NCERT Solutions Class 12 Accountancy Chapter 3 Reconstitution of a Partnership Firm Admission of a Partner

Question 10. Singh, Gupta and Khan are partners in a firm sharing profits in 3:2:3 ratio. They admitted Jain as a new partner. Singh surrendered 1/3 of his share in favour of Jain; Gupta surrendered 1/4 of his share in favour of Jain and Khan surrendered 1/5 in favour of Jain. Calculate new profit sharing ratio?
Answer: The initial profit sharing ratio among Singh, Gupta, and Khan is \( 3:2:3 \). The share surrendered by each partner is calculated below: \( \text{Singh's Sacrifice} = \frac{1}{3} \text{ of } \frac{3}{8} = \frac{1}{3} \times \frac{3}{8} = \frac{3}{24} \) \( \text{Gupta's Sacrifice} = \frac{1}{4} \text{ of } \frac{2}{8} = \frac{1}{4} \times \frac{2}{8} = \frac{2}{32} \) \( \text{Khan's Sacrifice} = \frac{1}{5} \text{ of } \frac{3}{8} = \frac{1}{5} \times \frac{3}{8} = \frac{3}{40} \) Now we find the remaining shares of the existing partners: \( \text{Singh's New Share} = \frac{3}{8} - \frac{3}{24} = \frac{9 - 3}{24} = \frac{6}{24} \) \( \text{Gupta's New Share} = \frac{2}{8} - \frac{2}{32} = \frac{8 - 2}{32} = \frac{6}{32} \) \( \text{Khan's New Share} = \frac{3}{8} - \frac{3}{40} = \frac{15 - 3}{40} = \frac{12}{40} \) The total share acquired by the new partner, Jain, is the sum of these sacrifices: \( \text{Jain's Share} = \frac{3}{24} + \frac{2}{32} + \frac{3}{40} = \frac{60 + 30 + 36}{480} = \frac{126}{480} \) To express the new ratio, we convert all fractions to have a common denominator of 480: Singh's share: \( \frac{6}{24} \times \frac{20}{20} = \frac{120}{480} \) Gupta's share: \( \frac{6}{32} \times \frac{15}{15} = \frac{90}{480} \) Khan's share: \( \frac{12}{40} \times \frac{12}{12} = \frac{144}{480} \) Jain's share: \( \frac{126}{480} \) Comparing the shares, the new profit sharing ratio is \( 120 : 90 : 144 : 126 \). Reducing this by dividing each number by 6 gives \( 20 : 15 : 24 : 21 \).
In simple words: We calculate how much share each old partner gives up and subtract it from their original share. Jain's share is the sum of what they surrendered, and then we adjust all fractions to a common base to find the new ratio.
Exam Tip: To avoid calculation mistakes, always ensure that the total of the new shares (including the new partner) sums up to exactly 1.

Question 11. Sandeep and Navdeep are partners in a firm sharing profits in 5:3 ratio. They admit C into the firm and the new profit sharing ratio was agreed at 4:2:1. Calculate the sacrificing ratio?
Answer: To find the sacrificing ratio, we subtract the new profit share of each partner from their original profit share. The initial profit sharing ratio of Sandeep and Navdeep is \( 5:3 \). Hence, their original shares are: \( \text{Sandeep's Old Share} = \frac{5}{8} \) \( \text{Navdeep's Old Share} = \frac{3}{8} \) The agreed new profit sharing ratio among Sandeep, Navdeep, and C is \( 4:2:1 \). Therefore, their updated shares are: \( \text{Sandeep's New Share} = \frac{4}{7} \) \( \text{Navdeep's New Share} = \frac{2}{7} \) Now, let's calculate the sacrifice made by each partner: \( \text{Sandeep's Sacrifice} = \text{Old Share} - \text{New Share} \) \( \implies \text{Sandeep's Sacrifice} = \frac{5}{8} - \frac{4}{7} = \frac{35 - 32}{56} = \frac{3}{56} \) \( \text{Navdeep's Sacrifice} = \text{Old Share} - \text{New Share} \) \( \implies \text{Navdeep's Sacrifice} = \frac{3}{8} - \frac{2}{7} = \frac{21 - 16}{56} = \frac{5}{56} \) The sacrificing ratio between Sandeep and Navdeep is \( \frac{3}{56} : \frac{5}{56} \), which simplifies to \( 3:5 \).
In simple words: The sacrificing ratio shows how much of their profits Sandeep and Navdeep gave up for the new partner. We find this by subtracting their new shares from their old ones, which gives us 3:5.
Exam Tip: The sacrificing ratio is specifically used to distribute the goodwill premium brought in by the incoming partner.

Question 12. Rao and Swami are partners in a firm sharing profits and losses in 3:2 ratio. They admit Ravi as a new partner for 1/8 share in the profits. The new profit sharing ratio between Rao and Swami is 4:3. Calculate new profit sharing ratio and sacrificing ratio?
Answer: First, we determine the new profit sharing shares for each partner. The incoming partner, Ravi, is admitted for a \( \frac{1}{8} \) share of the profits. Thus, the remaining share left for Rao and Swami is: \( \text{Combined Share of Rao and Swami} = 1 - \frac{1}{8} = \frac{7}{8} \) The remaining profit share is divided between Rao and Swami in their newly agreed ratio of \( 4:3 \): \( \text{Rao's New Share} = \frac{7}{8} \times \frac{4}{7} = \frac{28}{56} \) \( \text{Swami's New Share} = \frac{7}{8} \times \frac{3}{7} = \frac{21}{56} \) Expressing Ravi's share with the same denominator of 56: \( \text{Ravi's Share} = \frac{1}{8} = \frac{7}{56} \) Therefore, the new profit sharing ratio of Rao, Swami, and Ravi is: \( \frac{28}{56} : \frac{21}{56} : \frac{7}{56} \implies 28:21:7 \implies 4:3:1 \) Next, we calculate the sacrificing ratio of the existing partners: \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Rao: \( \text{Old Share} = \frac{3}{5} \), \( \text{New Share} = \frac{4}{8} \) \( \implies \text{Rao's Sacrifice} = \frac{3}{5} - \frac{4}{8} = \frac{24 - 20}{40} = \frac{4}{40} \) For Swami: \( \text{Old Share} = \frac{2}{5} \), \( \text{New Share} = \frac{3}{8} \) \( \implies \text{Swami's Sacrifice} = \frac{2}{5} - \frac{3}{8} = \frac{16 - 15}{40} = \frac{1}{40} \) The sacrificing ratio between Rao and Swami is \( \frac{4}{40} : \frac{1}{40} \implies 4:1 \).
In simple words: After giving Ravi his 1/8 share, the remaining 7/8 is split between Rao and Swami in a 4:3 ratio. This gives a new ratio of 4:3:1, and their sacrifices work out to 4:1.
Exam Tip: When old partners decide to share the remaining profits in a specific new ratio, calculate their new shares first before computing the sacrifices.

