Question

X and Y were partners sharing profits in the ratio of 3 : 2. They admitted P and Q as new partners. X surrendered 1/3rd of his share in favour of P and Y surrendered 1/4th of his share in favour of Q. Calculate new profit-sharing ratio of X, Y, P and Q.

Answer 1

Old Ratio = X : Y = 3 : 2
Sacrificing Ratio = Old Ratio × Surrender Ratio
X's Sacrificing Share = `3/5 xx 1/3 = 3/15`

Y's Sacrificing Share = `2/5 xx 1/4 = 2/20`

New Ratio = Old Ratio − Sacrificing Ratio
X's share = `3/5 - 3/15 = 6/15`

Y's share = `2/5 - 2/20 = 6/20`

P’s share = X’s Sacrifiece = `3/15`

Q’s share = Y’s Sacrifice = `2/20`

New Profit Sharing Ratio = X : Y : P : Q

                                        = `6/15 : 6/20 : 3/15 : 2/20`

                                        = `[ 24 : 18 : 12 : 6 ]/60`

                                       = or 10 : 6: 4 :5 respectively.