A, B and C were partners sharing profits and losses in the ratio of 5 : 3 : 2. They admitted D into partnership for 1/6th share in profits, half (1/2) of which was given by A and the remaining half was given by B and C in the ratio 3 : 2. The new profit sharing ratio will be :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 : 3 : 2 : 2
Old ratio of A, B and C = 5 : 3 : 2.
D admitted with 1/6th share
A sacrifice = 1/2 x 1/6
= 1/12
Remaining share of D = 1/6 -1/12
= 1/12
1/12 is shared by B and C in the ratio 3 : 2.
B sacrifice = 1/12 x 3/5
= 3/60
C sacrifice = 1/12 x 2/5
= 2/60
A's new share = 5/10 - 1/12
= (30-5)/60
= 25/60
B's new share = 3/10 - 3/60
= (18-3)/60
= 15/60
C's new share = 2/10 - 2/60
= (12-2)/60
= 10/60
New ratio between A, B, C & D = 25/60 : 15/60 : 10/60 : 1/6
= 25/60 : 15/60 : 10/60 : 10/60
= 25:15:10:10
= 5:3:2:2