Question 13. Compute the value of goodwill on the basis of four years’ purchase of the average profits based on the last five years? The profits for the last five years were as follows:

Answer: To calculate the value of goodwill, we first find the average profits over the five-year period. The total profit for the last five years is: \( \text{Total Profits} = \text{Rs. } 40,000 + \text{Rs. } 50,000 + \text{Rs. } 60,000 + \text{Rs. } 50,000 + \text{Rs. } 60,000 = \text{Rs. } 2,60,000 \) The average annual profit is computed as: \( \text{Average Profit} = \frac{\text{Total Profits}}{\text{Number of Years}} \) \( \implies \text{Average Profit} = \frac{\text{Rs. } 2,60,000}{5} = \text{Rs. } 52,000 \) Now, we value the goodwill based on 4 years' purchase of this average profit: \( \text{Goodwill} = \text{Average Profit} \times \text{Number of Years' Purchase} \) \( \implies \text{Goodwill} = \text{Rs. } 52,000 \times 4 = \text{Rs. } 2,08,000 \).
In simple words: We add up the profits of the last five years and divide by five to get the average profit of Rs. 52,000. Then we multiply this by four to get the goodwill of Rs. 2,08,000.
Exam Tip: Ensure you do not confuse the number of years of profits (5 years) with the number of years of purchase (4 years) when calculating goodwill.

Question 14. Capital employed in a business is Rs. 2,00,000. The normal rate of return on capital employed is 15%. During the year 2002 the firm earned a profit of Rs. 48,000. Calculate goodwill on the basis of 3 years purchase of super profit?
Answer: To calculate the value of goodwill under the super profit method, we follow these steps: 1. **Calculate the Normal Profit:** The normal profit is the expected return on the capital employed in the business at the normal rate of return. \( \text{Normal Profit} = \text{Capital Employed} \times \frac{\text{Normal Rate of Return}}{100} \) \( \implies \text{Normal Profit} = \text{Rs. } 2,00,000 \times \frac{15}{100} = \text{Rs. } 30,000 \) 2. **Calculate the Super Profit:** Super profit is the excess of actual profit earned by the firm over its normal profit. \( \text{Super Profit} = \text{Actual Profit} - \text{Normal Profit} \) \( \implies \text{Super Profit} = \text{Rs. } 48,000 - \text{Rs. } 30,000 = \text{Rs. } 18,000 \) 3. **Calculate the Goodwill:** Goodwill is determined by multiplying the super profit by the number of years of purchase. \( \text{Goodwill} = \text{Super Profit} \times \text{Number of Years' Purchase} \) \( \implies \text{Goodwill} = \text{Rs. } 18,000 \times 3 = \text{Rs. } 54,000 \).
In simple words: First, we calculate that a normal business would earn Rs. 30,000 on this capital. Since our firm earned Rs. 48,000, we made a super profit of Rs. 18,000, which we multiply by three to find the goodwill.
Exam Tip: Super profit represents the extra earning capacity of a firm. Remember, if the actual profit is less than the normal profit, the super profit is nil, and the goodwill is valued at zero.

Question 15. The books of Ram and Bharat showed that the capital employed on 31.12.2002 was Rs. 5,00,000 and the profits for the last 5 years : 2002 Rs. 40,000; 2003 Rs. 50,000; 2004 Rs. 55,000; 2005 Rs. 70,000 and 2006 Rs. 85,000. Calculate the value of goodwill on the basis of 3 years purchase of the average super profits of the last 5 years assuming that the normal rate of return is 10%?
Answer: To find the value of goodwill using the average super profit method: 1. **Calculate the Normal Profit:** \( \text{Normal Profit} = \text{Capital Employed} \times \text{Normal Rate of Return} \) \( \implies \text{Normal Profit} = \text{Rs. } 5,00,000 \times \frac{10}{100} = \text{Rs. } 50,000 \) 2. **Calculate the Average Profit:** We compute the average of the profits earned over the five-year period. \( \text{Total Profits} = \text{Rs. } 40,000 + \text{Rs. } 50,000 + \text{Rs. } 55,000 + \text{Rs. } 70,000 + \text{Rs. } 85,000 = \text{Rs. } 3,00,000 \) \( \text{Average Profit} = \frac{\text{Total Profits}}{5} \) \( \implies \text{Average Profit} = \frac{\text{Rs. } 3,00,000}{5} = \text{Rs. } 60,000 \) 3. **Calculate the Super Profit:** \( \text{Super Profit} = \text{Average Profit} - \text{Normal Profit} \) \( \implies \text{Super Profit} = \text{Rs. } 60,000 - \text{Rs. } 50,000 = \text{Rs. } 10,000 \) 4. **Calculate the Goodwill:** Goodwill is valued at 3 years' purchase of the super profit. \( \text{Goodwill} = \text{Super Profit} \times \text{Number of Years' Purchase} \) \( \implies \text{Goodwill} = \text{Rs. } 10,000 \times 3 = \text{Rs. } 30,000 \).
In simple words: We find the average profit over 5 years is Rs. 60,000. The standard industry return is Rs. 50,000. The difference is the super profit of Rs. 10,000, which we multiply by three to get a goodwill of Rs. 30,000.
Exam Tip: Always clearly list the steps of calculation: Average Profit, Normal Profit, Super Profit, and then Goodwill, as CBSE step-marking rewards each phase of the solution.

