Question

A and B were partners sharing profits in the ratio of 5 : 3. On 1st April, 2021 they admitted C as a new partner for 1/4th share which he acquired from A and B in the ratio of 3 : 2. On 1st April 2022, another new partners D was admitted for 1/6th share which he acquires 1/10 from A and 1/15 from C. On 1st April, 2023 A dies and his share was taken over by B, C and D equally.

Calculate:

1. New profit sharing ratio of A, B and C on C's admission.
2. New profit sharing ratio of A, B, C and D on D’s admission.
3. New profit sharing ratio of B, C and D on A's Death.

Answer 1

(i) Old Ratio of A and B: 5 : 3 (Share: `A = 5/8, B = 3/8`)

C's Share: `1/4`

Sacrifice details: C acquires his `1/4` share from A and B in the ratio of 3 : 2.

Share sacrificed by A: `1/4 xx 3/5 = 3/20`

Share sacrificed by A: `1/4 xx 2/5 = 2/20`

A's New Share: `5/8 - 3/20 = (25 - 6)/40 = 19/40`

B's New Share: `3/8 - 2/20 = (15 - 4)/40 = 11/40`

C's New Share: `1/4 = 10/40`

New Ratio of A, B, and C = 19 : 11 : 10

(ii) Old Ratio of A, B, and C: 19 : 11 : 10 `("Shares:" A = 19/40, B = 11/40, C = 10/40)`

D's Share: `1/6`

Sacrifice details: D acquires `1/10` from A and `1/15` from C.

A's New Share = `19/40 - 1/10 = (19 - 4)/40 = 15/40 = 45/120`

B's New Share = `11/40 = 33/120` (No change)

C's New Share = `10/40 - 1/15 = (30 - 8)/120 = 22/120`

D's New Share = `1/6 = 20/120`

New Ratio of A, B, C, and D = 45 : 33 : 22 : 20

(iii) Ratio before A's death: `A = 45/120, B = 33/120, C = 22/120, D = 20/120`

A's Share = `45/120`

Takeover details: A's share is taken over by B, C, and D equally.

Share gained by each continuing partner: `45/120 ÷ 3 = 15/120`

B's New Share: `33/120 + 15/120 = 48/120`

C's New Share: `22/120 + 15/120 = 37/120`

D's New Share: `20/120 + 15/120 = 35/120`

New Ratio of B, C, and D = 48 : 37 : 35