Question

A and B are in partnership sharing profits and losses as 3 : 2. C is admitted for 1/4th share. Afterwards D enters for 20 paise in the rupee. Compute profit-sharing ratio of A, B, C and D after D's admission.

Answer 1

Old Ratio = A : B = 3 : 2
C’s admitted for  `1/4` share of profit
Let the combined share of profit of all partners be = 1
Combined share of A and B after C’s admission = 1 − C’s share
= 1 - `1/4 = 3/4`

New Ratio = Old Ratio × Combined share of A and B
A's = `3/5 xx 3/4 = 9/20`

B's = `2/5 xx 3/4 = 6/20`

New Profit Sharing Ratio after C's admission = A : B : C
= `9/20 : 6/20 : 1/4`

= `[9 : 6 : 5]/20` = 9 : 6 : 5.

Profit sharing ratio after C’s admission will become old ratio to determine the ratio after D’s admission
Ratio before D's admission = A : B : C = 9 : 6 : 5

D is admitted for `20/100` share of profit

Let combined share of all partners after D’s admission = 1
Combined share of A, B and C after D’s admission = 1 − D’s share 
= 1 - `20/100`
=`80/100`

New Ratio = Old Ratio × Combined share of A, B, and C
A's = `9/20 xx 80/100 = 72/200`

B's = `6/20 xx 80/100 = 48/200`

C's = `5/20 xx 80/100 = 40/200`

New Profit Sharing ratio after C's admission = A : B : C : D
= `72/200 : 48/200 : 40/200 : 20/100`

= `[72 : 48 : 40 : 40]/200`

= 9 : 6 : 5 : 5.