Question

A, B and C are partners sharing in the ratio of 4 : 3 : 2. They admit D for `1/9`th share. It is agreed that A would retain his original share. Calculate the new ratios and sacrificing ratios.

Answer 1

Calculation of New Profit Sharing Ratio:

D’s share = `1/9`; A = `4/9`

Remaining share for B and C = `1 - (1/9 + 4/9)`

= `1 - 5/9`

= `4/9`

This will be divided between B and C in their old ratio i.e., 3 : 2

Hence, the new share of B = `3/5 xx 4/9`

= `12/45`

New share of C = `2/5 xx 4/9`

= `8/45`

The new ratio of A, B, C, and D:

A = `4/9`

= `(4 xx 5)/(9 xx 5)`

= `20/45`

B = `12/45`

C = `8/45`

D = `1/9`

= `(1 xx 5)/(9 xx 5)`

= `5/45`

Thus, the new ratio of A, B, C, and D = `20/45 : 12/45 : 8/45 : 5/45` or 20 : 12 : 8 : 5

Calculation of Sacrificing Ratio:

Sacnfice made by A = `4/9 - 20/45`

= `(4 xx 5)/(9 xx 5) - 20/45`

= `20/45 - 20/45`

= 0

Sacnfice made by B = `3/9 - 12/45`

= `(3 xx 5)/(9 xx 5) - 12/45`

= `15/45 - 12/45`

= `(15 - 12)/45`

= `3/45`

Sacnfice made by C = `2/9 - 8/45`

= `(2 xx 5)/(9 xx 5) - 8/45`

= `10/45 - 8/45`

= `(10 - 8)/45`

= `2/45`

Thus, Sacrificing Ratio among A, B, and C = `0 : 3/45 : 2/45` or 3 : 2