X and Y are two equal partners in a firm. On 1st January, 2004 they admitted Z on the condition that he will bring Rs. 10,000 as capital and Rs. 5000 as goodwill. In future they will share profits in the ratio of 2 : 1 : 2. The proportion of goodwill distribution between X and Y will be:

The correct answer is A. 1 : 1.

The total amount of goodwill is Rs. 5000. X and Y are two equal partners and they will share the goodwill in the ratio of their existing capitals. The existing capitals of X and Y are equal and each of them has a capital of Rs. 10000. So, the ratio of goodwill to be shared by X and Y is 10000 : 10000 = 1 : 1.

The amount of goodwill to be shared by Z is Rs. 5000. Since Z is to share the profits in the ratio of 2 : 1 with X and Y, he will get 2/5 of the total goodwill. So, the amount of goodwill to be shared by Z is 2/5 * 5000 = Rs. 2000.

The amount of goodwill to be shared by X and Y is Rs. 5000 – Rs. 2000 = Rs. 3000. Since X and Y are to share the goodwill in the ratio of 1 : 1, they will each get 1/2 of the goodwill. So, the amount of goodwill to be shared by X is 1/2 * 3000 = Rs. 1500.

The amount of goodwill to be shared by Y is also Rs. 1500.

Therefore, the proportion of goodwill distribution between X and Y is 1 : 1.