Question

R and S are partners sharing profits in the ratio of 5 : 3. T joins the firm as a new partner. R gives 1/4th of his share and S gives 1/5th of his share to the new partner. Find out new profit-sharing ratio.

Answer 1

Old Ratio = R : S
                = 5 : 3
Sacrificing Ratio = Old Ratio × Surrender Ratio
R's = `5/8 xx 1/4 = 5/32`

S's = `3/8 xx 1/5 = 3/40`

New Ratio = Old Ratio − Sacrificing Ratio
R's = `5/8 - 5/32 = 15/32`

S's = `3/8 - 3/40 = 12/40`
T's share = R's sacrifice + S's Sacrifice
               = `5/32 + 3/40 = [ 25 + 12 ]/160 = 37/160`
New Profit Sharing Ratio = R : S : T
                                         = `15/32 : 12/40 : 37/160`

                                        = `[ 75 : 48 : 37]/160`

∴New Profit Sharing Ratio = 75 : 48 : 37