Key Information Extraction

Identify the crucial details from the question:

• Existing Partners' Capitals: Ram (₹ 4,80,000), Shyam (₹ 3,10,000)
• New Partner: Ganesh
• Ganesh's Profit Share: 1/4
• Ganesh's Capital Contribution: ₹ 3,00,000
• Objective: Calculate Ganesh's share of goodwill.

Goodwill Calculation Steps

The goodwill brought by a new partner is calculated based on the firm's valuation. Here’s how:

Step 1: Determine the Implied Total Capital of the Firm

This is calculated based on the new partner's capital contribution and their share in the firm's profits.

If Ganesh's capital of ₹ 3,00,000 represents his 1/4 share, the total capital of the firm is implied as:

$ \text{Implied Total Capital} = \frac{\text{Ganesh's Capital}}{\text{Ganesh's Profit Share}} $

$ \text{Implied Total Capital} = \frac{₹ 3,00,000}{1/4} = ₹ 3,00,000 \times 4 = ₹ 12,00,000 $

Step 2: Calculate the Total Capital Actually Contributed

Sum the capital contributions of all partners (existing and new).

$ \text{Total Contributed Capital} = \text{Ram's Capital} + \text{Shyam's Capital} + \text{Ganesh's Capital} $

$ \text{Total Contributed Capital} = ₹ 4,80,000 + ₹ 3,10,000 + ₹ 3,00,000 = ₹ 10,90,000 $

Step 3: Calculate the Total Goodwill of the Firm

The difference between the implied total capital and the total contributed capital represents the firm's total goodwill.

$ \text{Total Goodwill} = \text{Implied Total Capital} - \text{Total Contributed Capital} $

$ \text{Total Goodwill} = ₹ 12,00,000 - ₹ 10,90,000 = ₹ 1,10,000 $

Step 4: Determine Ganesh's Share of Goodwill

Ganesh's share of goodwill is his profit-sharing ratio applied to the total goodwill of the firm.

$ \text{Ganesh's Share of Goodwill} = \text{Ganesh's Profit Share} \times \text{Total Goodwill} $

$ \text{Ganesh's Share of Goodwill} = \frac{1}{4} \times ₹ 1,10,000 = ₹ 27,500 $

Conclusion

Ganesh's share of goodwill amounts to ₹ 27,500.