Question 16. Rajan and Rajani are partners in a firm. Their capitals were Rajan Rs. 3, 00,000; Rajani Rs. 2,00,000. During the year 2002 the firm earned a profit of Rs. 1, 50,000. Calculate the value of goodwill of the firm assuming that the normal rate of return is 20%?
Answer: To determine the goodwill of the firm, we use the Capitalisation of Average Profit method. 1. **Calculate the Total Capital Employed:** The capital employed is the sum of the capitals of all partners. \( \text{Capital Employed} = \text{Rajan's Capital} + \text{Rajani's Capital} \) \( \implies \text{Capital Employed} = \text{Rs. } 3,00,000 + \text{Rs. } 2,00,000 = \text{Rs. } 5,00,000 \) 2. **Calculate the Capitalised Value of the Business:** This is the capital needed to earn the current profit at the normal rate of return. \( \text{Capitalised Value} = \text{Actual Profit} \times \frac{100}{\text{Normal Rate of Return}} \) \( \implies \text{Capitalised Value} = \text{Rs. } 1,50,000 \times \frac{100}{20} = \text{Rs. } 7,50,000 \) 3. **Calculate the Value of Goodwill:** Goodwill is the difference between the capitalized value of the profits and the actual capital employed. \( \text{Goodwill} = \text{Capitalised Value} - \text{Capital Employed} \) \( \implies \text{Goodwill} = \text{Rs. } 7,50,000 - \text{Rs. } 5,00,000 = \text{Rs. } 2,50,000 \).
In simple words: To make Rs. 1,50,000 under normal conditions, a firm needs Rs. 7,50,000. Since we did it with just Rs. 5,00,000 of capital, our reputation and goodwill are worth the difference of Rs. 2,50,000.
Exam Tip: Under the capitalization method, the goodwill is the excess of capitalized value over the net assets (capital employed). This is also known as capitalization of average profits.

Question 17. A business has earned average profits of Rs. 1, 00,000 during the last few years. Find out the value of goodwill by capitalization method, given that the assets of the business are Rs. 10, 00,000 and its external liabilities are Rs. 1,80,000. The normal rate of return is 10%?
Answer: To calculate the value of goodwill using the capitalization method: 1. **Calculate the Capital Employed (Net Assets):** Capital employed is the excess of total assets over external liabilities. \( \text{Capital Employed} = \text{Total Assets} - \text{External Liabilities} \) \( \implies \text{Capital Employed} = \text{Rs. } 10,00,000 - \text{Rs. } 1,80,000 = \text{Rs. } 8,20,000 \) 2. **Calculate the Capitalised Value of the Average Profit:** This represents the amount of capital required to yield the average profit at the standard rate of return. \( \text{Capitalised Value} = \text{Average Profit} \times \frac{100}{\text{Normal Rate of Return}} \) \( \implies \text{Capitalised Value} = \text{Rs. } 1,00,000 \times \frac{100}{10} = \text{Rs. } 10,00,000 \) 3. **Calculate the Value of Goodwill:** \( \text{Goodwill} = \text{Capitalised Value} - \text{Capital Employed} \) \( \implies \text{Goodwill} = \text{Rs. } 10,00,000 - \text{Rs. } 8,20,000 = \text{Rs. } 1,80,000 \).
In simple words: The actual capital invested in the business is Rs. 8,20,000 (assets minus liabilities). To earn Rs. 1,00,000 at a 10% rate, a business usually needs Rs. 10,00,000. The difference of Rs. 1,80,000 is our goodwill.
Exam Tip: Remember that Capital Employed can be calculated using either the Liabilities Side Approach or the Assets Side Approach. Here, we used the Assets Side Approach: Assets minus External Liabilities.

Question 18. Verma and Sharma are partners in a firm sharing profits and losses in the ratio of 5:3. They admitted Ghosh as a new partner for 1/5 share of profits. Ghosh is to bring in Rs. 20,000 as capital and Rs. 4,000 as his share of goodwill premium. Give the necessary journal entries: a) When the amount of goodwill is retained in the business. b) When the amount of goodwill is fully withdrawn. c) When 50% of the amount of goodwill is withdrawn. d) When goodwill is paid privately
Answer: Since there is no information on how Ghosh acquires his share from Verma and Sharma, the old profit-sharing ratio of \( 5:3 \) is assumed to be their sacrificing ratio. **Distribution of Goodwill Premium (Rs. 4,000):** - Verma's Share: \( \text{Rs. } 4,000 \times \frac{5}{8} = \text{Rs. } 2,500 \) - Sharma's Share: \( \text{Rs. } 4,000 \times \frac{3}{8} = \text{Rs. } 1,500 \) Below are the necessary journal entries for each scenario:

Case (a): When goodwill is retained in the business

Case (b): When goodwill is fully withdrawn

Case (c): When 50% of the goodwill is withdrawn

Case (d): When goodwill is paid privately

Note: Since the goodwill premium is settled privately, no entry for goodwill is passed in the books of the firm.
In simple words: When a new partner brings cash for capital and goodwill, we record it. The goodwill amount is then shared between the old partners in their sacrificing ratio (5:3). If they withdraw it, we debit their capital and credit cash. If paid privately, we don't record the goodwill transaction at all.
Exam Tip: Remember that no journal entry is ever passed in the firm's books if goodwill is settled privately between partners.

Question 19. A and B are partners in a firm sharing profits and losses in the ratio of 3:2. They decide to admit C into partnership with 1/4 share in profits. C will bring in Rs. 30,000 for capital and the requisite amount of goodwill premium in cash. The goodwill of the firm is valued at Rs, 20,000. The new profit sharing ratio is 2:1:1. A and B withdraw their share of goodwill. Give necessary journal entries?
Answer: Let's first calculate the sacrificing ratio of the existing partners: \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Partner A: \( \text{Old Share} = \frac{3}{5} \), \( \text{New Share} = \frac{2}{4} \) \( \implies \text{A's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} \) For Partner B: \( \text{Old Share} = \frac{2}{5} \), \( \text{New Share} = \frac{1}{4} \) \( \implies \text{B's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} \) Thus, the sacrificing ratio of A and B is \( 2:3 \). **Calculation of C's share of goodwill:** Total goodwill of the firm is Rs. 20,000. Since C is admitted for a \( \frac{1}{4} \) share, C's share of the goodwill premium is: \( \text{C's Goodwill Share} = \text{Rs. } 20,000 \times \frac{1}{4} = \text{Rs. } 5,000 \) This premium is distributed to A and B in their sacrificing ratio (\( 2:3 \)): - A's share: \( \text{Rs. } 5,000 \times \frac{2}{5} = \text{Rs. } 2,000 \) - B's share: \( \text{Rs. } 5,000 \times \frac{3}{5} = \text{Rs. } 3,000 \) Below are the required journal entries:

In simple words: We find the sacrificing ratio to be 2:3. C brings Rs. 35,000 (Rs. 30,000 capital and Rs. 5,000 goodwill). The Rs. 5,000 is shared in a 2:3 ratio, and then both partners withdraw their cash shares from the business.
Exam Tip: Always remember that C's goodwill premium share is based on C's profit share of the total firm's goodwill value (1/4 of Rs. 20,000).

