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

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*1/3= 1/15 Y takes= 1/5*2/3= 2/15
X's new share is 2/5+1/15= 7/15
Y's new share= 2/5+2/15= 8/15
So, new ratio is 7:8