Partnership ratio problem

You first said that ans is c) 12/54. That’s why I gave just the correct answer thinking that you might also get the same answer provided by me. Now you have modified your question with (b) and so I’ll modify my answer also. J

Profit sharing ratio between A, B and C if 3:2:1 = 3/6 : 2/6 : 1/6

A has given his 1/3^rd share to D. So his new ratio will be [3/6 x (1-1/3)] = 3/6 x 2/3 = 1/3

Similarly:

 for B: [2/6 x (1-1/6)] = 2/6 x 5/6 = 10/36 = 5/18

for C: [1/6 x (1-1/9)] = 1/6 x 8/9 = 8/54

Therefore, share of D = 1- [1/3 + 5/18 + 8/54] ; 1 being the total profit.

Solving this equation you will get 1-(41/54) = 13/54.

Now Clear??

before D

share of A is 3/(3+2+1) i.e. 1/2

share of B is 2/(3+2+1) i.e. 1/3

share of C is 1/(3+2+1) i.e. 1/6

now share of D is 1/3(1/2)+1/6(1/3)+1/9(1/6) = 9/54 + 3/54 + 1/54 = 13/54