Question 20. Arti and Bharti are partners in a firm sharing profits in 3:2 ratio, they admitted Sarthi for 1/4 share in the profits of the firm. Sarthi brings Rs. 50,000 for his capital and Rs. 10,000 for his 1/4 share of goodwill. Goodwill already appears in the books of Arti and Bharti at Rs. 5,000. The new profit sharing ratio between Arti, Bharti and Sarthi will be 2:1:1. Record the necessary journal entries in the books of the new firm?
Answer: To address the admission of Sarthi: 1. **Write off Existing Goodwill:** Any goodwill already appearing in the books must be written off between old partners in their old profit sharing ratio (\( 3:2 \)). - Arti's write-off: \( \text{Rs. } 5,000 \times \frac{3}{5} = \text{Rs. } 3,000 \) - Bharti's write-off: \( \text{Rs. } 5,000 \times \frac{2}{5} = \text{Rs. } 2,000 \) 2. **Calculate the Sacrificing Ratio:** \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Arti: \( \text{Arti's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} \) For Bharti: \( \text{Bharti's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} \) The sacrificing ratio between Arti and Bharti is \( 2:3 \). 3. **Distribution of Sarthi's Goodwill Premium (Rs. 10,000):** The premium is distributed in the sacrificing ratio (\( 2:3 \)): - Arti's share: \( \text{Rs. } 10,000 \times \frac{2}{5} = \text{Rs. } 4,000 \) - Bharti's share: \( \text{Rs. } 10,000 \times \frac{3}{5} = \text{Rs. } 6,000 \) Below are the necessary journal entries:

In simple words: We write off the old Rs. 5,000 goodwill by dividing it in their 3:2 old ratio. When Sarthi brings Rs. 60,000, we credit Rs. 50,000 as capital and Rs. 10,000 as goodwill premium. The goodwill is then shared between Arti and Bharti in their sacrificing ratio of 2:3.
Exam Tip: Remember to write off existing goodwill in the OLD profit-sharing ratio, whereas the new goodwill premium is always distributed in the SACRIFICING ratio.

Question 21. X and Y are partners in a firm sharing profits and losses in 4:3 ratio. They admitted Z for 1/8 share. Z brought Rs. 20,000 for his capital and Rs. 7,000 for his 1/8 share of goodwill. Subsequently X, Y and Z decided to show goodwill in their books at Rs. 40,000. Show necessary journal entries in the books of X, Y and Z?
Answer: Since there is no other information regarding the new ratio or how Z acquires his share, the old ratio of \( 4:3 \) is used as the sacrificing ratio. **Distribution of Z's Goodwill Premium (Rs. 7,000):** - X's share of premium: \( \text{Rs. } 7,000 \times \frac{4}{7} = \text{Rs. } 4,000 \) - Y's share of premium: \( \text{Rs. } 7,000 \times \frac{3}{7} = \text{Rs. } 3,000 \) Below are the required journal entries:

In simple words: Z brings Rs. 27,000 in cash, representing Rs. 20,000 capital and Rs. 7,000 goodwill premium. The Rs. 7,000 is divided between X and Y in their sacrificing ratio of 4:3.
Exam Tip: In the absence of details on how the new partner's share is acquired, the old profit-sharing ratio is taken as the sacrificing ratio. Under Accounting Standard 26 (AS 26), internally generated goodwill is not recorded in the books of accounts.

Question 22. Aditya and Balan are partners sharing profits and losses in 3:2 ratio. They admitted Christopher for 1/4 share in the profits. The new profit sharing ratio agreed was 2:1:1. Christopher brought Rs. 50,000 for his capital. His share of goodwill was agreed to at Rs. 15,000. Christopher could bring only Rs. 10,000 out of his share of goodwill. Record necessary journal entries in the books of the firm?
Answer: To account for Christopher's admission: 1. **Calculate the Sacrificing Ratio:** \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Aditya: \( \text{Aditya's Sacrifice} = \frac{3}{5} - \frac{2}{4} = \frac{12 - 10}{20} = \frac{2}{20} \) For Balan: \( \text{Balan's Sacrifice} = \frac{2}{5} - \frac{1}{4} = \frac{8 - 5}{20} = \frac{3}{20} \) Thus, the sacrificing ratio is \( 2:3 \). 2. **Calculate Goodwill Distribution:** The agreed share of goodwill for Christopher is Rs. 15,000. Since he could bring only Rs. 10,000 in cash, the remaining Rs. 5,000 is debited to his Capital Account (or Current Account). The entire Rs. 15,000 is distributed between Aditya and Balan in their sacrificing ratio (\( 2:3 \nobreak \)): - Aditya's share: \( \text{Rs. } 15,000 \times \frac{2}{5} = \text{Rs. } 6,000 \) - Balan's share: \( \text{Rs. } 15,000 \times \frac{3}{5} = \text{Rs. } 9,000 \) Below are the required journal entries:

In simple words: Christopher is supposed to pay Rs. 15,000 for goodwill but brings only Rs. 10,000. We record the cash received, and then we distribute the full Rs. 15,000 to Aditya and Balan in their 2:3 sacrificing ratio, taking the unpaid Rs. 5,000 from Christopher's capital account.
Exam Tip: If a new partner brings only a part of their share of goodwill in cash, the unpaid portion should be adjusted by debiting their capital (or current) account.

