Question

A, B and C are partners sharing profits in 3:2:2 ratio. They admitted D as a new partner for 1/5 share which he acquired from A, B and C in 2:2:1 ratio respectively. Calculate new profit sharing ratio?

Answer 1

Old Ratio = A : B : C

                = 3 : 2 : 2

               = `3/7 : 2/7 : 2/7`

D admits for `1/5` share in the new firm which he takes `1/5` in the ratio 2:2:1 from A, B and C.

A’s sacrifice = D’s share × `2/5`

= `1/5 xx 2/5 = 2/25`

B’s sacrifice = D’s share × `2/5`

= `1/5 xx 2/5 = 2/25`

C’s sacrifice = D’s share × `1/5`

= `1/5 - 1/5 = 1/25`

New Ratio = Old Ratio − Sacrificing Ratio

A = `3/7 - 2/25`

   = `[ 75 -14 ]/175 = 61/175`

B = `2/7 - 2/25`

   = `[ 50 - 14]/175 = 36/175`

C = `2/7 - 1/25`

   = `[ 50 -7]/175 = 43/175`

New Ratio = A : B : C : D

                  = `61/175 : 36/175 : 43/175 : 1/5`

                 = `[ 61 : 36 : 43 : 35 ]/175`

                 = `61 : 36 : 43 : 35`