Question

P and Q are partners sharing profits in 2:1 ratio. They admitted R into partnership giving him 1/5 share which he acquired from P and Q in 1:2 ratio. Calculate new profit sharing ratio?

Answer 1

Old Ratio = P : Q 

                = 2 : 1

                = `2/3 : 1/3`

R admits for `1/5` share in the new firm which he takes from `1/3`  from P and  `2/3` from Q.

P’s sacrifice = R’s share × `1/3`

= `1/5 xx 1/3 = 1/15`

Q’s sacrifice = R’s share × `2/3`

= `1/5 xx 2/3 = 2/15`

New Ratio = Old Ratio − Sacrificing Ratio

P = `2/3 - 1/15`

   = `[10 -1]/15 = 9/15`

Q = `1/3 - 2/15`

    = `[5 - 2]/15 = 3/15`

New Ratio = P : Q : R

                 = `9/15 : 3/15 : 1/5`

                = ` [ 9 : 3 : 3]/15`

               =  `3 : 1 : 1`