Question 23. Amar and Samar were partners in a firm sharing profits and losses in 3:1 ratio. They admitted Kanwar for 1/4 share of profits. Kanwar could not bring his share of goodwill premium in cash. The Goodwill of the firm was valued at Rs. 80,000 on Kanwar’s admission. Record necessary journal entry for goodwill on Kanwar’s admission.
Answer: To account for Kanwar's goodwill when he is unable to bring his share in cash: 1. **Calculate Kanwar's Share of Goodwill:** The total goodwill value of the firm is Rs. 80,000. Kanwar's share is \( \frac{1}{4} \). \( \text{Kanwar's Goodwill Share} = \text{Rs. } 80,000 \times \frac{1}{4} = \text{Rs. } 20,000 \) 2. **Identify the Sacrificing Ratio:** Since there is no other information, the old profit sharing ratio of \( 3:1 \) is considered the sacrificing ratio. 3. **Distribution of Goodwill:** The Rs. 20,000 is credited to the old partners in their sacrificing ratio (\( 3:1 \)): - Amar's share: \( \text{Rs. } 20,000 \times \frac{3}{4} = \text{Rs. } 15,000 \) - Samar's share: \( \text{Rs. } 20,000 \times \frac{1}{4} = \text{Rs. } 5,000 \) Since Kanwar did not bring this premium in cash, we adjust it by debiting his Capital Account. Below is the necessary journal entry:

In simple words: Kanwar cannot pay his Rs. 20,000 share of goodwill in cash. So, we adjust it by debiting his capital account and crediting Amar and Samar in their old ratio of 3:1.
Exam Tip: When a new partner cannot bring any goodwill premium in cash, adjust their share of goodwill by debiting their capital (or current) account and crediting the old partners in their sacrificing ratio.

Question 24. Mohan Lal and Sohan Lal were partners in a firm sharing profits and losses in 3:2 ratio. They admitted Ram Lal for 1/4 share on 1.1.2003. It was agreed that goodwill of the firm will be valued at 3 years purchase of the average profits of last 4 years which were Rs. 50,000 for 2003, Rs. 60,000 for 2004, Rs. 90,000 for 2005 and Rs. 70,000 for 2006. Ram Lal did not bring his share of goodwill premium in cash. Record the necessary journal entries in the books of the firm on Ram Lal’s admission when: a) Goodwill already appears in the books at Rs. 2,02,500. b) Goodwill appears in the books at Rs. 2,500. c) Goodwill appears in the books at Rs. 2,05,000.
Answer: First, let us calculate the valuation of the firm's goodwill: 1. **Calculate Average Profit:** \( \text{Average Profit} = \frac{\text{Rs. } 50,000 + \text{Rs. } 60,000 + \text{Rs. } 90,000 + \text{Rs. } 70,000}{4} \) \( \implies \text{Average Profit} = \frac{\text{Rs. } 2,70,000}{4} = \text{Rs. } 67,500 \) 2. **Calculate Goodwill of the Firm:** Goodwill is valued at 3 years' purchase of average profits. \( \text{Goodwill} = \text{Average Profit} \times 3 \) \( \implies \text{Goodwill} = \text{Rs. } 67,500 \times 3 = \text{Rs. } 2,02,500 \) 3. **Calculate Ram Lal's Share of Goodwill:** Ram Lal is admitted for a \( \frac{1}{4} \) share. \( \text{Ram Lal's Goodwill Share} = \text{Rs. } 2,02,500 \times \frac{1}{4} = \text{Rs. } 50,625 \) Since Ram Lal is unable to bring this premium in cash, it is adjusted through his Capital Account by debiting Rs. 50,625. This amount is credited to Mohan Lal and Sohan Lal in their sacrificing ratio (\( 3:2 \)): - Mohan Lal's share: \( \text{Rs. } 50,625 \times \frac{3}{5} = \text{Rs. } 30,375 \) - Sohan Lal's share: \( \text{Rs. } 50,625 \times \frac{2}{5} = \text{Rs. } 20,250 \) In each of the three scenarios below, we must first write off the existing goodwill in the old profit sharing ratio (\( 3:2 \)) and then pass the adjustment entry for Ram Lal's share of goodwill:

Case a) When existing goodwill is Rs. 2,02,500

Case b) When existing goodwill is Rs. 2,500

Case c) When existing goodwill is Rs. 2,05,000

In simple words: First we calculate the firm's goodwill as Rs. 2,02,500, meaning Ram Lal's share is Rs. 50,625. For each case, we first write off whatever old goodwill is in the books by debiting Mohan Lal and Sohan Lal in their 3:2 ratio. Then we record the adjustment for Ram Lal's goodwill from his capital.
Exam Tip: Be sure to write off the old goodwill appearing in the balance sheet before recording the entry for the new partner's goodwill.

Question 25. Rajesh and Mukesh are equal partners in a firm. They admit Hari into partnership and the new profit sharing ratio between Rajesh, Mukesh and Hari is 4:3:2. On Hari’s admission goodwill of the firm is valued at Rs. 36,000. Hari is unable to bring his share of goodwill premium in cash. Rajesh, Mukesh and Hari decided not to show goodwill in their balance sheet. Record necessary journal entries for the treatment of goodwill on Hari’s admission.
Answer: To account for Hari's admission and the goodwill adjustments: 1. **Calculate the Sacrificing Ratio:** \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Rajesh: \( \text{Rajesh's Sacrifice} = \frac{1}{2} - \frac{4}{9} = \frac{9 - 8}{18} = \frac{1}{18} \) For Mukesh: \( \text{Mukesh's Sacrifice} = \frac{1}{2} - \frac{3}{9} = \frac{9 - 6}{18} = \frac{3}{18} \) The sacrificing ratio between Rajesh and Mukesh is \( 1:3 \). 2. **Calculate Hari's Share of Goodwill:** The total goodwill of the firm is valued at Rs. 36,000. Hari's share is \( \frac{2}{9} \). \( \text{Hari's Goodwill Share} = \text{Rs. } 36,000 \times \frac{2}{9} = \text{Rs. } 8,000 \) We distribute this Rs. 8,000 between Rajesh and Mukesh in their sacrificing ratio (\( 1:3 \)): - Rajesh's share: \( \text{Rs. } 8,000 \times \frac{1}{4} = \text{Rs. } 2,000 \) - Mukesh's share: \( \text{Rs. } 8,000 \times \frac{3}{4} = \text{Rs. } 6,000 \) Below is the required journal entry:

In simple words: Hari's share of goodwill is Rs. 8,000 (2/9 of Rs. 36,000). Since he cannot pay in cash, we debit his capital account and credit Rajesh and Mukesh with Rs. 2,000 and Rs. 6,000 respectively, based on their 1:3 sacrificing ratio.
Exam Tip: Always double-check your sacrificing ratio calculations when the old ratio is equal but the new ratio is unequal, as it is a common area where students make arithmetic errors.

