Question : P and S are partners sharing profits in the ratio of 3 : 2. R is admitted with 1/5th share and he brings in Rs.42,000 as his share of goodwill which is Credited to the Capital Accounts of P and S respectively with Rs.31,500 and Rs.10,500. New profit sharing ratio will be -
Option 1: 3 : 2 : 5
Option 2: 9 : 7 : 4
Option 3: 7 : 9 : 4
Option 4: 3 : 1 : 5
Correct Answer: 9 : 7 : 4
Solution : As here P and S has 3:2 as ratio before , they admit a new partner R for a share of 1/5 and he brings ₹42,000 as his share of goodwill which is credited to capital accounts of P and S with Rs.31,500 and Rs.10,500, the goodwill is divided between P and S in the ratio :-
= 31,500 : 10,500
= 3 : 1 (in the ratio of goodwill ), we will calculate the sacrifice made by P and S in the favor of new partner R's share of 1/5 =
sacrifice made by P = 1/5 * 3/4
= 3/20
sacrifice made by S = 1/5 * 1/4
= 1/20
now from this sacrifice we will calculate, the new profit sharing ratio of P and S :-
P's new ratio = old ratio - sacrifice made by P
= 3/5 - 3/2
= 9/20
S's new ratio = old ratio - sacrifice made by S
= 2/5 - 1/20
= 7/20
R's ratio = 1/5 0r 4/20 [ 9/20 : 7/20 : 1/5 = (9 + 7 + 4) / 20 ]
so, the new profit sharing ratio between P and S and R will be :-
= 9/20 : 7/20 : 4/20
= 9 : 7 : 4
Hence the correct answer is option 2.
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