A, B, C and D are in partnership sharing profits and losses in the ratio

16 :- A, B, C and D are in partnership sharing profits and losses in the ratio of 36 : 24 : 20 : 20 respectively. E joins the partnership for 20% share and A, B, C and D in future would share profits among themselves as 3/10 : 4/10 : 2/10 : 1/10.
Calculate new profit sharing ratio after E’s admission.

Solution:- Old ratio of A, B, C and D is 9:8:5:5
Let the total profit share of the firm be 1
E was admitted for 20% share or 1/5th share
Remaining share for A, B, C and D is 1 – 1/5 = 4/5
They will distribute the remaining share in 3:4:2:1

A’s new share = 4/5 x 3/10 = 12/50
B’s new share = 4/5 x 4/10 = 16/50
C’s new share = 4/5 x 2/10 = 8/50
D’s new share = 4/5 x 1/10 = 4/50
E’s share = 1/5 x 10/10 = 10/50

Thus, New PSR of A, B, C, D and E is 12:16:8:4:!0 or 6:8:4:2:5