Question

A, B and C are partners in a firm sharing profits in 4 : 3 : 3 ratio. They decided to admit their manager D into the partnership. A surrendered `1/4` of his share in favour of D; B surrendered `1/5` of his share in favour of D, and C surrendered `1/6` of his share in favour of D. Calculate the new profit sharing ratio.

Answer 1

Calculation of Surrendered share:

A’s old share = `4/10`

A’s surrendered = `1/4 xx 4/10` in favour of D

= `4/40`

= `1/10`

B’s old share = `3/10`

B’s surrendered = `1/5 xx 3/10` in favour of D

= `3/50`

C’s old share = `3/10`

C’s surrendered = `1/6 xx 3/10` in favour of D

= `3/60`

= `1/20`

Calculate the new shares of the old partners:

A’s new share after surrendering `1/10` in favour of D

= `4/10 - 1/10`

= `3/10`

B’s new share after surrendering `3/50` in favour of D

= `3/10 - 3/50`

= `(3 xx 5)/(10 xx 5) - 3/50`

= `15/50 - 3/50`

= `12/50`

C’s new share after surrendering `1/20` in favour of D

= `3/10 - 1/20`

= `(3 xx 2)/(10 xx 2) - 1/20`

= `6/20 - 1/20`

= `5/20`

Calculate the new partner’s share:

D’s share is the total of `1/10` from A, `3/50` from B, and `1/20` from C

A = `1/10`

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

= `10/100`

B = `3/50`

= `(3 xx 2)/(50 xx 2)`

= `6/100`

C = `1/20`

= `(1 xx 5)/(20 xx 5)`

= `5/100`

= `(10 + 6 + 5)/100`

= `21/100`

The New Ratio of A, B, C, and D:

A = `3/10`

= `(3 xx 10)/(10 xx10)`

= `30/100'

B = `12/50`

= `(12 xx 2)/(50 xx 2)`

= `24/100'

C = `5/20`

= `(5 xx 5)/(20 xx 5)`

= `25/100'

Hence, the New Ratio of A, B, C, and D = `30/100 : 24/100 25/100 : 21/100` or 30 : 24 : 25 : 21