Question

Rao and Swami are partners in a firm sharing profits and losses in 3:2 ratio. They admit Ravi as a new partner for 1/8 share in the profits. The new profit sharing ratio between Rao and Swami is 4:3. Calculate new profit sharing ratio and sacrificing ratio?

Answer 1

Old Ratio = Rao : Swami

                = 3 ; 2

Ravi admits for `1/8` share of profit in the new firm.

Let the New Firm Profit = 1

Combined share of Rao and Swami in the new firm

= 1 − Ravi’s share of profit

= 1 − `1/8`

=`7/8`

New Ratio = Combined Share of Rao and Swami × Proportion of Rao and Swami in the combined share

Rao = `7/8 xx 4/7 = 28/56`

Swami = `7/8 xx 3/7 = 21/56`         

New Ratio = Rao : Swami : C

                  = `28/56 : 21/56 : 1/8`

                 = `[ 28 : 21 : 7]/56`

                 =  `4 : 3 : 1`

Sacrificing Ratio = Old Ratio − New Ratio

Rao = `3/4 - 4/8 = [ 24 -20]/40 = 4/40`

Swami = `2/5 - 3/8 = [ 16 -15 ]/40 = 1/40`

Sacrificing Ratio = Rao : Swami

                          = `4/40 - 1/40`

                          = ` 4 : 1`