Partnership ratio problem

1 . A B C are partners sharing profits and losses at the ration of 3:2:1 . They agreee to admit D into the firm

A,B,C agreed to give 1/3 , 1/6 , 1/9 share of their profit . The share of profit on D will be?

a) 1/10

b) 13/54

c) 12/54

d) 10/55

ans : b) 13/54     please explain how ? we will get

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