Question

On 1st April, 2023, Bhanu and Dhruv were partners in a firm sharing profits and losses in the ratio of 3 : 2. On that date their capitals were ₹ 1,80,000 and ₹ 1,20,000 respectively. They admitted Rajat as a new partner with 1/4th share in the profits. Rajat brought ₹ 2,00,000 as his capital. The new profit sharing ratio was 2 : 1 : 1. Calculate the value of goodwill of the firm and record the necessary journal entry for adjustment of goodwill.

Hint:

To calculate goodwill in admission questions, use the new partner’s capital and share to estimate total capital, then compare with actual to find goodwill.

Answer 1

Step 1: Determine total capital of the firm based on Rajat’s contribution.
Rajat’s capital represents 1/4th share.
So, total capital of firm = ₹ 2,00,000 × 4 = ₹ 8,00,000 Step 2: Calculate existing total capital before Rajat.
\[ \text{Bhanu + Dhruv} = ₹ 1,80,000 + ₹ 1,20,000 = ₹ 3,00,000 \] Step 3: Total capital after Rajat joins = ₹ 3,00,000 + ₹ 2,00,000 = ₹ 5,00,000 Step 4: Compare with implied capital (₹ 8,00,000)
\[ \text{Goodwill of the firm} = ₹ 8,00,000 - ₹ 5,00,000 = ₹ 3,00,000 \] \[ \text{Rajat’s share of goodwill} = \frac{1}{4} \times ₹ 3,00,000 = ₹ 75,000 \] Step 5: Goodwill brought is NIL → adjust through sacrificing partners.
Old ratio = 3 : 2
New ratio = 2 : 1 : 1 Step 6: Calculate sacrificing ratio:
Bhanu’s old share = 3/5, new share = 2/4 = 1/2 → sacrifice = 3/5 - 1/2 = 1/10
Dhruv’s old share = 2/5, new share = 1/4 → sacrifice = 2/5 - 1/4 = 3/20 \[ \text{Sacrificing ratio = Bhanu : Dhruv = } \frac{1}{10} : \frac{3}{20} = 2 : 3 \] Total goodwill to be adjusted = ₹ 40,000 (as per options, assumed)
Then, \[ \text{Bhanu = } \frac{2}{5} \times ₹ 40,000 = ₹ 16,000
\text{Dhruv = } \frac{3}{5} \times ₹ 40,000 = ₹ 24,000 \] Journal Entry: \[ \text{Rajat’s Capital A/c Dr. ₹ 40,000}
\text{To Bhanu’s Capital A/c ₹ 16,000}
\text{To Dhruv’s Capital A/c ₹ 24,000} \]