Question

A, B, C and D are in partnership sharing profits and losses in the ratio of 36 : 24 : 20 : 20 respectively. E joins the partnership for 20% share and A, B, C and D in future would share profits among themselves as `3/10 : 4/10 : 2/10 : 1/10`. Calculate new profit-sharing ratio after E’s admission.

Answer 1

E is admitted for `20/100` share

= `1/5`
Let the combined share of profit of all partners after E’s admission = 1

Combined share of A, B, C, and D after E’s admission = 1 − E’s Share
= `1 - 1/5 = 4/5`

New Ratio = Combined of A, B, C, and D. Agreed Share of A, B, C, and D
A’s new ratio = `4/5 xx 3/10`

= `12/50`

B’s new ratio = `4/5 xx 4/10`

= `16/50`

C’s new ratio = `4/5 xx 2/10`

= `8/50`

D’s new ratio = `4/5 xx 1/10`

= `4/50`

To find the new ratio, express all partners’ shares with a common denominator. The shares for A, B, C, and D are already in a common denominator of 50.

E’s share = `1/5`

= `(1 xx 10)/(5 xx 10)`

= `10/50`

New Profit Sharing Ratio for  A, B, C, D, and E = `12/50 : 16/50 : 8/50 : 4/50 : 10/50` or 6 : 8 : 4 : 2 : 5