Question

A and B are partners sharing profits and losses in the ratio of 2 : 5. They admit C on the condition that he will bring ₹ 14,000 as his share of goodwill to be distributed between A and B. C's share in the future profits or losses will be 1/4th. What will be the new profit-sharing ratio and what amount of goodwill brought in by C will be received by A and B? 

Answer 1

Old Ratio = A : B = 2 : 5

C is admitted for `1/4` share
Let the combined share of A, B and C be = 1
Combined share of A and B after C’s admission = 1 − C’s share
= 1- `1/4` = `3/4`

New Ratio = Old Ratio × Combined share of A and B
A's = `2/7 xx 3/4 = 6/28`

B's = `5/7 xx 3/4 = 15/28`

New Profit Sharing Ratio = A : B : C
                                        = `6/28 : 15/28 : 1/4`

                                       = `[ 6:15:7]/28`

                                       = 6 : 15 : 7
Distribution of C’s share of Goodwill
C’s share of Goodwill = Rs 14,000

A's will get = 14,000 x `2/7` = Rs. 4,000

B will get =14,000 x `5/7` = Rs. 10,000