X, Y and Z have been sharing profits in the ratio of 4 : 2 : 1. Z retires. X and Y take Z's share equally. What will be the new profit sharing ratio among existing partners?

9:5

The correct answer is option 3- 9:5.

Old ratio = 4:2:1 (X,Y & Z)
Share of Z = 1/7

Gain of X =1/2*1/7
               =1/14

Gain of Y = 1/2*1/7
               =1/14

New share = Old share + gained share

New Share of X = 4/7+1/14
                         = (8+1)/14
                         = 9/14

New Share of Y = 2/7+1/14
                         = (4+1)/14
                         = 5/14

New ratio between X & Y = 9/14 :5/14
                                        = 9:5