Hemant and Naman are partners in a firm sharing profits in the ratio of 3:2. Their capitals were Rs. 80,000 and Rs. 50,000 respectively. They admitted Samrat on Jan. 1, 2025 as a new partner for 1/5 share in the future profits Samrat brought Rs. 60.000 as his capital. Calculate the yalue of goodwill of the firm ?

The correct option is Rs. 1,10,000.

Here is the step-by-step calculation to determine the value of the hidden goodwill of the firm:

Step 1: Calculate the total capitalized value (total capital) of the new firm
The total capital of the firm is calculated based on the capital brought in by the newly admitted partner, Samrat, and his profit share.
Samrat's capital = Rs. 60,000
Samrat's share of profit = ¹⁄₅

$$\text{Total Capital of the New Firm}=\text{Samrat's Capital}\times \frac{1}{\text{Samrat's Share of Profit}}$$

$$\text{Total Capital of the New Firm}=\text{Rs. 60,000}\times \frac{5}{1}=\text{Rs. 3,00,000}$$

Step 2: Calculate the combined actual capital of all the partners
This is the sum of the capitals of the existing partners (Hemant and Naman) and the new partner (Samrat).
Hemant's Capital = Rs. 80,000
Naman's Capital = Rs. 50,000
Samrat's Capital = Rs. 60,000

$$\text{Combined Actual Capital}=\text{Hemant's Capital}+\text{Naman's Capital}+\text{Samrat's Capital}$$

$$\text{Combined Actual Capital}=\text{Rs. 80,000}+\text{Rs. 50,000}+\text{Rs. 60,000}=\text{Rs. 1,90,000}$$

Step 3: Calculate the value of the goodwill of the firm
Goodwill of the firm represents the excess of the total capitalized value of the firm over the combined actual capital of all partners.

$$\text{Value of Goodwill}=\text{Total Capital of the New Firm}-\text{Combined Actual Capital}$$

$$\text{Value of Goodwill}=\text{Rs. 3,00,000}-\text{Rs. 1,90,000}=\text{Rs. 1,10,000}$$

Therefore, the value of the goodwill of the firm is Rs. 1,10,000.