Question 26. Amar and Akbar are equal partners in a firm. They admitted Anthony as a new partner and the new profit sharing ratio is 4:3:2. Anthony could not bring this share of goodwill Rs. 45,000 in cash. It is decided to do adjustment for goodwill without opening goodwill account. Pass the necessary journal entry for the treatment of goodwill?
Answer: To adjust for Anthony's goodwill when he is unable to bring his share in cash: 1. **Calculate the Sacrificing Ratio:** \( \text{Sacrifice} = \text{Old Share} - \text{New Share} \) For Amar: \( \text{Amar's Sacrifice} = \frac{1}{2} - \frac{4}{9} = \frac{9 - 8}{18} = \frac{1}{18} \) For Akbar: \( \text{Akbar's Sacrifice} = \frac{1}{2} - \frac{3}{9} = \frac{9 - 6}{18} = \frac{3}{18} \) The sacrificing ratio between Amar and Akbar is \( 1:3 \). 2. **Distribution of Anthony's Goodwill (Rs. 45,000):** Since Anthony cannot bring his goodwill share of Rs. 45,000 in cash, we debit his Capital Account and credit the old partners in their sacrificing ratio (\( 1:3 \)): - Amar's share: \( \text{Rs. } 45,000 \times \frac{1}{4} = \text{Rs. } 11,250 \) - Akbar's share: \( \text{Rs. } 45,000 \times \frac{3}{4} = \text{Rs. } 33,750 \) Below is the required journal entry:

In simple words: Anthony's share of goodwill is Rs. 45,000. Because he is unable to pay in cash, we debit his capital and credit Amar with Rs. 11,250 and Akbar with Rs. 33,750, following their 1:3 sacrificing ratio.
Exam Tip: Adjusting goodwill "without opening goodwill account" simply means adjusting it directly through the partners' capital or current accounts.

Question 27. Given below is the Balance Sheet of A and B, who are carrying on partnership business on 31.12.2006. A and B share profits and losses in the ratio of 2:1. C is admitted as a partner on the date of the balance sheet on the following terms: (i) C will bring in Rs. 1,00,000 as his capital and Rs. 60,000 as his share of goodwill for 1/4 share in the profits. (ii) Plant is to be appreciated to Rs. 1, 20,000 and the value of buildings is to be appreciated by 10%. (iii) Stock is found over valued by Rs. 4,000. (iv) A provision for bad and doubtful debts is to be created at 5% of debtors. (v) Creditors were unrecorded to the extent of Rs. 1,000. Pass the necessary journal entries, prepare the revaluation account and partners’ capital accounts, and show the Balance Sheet after the admission of C.
Answer: Below is the original Balance Sheet of the firm before C's admission:

The required accounts, journal entries, and new Balance Sheet are presented below:

Journal Entries

Revaluation Account

Partners' Capital Account

Balance Sheet of A, B and C (after admission of C)

In simple words: Revaluing assets and liabilities results in a net gain of Rs. 27,000, which is split 2:1 between A and B. C brings Rs. 1,00,000 capital and Rs. 60,000 goodwill, bringing the bank balance up to Rs. 2,00,000. Finally, we prepare the updated balance sheet.
Exam Tip: In comprehensive admission problems, remember to add the capital and goodwill brought by the new partner to the cash/bank balance in the new Balance Sheet.

Question 28. Leela and Meeta were partners in a firm sharing profits and losses in the ratio of 5:3. On Is Jan. 2007 they admitted Om as a new partner. On the date of Om’s admission the balance sheet of Leela and Meeta showed a balance of Rs. 16,000 in general reserve and Rs. 24,000 (Cr) in Profit and Loss Account. Record necessary journal entries for the treatment of these items on Om’s admission. The new profit sharing ratio between Leela, Meeta and Om was 5:3:2.
Answer: At the time of admission of a new partner, accumulated profits and reserves must be transferred to the existing partners in their old profit sharing ratio (\( 5:3 \)). **Distribution of General Reserve (Rs. 16,000):** - Leela's share: \( \text{Rs. } 16,000 \times \frac{5}{8} = \text{Rs. } 10,000 \) - Meeta's share: \( \text{Rs. } 16,000 \times \frac{3}{8} = \text{Rs. } 6,000 \) **Distribution of Profit and Loss Account Credit Balance (Rs. 24,000):** - Leela's share: \( \text{Rs. } 24,000 \times \frac{5}{8} = \text{Rs. } 15,000 \) - Meeta's share: \( \text{Rs. } 24,000 \times \frac{3}{8} = \text{Rs. } 9,000 \) Below are the necessary journal entries:

In simple words: When Om is admitted, the accumulated general reserve of Rs. 16,000 and P&L profit of Rs. 24,000 must be distributed to Leela and Meeta in their old 5:3 ratio. Om has no share in these past earnings.
Exam Tip: Always distribute reserves and accumulated profits or losses in the OLD ratio among the OLD partners, as these profits were earned before the new partner was admitted.

Question 29. Amit and Viney are partners in a firm sharing profits and losses in 3:1 ratio. On 1.1.2007 they admitted Ranjan as a partner. On Ranjan’s admission the profit and loss account of Amit and Viney showed a debit balance of Rs. 40,000. Record necessary journal entry for the treatment of the same.
Answer: A debit balance in the Profit and Loss Account indicates an accumulated loss. Upon admitting a new partner, this loss must be written off to the old partners' capital accounts in their old profit-sharing ratio (\( 3:1 \)). **Distribution of Accumulated Loss (Rs. 40,000):** - Amit's share of loss: \( \text{Rs. } 40,000 \times \frac{3}{4} = \text{Rs. } 30,000 \) - Viney's share of loss: \( \text{Rs. } 40,000 \times \frac{1}{4} = \text{Rs. } 10,000 \) Below is the required journal entry:

In simple words: An accumulated loss of Rs. 40,000 is written off by dividing it in their 3:1 old ratio, which reduces Amit's capital by Rs. 30,000 and Viney's capital by Rs. 10,000.
Exam Tip: Always remember that a debit balance in the P&L account is an asset-side item showing accumulated loss. It is debited to old partners' capital accounts when writing it off.

