A, B, C were partners in afirm sharing profit and losses in the ratio 9:6:5 D is admitted as new partner for 1/4th share B sacrifices 1/20th share from his share and rest of sacrifice made by A and C in the ratio of 3:1 calculate sacrificing ratio and new profit sharing ratio

Dear student,
In this question, D is admitted for 1/4 th share.
First of all we will calculate sacrifice made by partners.
sacrifice made by B = 1/20 or 4/80
and rest of sacrifice made by A and C in the ratio of 3:1 
remaining sacrifice made by A & C = 1/4 - 1/20 = 4/20
Sacrifice made by A = 3/4 X 4/20 = 12/80
Sacrifice made by C = 1/4 x 4/20 =4/80 
SACRIFING RATIO OF A,B & C = 12:4:4 OR 3:1:1

New profit sharing ratio 
  new share = old share - sacrificed share
  A -   9/20 - 12/80 = 24/80
  B - 6/20 - 4/80 = 20/80
  C- 5/20-4/80 = 16/80
 D = 1/4 - 0 = 1/4 0R 20/80
NEW PROFIT SHARING RATIO  OF A,B,C & D = 24:20:16:20 OR 6:5:4:5

Regards

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