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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?
Solution
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`
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