A and B are partners in a firm and share profits and losses in the ratio of 3 ∶ 2. C joins firm as a new partner and contributes ₹6,000 as a premium for goodwill in cash. Here, the premium for goodwill shall be shared by A and B on the basis of new profit sharing ratio, that is 5 ∶ 3 ∶ 2 as
₹3,000 ∶ ₹3,000
Understanding Premium for Goodwill in Partnership
When a new partner is admitted into a firm, they often bring in an amount as premium for goodwill. This amount is compensation for the old partners for their share of the future profits that the new partner will now enjoy. The total premium for goodwill brought in by C is ₹6,000.
Distribution of Premium for Goodwill
The premium for goodwill brought in by the incoming partner is typically distributed among the old partners who have sacrificed a portion of their profit share in favour of the new partner. The distribution ratio is the sacrificing ratio of the old partners.
In this problem, A and B are the old partners. C is the new partner. The premium for goodwill of ₹6,000 needs to be shared between A and B.
The question mentions the old profit sharing ratio of A and B is 3:2 and the new profit sharing ratio of A, B, and C is 5:3:2. However, the premium for goodwill is shared among the old partners (A and B) based on their sacrifice, not the new overall ratio of all partners.
Calculating the Share of Premium for Goodwill
The problem provides the correct answer distribution as ₹3,000 ∶ ₹3,000 for A and B. This implies that the premium for goodwill of ₹6,000 is shared equally between A and B.
Let's verify this distribution:
- A's share of premium for goodwill = Total premium × A's share in distribution ratio
- B's share of premium for goodwill = Total premium × B's share in distribution ratio
If the premium for goodwill is shared equally (in a 1:1 ratio) between A and B, then:
- A's share = ₹6,000 × $\frac{1}{1+1} = \text{₹}6,000 \times \frac{1}{2} = \text{₹}3,000$
- B's share = ₹6,000 × $\frac{1}{1+1} = \text{₹}6,000 \times \frac{1}{2} = \text{₹}3,000$
This calculation matches the distribution provided in the correct answer option, which is ₹3,000 ∶ ₹3,000. Although the question mentions sharing based on the new profit sharing ratio, the actual distribution shown in the correct option indicates an equal sharing of the premium for goodwill between A and B. The standard practice is to share the premium for goodwill in the sacrificing ratio. If A and B sacrificed equally, their sacrificing ratio would be 1:1, leading to this distribution.
Therefore, the premium for goodwill of ₹6,000 is shared as ₹3,000 for A and ₹3,000 for B.
| Particulars | Amount (₹) |
|---|---|
| Total Premium for Goodwill | 6,000 |
| A's Share | 3,000 |
| B's Share | 3,000 |
The premium for goodwill is credited to the old partners' capital accounts in their sharing ratio for goodwill.
Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
