Question

Radha and Rukmani are partners in a firm sharing profits in 3:2 ratio. They admitted Gopi as a new partner. Radha surrendered 1/3 of her share in favour of Gopi and Rukmani surrendered 1/4 of her share in favour of Gopi. Calculate new profit sharing ratio?

Answer 1

Old Ratio = Radha : Rukmani

                =  3 : 2

                = `3/5 : 2/5`

Radha surrendered in favour of Gopi = ` 1/3` of his share

Rukmani surrendered in favour of Gopi = `1/4` of his share

Sacrificing Ratio = Old Ratio × Surrender Ratio

Radha = `3/5 xx 1/3`

`= cancel3/5 xx 1/cancel3`

`= 1/5`

Rukmani = `2/5 xx 1/4`

`= cancel(2)^1/5 xx 1/cancel(4)^2`

`= 1/(5 xx 2)`

`= 1/10`

New Ratio = Old Ratio − Sacrificing Ratio

Radha = `3/5 - 1/5 = 2/5`

Rukmani = `2/5 - 1/10 = [ 4 -1 ]/10 = 3/10`

Gopi’s Share = Radha’s Sacrificing Ratio + Rukmani’s Sacrificing Ratio

= `1/5 + 1/10 = [ 2 + 1 ]/10`

= `3/10`

New Ratio = Radha : Rukmani : Gopi

                 = `2/5 : 3/10 : 3/10`

                 = `[ 4 : 3 : 3 ]/10`

                 = ` 4 : 3 : 3`