X, Y & Z are partners sharing profits in the ratio of 2/5,2/5 &1/5. If Z retires from the firm and his share is taken by the remaining partners in a ratio of 1:2, what will be the new ratio?

7:8

The correct answer is option 2- 7:8.

OLD RATIO = 2:2:1
Z retires and his share of 1/5 is taken by the remaining partners in 1:2 ratio.
So, X takes = 1/5 x 1/3
                  = 1/15
Y takes = 1/5 x 2/3
             = 2/15

X's new share = 2/5 + 1/15
                       = (6+1)/15
                       = 7/15
Y's new share = 2/5 + 2/15
                       = (6+2)/15
                       = 8/15

So, new ratio = 7/15 : 8/15
                       = 7:8