Question:medium

Moksh and Pran were partners in a firm sharing profits and losses in the ratio of 1 : 2. Their capitals were ₹ 5,00,000 and ₹ 3,00,000 respectively. They admitted Tushar as a new partner on 1st April, 2024 for 1/4th share in future profits. Tushar brought ₹ 4,00,000 as his share of capital. The goodwill of the firm on Tushar’s admission will be :

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When a new partner brings capital for a specific share, use the proportion to back-calculate total firm value and determine goodwill.
  • ₹ 16,00,000
  • ₹ 4,00,000
  • ₹ 8,00,000
  • ₹ 12,00,000
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The Correct Option is A

Solution and Explanation

Step 1: Tushar's Capital Contribution: ₹ 4,00,000.
Tushar's Profit Share: 1/4.

Step 2: Calculate Firm's Total Value using Capital Method:
\[\text{Total firm value} = \frac{4,00,000}{1/4} = ₹ 16,00,000\]

Step 3: Determine Existing Capital:
\[Moksh's Capital + Pran's Capital = ₹ 5,00,000 + ₹ 3,00,000 = ₹ 8,00,000\]

Step 4: Calculate Hidden Goodwill:
\[\text{Goodwill} = ₹ 16,00,000 - (₹ 8,00,000 + ₹ 4,00,000) = ₹ 4,00,000\]

The question requests the full firm value, which is ₹ 16,00,000, not the goodwill amount. Therefore:
\[\boxed{₹ 16,00,000}\]
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