Question

X,Y and Z are partners sharing profits and losses in the ratio of 5 : 3 : 2. They admit A into partnership and give him 1/5th share of profits. Find the new profit-sharing ratio.

Answer 1

Old Ratio = X : Y : Z
                = 5 : 3 : 2
A is admitted for `1/5` share of profit
Let the combined share of profit for all partners after A's admission be = 1
Combined share of X,Y and Z after A's admission = 1 - A's share
= 1 - `1/5`
= `4/5`
New Ratio = Old Ratio × Combined share of X, Y and Z
X's = `5/10 xx 4/5 = 20/50`

Y's = `3/10 xx 4/5 = 12/50`

Z's = `2/10 xx 4/5 = 8/50`

New Profit Sharing Ratio = X : Y : Z : A

                                        = `20/50 : 12/50 : 8/50 : 1/5`

                                        = `[ 20 : 12 : 8 : 10]/50`

                                        = 10 : 6 : 4 : 5