Question

Singh, Gupta and Khan are partners in a firm sharing profits in 3:2:3 ratio. They admitted Jain as a new partner. Singh surrendered 1/3 of his share in favour of Jain: Gupta surrendered 1/4 of his share in favour of Jain and Khan surrendered 1/5 in favour of Jain. Calculate new profit sharing ratio?

Answer 1

Old Ratio = Singh : Gupta : Khan

                = 3 : 2 : 3

                = `3/8 : 2/8 : 3/8`

Singh Surrender  = `1/3` of his share

Gupta Surrender = `1/4` of his share

Khan Surrender = `1/5` of his share

Sacrificing Ratio = Old Ratio × Surrender Ratio

Singh’s = `3/8 xx 1/3 = 3/24`

Gupta’s = `2/8 xx 1/4 = 2/32`

Khan’s = `3/8 xx 1/5 = 3/40`

New Ratio = Old Ratio − Sacrificing Ratio

Singh’s = `3/8 - 3/24 = [ 9 -3 ]/24 = 6/24`

Gupta’s = `2/8 - 2/32 = [ 8 -2]/32 = 6/32`

Khan’s = `3/8 - 3/40 = [ 15 - 3]/40 = 12/40`

New Ratio = Singh : Gupta : Khan : Jain

                  = `6/24 : 6/32 : 12/40 : 21/80`

                  = ` [120 : 90 : 144 : 126]/480`

                  = ` 20 : 15 : 24 : 21`