Admission of C as a Partner

Capital Contribution and Goodwill

A and B were in partnership sharing profits and losses in the ratio of 3:1. On 1st January 1982, they admitted C as a partner on the following terms:

- C brings Rs. 10,000 as his capital.
- C brings Rs. 5,000 for goodwill, half of which to be withdrawn by A.

Explanation

Capital Contribution

C's capital contribution of Rs. 10,000 would increase the total capital of the partnership. The new capital balance after C's admission can be calculated as follows:

A's capital balance = 3/4 x Total capital before admission
B's capital balance = 1/4 x Total capital before admission
C's capital balance = Rs. 10,000

Total capital after admission = A's capital balance + B's capital balance + C's capital balance
Total capital after admission = 3/4 x Total capital before admission + 1/4 x Total capital before admission + Rs. 10,000
Total capital after admission = Total capital before admission + Rs. 10,000

Therefore, the total capital of the partnership would increase by Rs. 10,000 after C's admission.

Goodwill

Goodwill is an intangible asset that represents the value of a business beyond its tangible assets. A and B had built up goodwill over time, which was reflected in the profits of the partnership. To compensate A for part of the goodwill, C was required to bring Rs. 5,000 for goodwill.

The half of the goodwill amount to be withdrawn by A would be calculated as follows:

Half of the goodwill amount = Rs. 5,000 / 2
Half of the goodwill amount = Rs. 2,500

Therefore, A would withdraw Rs. 2,500 from the goodwill amount brought in by C.

Conclusion

C's admission as a partner would increase the total capital of the partnership and his contribution towards goodwill would compensate A for part of the goodwill value.