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.

#### Solution

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.