X, Y & Z share profit in the ratio 3:2:1. On Z's retirement, his share was taken by X & Y in the ratio 2:1. Their new ratio will be...........

11:7

The correct answer is option 2- 11:7.

Old ratio = 3:2:1 (X, Y & Z)
Z retires
Gaining ratio = 2:1 (X & Y)

Z share = 1/6
X takes = 2/3 * 1/6
             = 2/18

Y takes = 1/3 * 1/6
             = 1/18

New share = Old share + Gained share

New share of X = 3/6 + 2/18
                         = (9+2)/18
                         = 11/18

New share of Y = 2/6 + 1/18
                         = (6+1)/18
                         = 7/18

New ratio between X & Y = 11/18 : 7/18
                                    = 11:7