Question 30. A and B share profits in the proportions of 3/4 and 1/4 . Their Balance Sheet on Dec. 31, 2006 was as follows

On Jan. 1, 2007, C was admitted into partnership on the following terms:
(a) That C pays Rs. 10,000 as his capital.
(b) That C pays Rs. 5,000 for goodwill. Half of this sum is to be withdrawn by A and B.
(c) That stock and fixtures be reduced by 10% and a 5%, provision for doubtful debts be created on Sundry Debtors and Bills Receivable.
(d) That the value of land and buildings be appreciated by 20%.
(e) There being a claim against the firm for damages, a liability to the extent of Rs. 1,000 should be created.
(f) An item of Rs. 650 included in sundry creditors is not likely to be claimed and hence should be written back.
Record the above transactions (journal entries) in the books of the firm assuming that the profit sharing ratio between A and B has not changed. Prepare the new Balance Sheet on the admission of C.
Answer:

In simple words: When C joins, we revalue the assets and liabilities, and split the resulting profit among A and B. C's capital and goodwill are brought in, and the old partners withdraw half of the goodwill cash, leading to a newly updated balance sheet.

Exam Tip: Always remember to adjust provisions on all specified assets, including Bills Receivable if mentioned, and ensure the reserve fund is fully distributed to the old partners before the admission of the new partner.

Question 31. A and B are partners sharing profits and losses in the ratio of 3:1. On 1st Jan. 2007 they admitted C as a new partner for 1/4 share in the profits of the firm. C brings Rs. 20,000 as for his 1/4 share in the profits of the firm. The capitals of A and B after all adjustments in respect of goodwill, revaluation of assets and liabilities, etc. has been worked out at Rs. 50,000 for A and Rs. 12,000 for B. It is agreed that partner’s capitals will be according to new profit sharing ratio. Calculate the new capitals of A and B and pass the necessary journal entries assuming that A and B brought in or withdrew the necessary cash as the case may be for making their capitals in proportion to their profit sharing ratio?
Answer:
First, we calculate the new profit-sharing ratio. If we assume the entire firm's profit share is 1:
Remaining share after C's 1/4 share is 3/4.
A's updated share = \( \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \)
B's updated share = \( \frac{3}{4} \times \frac{1}{4} = \frac{3}{16} \)
C's share is 1/4, which equals 4/16.
Thus, the revised profit-sharing ratio among A, B, and C is 9:3:4.

Next, we determine the firm's total capital based on C's contribution:
With C bringing in Rs. 20,000 for a 1/4 share, the total capital of the firm is Rs. \( 20,000 \times \frac{4}{1} = \) Rs. 80,000.
A's proportionate capital = Rs. \( 80,000 \times \frac{9}{16} = \) Rs. 45,000.
B's proportionate capital = Rs. \( 80,000 \times \frac{3}{16} = \) Rs. 15,000.

Comparing these required balances with the actual capital after adjustments:
- A's actual capital is Rs. 50,000, whereas the requirement is Rs. 45,000. Therefore, A withdraws the surplus of Rs. 5,000.
- B's actual capital is Rs. 12,000, whereas the requirement is Rs. 15,000. Therefore, B contributes the deficit of Rs. 3,000.

In simple words: We adjust A and B's capitals to match their new profit shares. Since C brought Rs. 20,000 for a quarter of the firm, the total capital must be Rs. 80,000, which we divide in the 9:3:4 ratio. Partners then pay in or take out cash to reach these target amounts.

Exam Tip: When adjusting capital based on a new partner's share, always find the total capital first using the formula: New Partner's Capital multiplied by the reciprocal of their share.

Question 32. Pinky, Qumar and Roopa partners in a firm sharing profits and losses in the ratio of 3:2:1. S is admitted as a new partner for 1/4 share in the profits of the firm, which she gets 1/8 from Pinky, and 1/16 each from Qmar and Roopa. The total capital of the new firm after Seema’s admission will be Rs. 2 40,000. Seema is required to bring in cash equal to 1/4 of the total capital of the new firm. The capitals of the old partners also have to be adjusted in proportion of their profit sharing ratio. The capitals of Pinky, Qumar and Roopa after all adjustments in respect of goodwill and revaluation of assets and liabilities have been made are Pinky Rs. 80,000, Qumar Rs. 30,000 and Roopa Rs. 20,000. Calculate the capitals of all the partners and record the necessary journal entries for doing adjustments in respect of capitals according to the agreement between the partners?
Answer:
First, we find the new profit-sharing ratio among the partners:
- Pinky's new share = \( \frac{3}{6} - \frac{1}{8} = \frac{12 - 3}{24} = \frac{9}{24} = \frac{18}{48} \)
- Qumar's new share = \( \frac{2}{6} - \frac{1}{16} = \frac{16 - 3}{48} = \frac{13}{48} \)
- Roopa's new share = \( \frac{1}{6} - \frac{1}{16} = \frac{8 - 3}{48} = \frac{5}{48} \)
- Seema's share = \( \frac{1}{4} = \frac{12}{48} \)
Thus, the new profit-sharing ratio is 18:13:5:12.

Given the total capital of the firm is Rs. 2,40,000, the required capitals of each partner are:
- Pinky's new capital = Rs. \( 2,40,000 \times \frac{18}{48} = \) Rs. 90,000
- Qumar's new capital = Rs. \( 2,40,000 \times \frac{13}{48} = \) Rs. 65,000
- Roopa's new capital = Rs. \( 2,40,000 \times \frac{5}{48} = \) Rs. 25,000
- Seema's new capital = Rs. \( 2,40,000 \times \frac{12}{48} = \) Rs. 60,000

In simple words: We first find the new profit-sharing ratio by deducting what each partner gave up to Seema. We then divide the total firm capital of Rs. 2,40,000 among all four partners using this new ratio, and each partner deposits cash to meet their target balance.

