C is admitted for 31 share and brings Rs 60,000 as capital.
If C's capital of Rs 60,000 represents 31 share, then:
Total value of the firm = Rs 60,000 × 3 = Rs 1,80,000
Now, let's find the actual combined capital:
A's capital = Rs 45,000
B's capital = Rs 45,000
C's capital = Rs 60,000
Total actual capital = Rs 1,50,000
The goodwill is the difference between the firm's total value (based on C's contribution) and the actual capital:
Goodwill = Rs 1,80,000 - Rs 1,50,000 = Rs 30,000
This Rs 30,000 represents the hidden value (goodwill) of the existing firm that C is paying for along with his capital contribution. When C pays Rs 60,000 for 31 share, he's essentially valuing the firm at Rs 1,80,000, but the tangible capital is only Rs 1,50,000. The difference of Rs 30,000 is the firm's goodwill.