and B are partners sharing profits and losses in the ratio of 5 : 4. C is admitted for  1/5th share. A and B decide to share equally in future. What will be the sacrificing Ratio?

7:2

The correct answer is option 3- 7:2.

Old ratio = 5:4 (A & B)
Share of C= 1/5
Let total share = 1
Remaining share after C = 1-1/5
                                     = 4/5
A & B share future profits equally. So 4/5 will be distributed between them equally.
New Share of A = 1/2*4/5
                       = 4/10

New Share of B = 1/2/*4/5
                       = 4/10

New profit ratio (A, B & C) = 4/10 :4/10: 1/5
                                       = 4/10:4/10:2/10
                                       = 4:4:2 or 2:2:1

Sacrifice = Old share - New share

Sacrifice of A = 5/9-2/5
                    = (25-18)/45
                    = 7/45

Sacrifice of B = 4/9-2/5
                    = (20-18)/45
                    = 2/45

Sacrificing Ratio = 7/45 : 2/45
                            = 7:2