Exam Tip: When a new partner acquires their share specifically from old partners (e.g., 1/8 from Pinky, 1/16 from Qumar and Roopa), subtract these individual sacrifices directly from the old shares to find the new ratio.

Question 33. The following was the Balance Sheet of Arun, Bablu and Chetan sharing profits and losses in the ratio of

They agreed to take Deepak into partnership and give him a share of 1/8 on the following terms: a) that Deepak should bring in Rs. 4,200 as goodwill and Rs. 7,000 as his Capital; (b) that furniture be depreciated by 12%; (c) that stock be depreciated by 10% (d) that a Reserve of 5% be created for doubtful debts: (e) that the value of land and buildings having appreciated be brought upto Rs. 31,000 ;(f) that after making the adjustments the capital accounts of the old partners (who continue to share in the same proportion as before) be adjusted on the basis of the proportion of Deepak’s Capital to his share in the business, i.e., actual cash to be paid off to, or brought in by the old partners as the case may be. Prepare Cash Account, Profit and Loss Adjustment Account (Revaluation Account) and the Opening Balance Sheet of the new firm.
Answer:

Working Notes for Profit-Sharing and Capitals:
- Remaining profit share = \( 1 - \frac{1}{8} = \frac{7}{8} \).
- Old ratio = 6:5:3.
- Arun's new share = \( \frac{7}{8} \times \frac{6}{14} = \frac{6}{16} \)
- Bablu's new share = \( \frac{7}{8} \times \frac{5}{14} = \frac{5}{16} \)
- Chetan's new share = \( \frac{7}{8} \times \frac{3}{14} = \frac{3}{16} \)
- Deepak's share = \( \frac{1}{8} = \frac{2}{16} \).
- Thus, the new profit-sharing ratio is 6:5:3:2.

With Deepak introducing Rs. 7,000 for a 1/8 share:
- Total firm capital = Rs. \( 7,000 \times \frac{8}{1} = \) Rs. 56,000.
- Arun's required capital = Rs. \( 56,000 \times \frac{6}{16} = \) Rs. 21,000.
- Bablu's required capital = Rs. \( 56,000 \times \frac{5}{16} = \) Rs. 17,500.
- Chetan's required capital = Rs. \( 56,000 \times \frac{3}{16} = \) Rs. 10,500.
- Deepak's capital = Rs. 7,000.
In simple words: We revalue the assets first and distribute the profit to the old partners. Next, we determine the new required capitals based on Deepak's capital, and the partners pay in or withdraw cash to adjust their balances to these new target amounts.

Exam Tip: Make sure to read the appreciation terms carefully - "brought upto" means the new value is the stated amount, so find the difference between the old and new book values for the revaluation account.

Question 34. Azad and Babli are partners in a firm sharing profits and losses in the ratio of 2:1. Chintan is admitted into the firm with 1/4 share in profits. Chintan will bring in Rs. 30,000 as his capital and the capitals of Azad and Babli are to be adjusted in the profit sharing ratio. The Balance Sheet of Azad and Babli as on December 31, 2006 (before Chintan’s admission) was as follows:

It was agreed that:
i) Chintan will bring in Rs. 12,000 as his share of goodwill premium.
ii) Buildings were valued at Rs. 45,000 and Machinery at Rs. 23,000.
iii) A provision for doubtful debts is to be created @ 6% on debtors.
iv) The capital accounts of Azad and Babli are to be adjusted by opening current accounts.
Record necessary journal entries, show necessary ledger accounts and prepare the Balance Sheet after admission.
Answer:

Calculations:
- Chintan's share = 1/4.
- Total firm capital on base of Chintan's capital = Rs. \( 30,000 \times \frac{4}{1} = \) Rs. 1,20,000.
- New Ratio = 2:1:1.
- Azad's new capital = Rs. \( 1,20,000 \times \frac{2}{4} = \) Rs. 60,000.
- Babli's new capital = Rs. \( 1,20,000 \times \frac{1}{4} = \) Rs. 30,000.
In simple words: We calculate the new capital requirements based on Chintan's capital of Rs. 30,000. Any surplus in the old partners' capital accounts is transferred to their current accounts, which we list on the liabilities side of the final balance sheet.

Exam Tip: When capitals are adjusted by opening current accounts, do not pay or receive cash. Instead, debit the capital account and credit the current account for any surplus capital (or vice versa for a deficit).

Question 35. Ashish and Dutta were partners in a firm sharing profits in 3:2 ratio. On Jan. 01, 2007 they admitted Vimal for 1/5 share in the profits. The Balance Sheet of Ashish and Dutta as on Jan. 01, 2007 was as follows:

It was agreed that:
i) The value of Land and Building be increased by Rs. 15,000.
ii) The value of plant be increased by 10,000.
iii) Goodwill of the firm be valued at Rs. 20,000.
iv) Vimal to bring in capital to the extent of 1/5th of the total capital of the new firm.
Record the necessary journal entries and prepare the Balance Sheet of the firm after Vimal’s admission.
Answer:

Calculation Details:
- Total adjusted capital of Ashish and Dutta = Rs. 97,400 + Rs. 46,600 = Rs. 1,44,000.
- This sum of Rs. 1,44,000 represents a 4/5 share (remaining share) of the firm's capital.
- Total capital of the new firm = Rs. \( 1,44,000 \times \frac{5}{4} = \) Rs. 1,80,000.
- Vimal's capital contribution = Rs. \( 1,80,000 \times \frac{1}{5} = \) Rs. 36,000.
- Vimal's share of goodwill = Rs. \( 20,000 \times \frac{1}{5} = \) Rs. 4,000.
- Sacrificing ratio of Ashish and Dutta is 3:2. Therefore, Vimal's Current Account is debited by Rs. 4,000, and Ashish and Dutta's capital accounts are credited by Rs. 2,400 and Rs. 1,600 respectively.
In simple words: We find Vimal's capital contribution by summing up the old partners' capitals after adjusting them for revaluation and goodwill. Since Vimal has a 1/5th share, the old partners have a 4/5th share, allowing us to find the total firm capital and Vimal's portion.

Exam Tip: If a new partner is unable to bring their share of goodwill in cash, always debit their current account rather than their capital account to keep their capital contribution intact.