NCERT Solutions Class 12 Accountancy Partnership Accounts Chapter 3

Q.1 Identify various matters that need adjustments at the time of admission of a new partner.

Ans. Following are the problems that may arise at the time of admission of a partner:

• New profit sharing ratio.
• Sacrificing ratio.
• Valuation and adjustment of goodwill.
• Revaluation of assets and reassessment of liabilities.
• Distribution of accumulated profits or losses and reserves.
• Adjustment of partners’ capital.

Q.2 Why it is necessary to ascertain new profit sharing ratio even for old partners when a new partner is admitted?

Ans. When a new partner is admitted, he acquires his share in profits from the old partners and thus reduces the old partners share in profit. Hence the problem of determining the new profit sharing ratio simply involves the determination of old partners’ new share in the profits of the reconstituted firm.

Q.3 What is sacrificing ratio? Why is it calculated?

Ans. Sacrificing ratio is the ratio in which the old partners have surrendered a part of their profit sharing ratio in favour of the incoming partner. This ratio is calculated as given below:

Sacrifice = Old Share – New Share

This ratio is calculated to facilitate the sharing of premium brought in by the new partner. This premium is shared by the old partners is sacrificing ratio.

Q.4 On what occasions sacrificing ratio is used?

Ans. Following are the occasions sacrificing ratio is used:

• For disturbing amount of goodwill among old partners.
• For calculating new profit sharing ratio.

Q.5If some goodwill already exists in the books and the new partner brings in his share of goodwill in cash, how will you deal with existing amount of goodwill?

Ans. The existing amount of goodwill will be written off by debiting old partner capital accounts in old ratio and creating goodwill /Premium account as shown below:

Q.6 Why there is need for the revaluation of assets and liabilities on the admission of a partner?

Ans. Assets and liabilities should be revalued so that these are shown at the proper value and the resulting profit or loss on such revaluation is transferred to old partners in old ratio. Further the new partner acquires a right to share the assets of the partnership firm. So also they should be shown in the Balance Sheet as the present value and any gain or loss because of revaluation should belong to the old partners.

Q.7 Do you advise that assets and liabilities must be revalued at the time of admission of a partner? If so, Why? Also describe how is this treated in the book of account?

Ans. Assets and Liabilities should be revalued so that these are shown at the proper value and the resulting profit or loss on such revaluation is transferred to old partners in the old ratio. At times there may also be some unrecorded assets and liabilities of the firm. These also have to be brought into the books of the firm. Further the new partner acquires a right to share the assets of the partnership firm. So also assets and liabilities should be shown in the Balance Sheet at the present value and any gain or loss because of revaluation should not borne by the new partner.

Revaluation account is a nominal account. Revaluation account is credited with the increase in value of each asset and decrease in liabilities because it is a gain. It is debited with the decrease in value of each asset and increase in liabilities because it is a loss. Similarly, unrecorded assets are credited and unrecorded liabilities are debited to the revaluation account. If revaluation account finally shows credit balance, then it indicates profit and if revaluation account shows debit balance, then it indicates loss.

Q.8 What is goodwill? What factors affect goodwill?

Ans. Goodwill is the money value of reputation of a firm in respect of the profits expected in future over and above the normal profits.

The factors that affect the value of goodwill:

Nature of Business: A firm that produces high value added products or having a stable demand is able to earn more profits and therefore has more goodwill.

Favourable location: If the business is centrally located or is at a place having customer traffic, the goodwill will have high than those businesses which are not so located.

Efficiency of management: If the management of a firm is more efficient and reputed, the value of goodwill in such business will be more as compared to be business whose management is not efficient.

Time Factor: The business which is running for the last several years on profitable lines will have more goodwill than a business which has been established only recently.

Patent: If the firm has its own patent, highly in demand than its value of goodwill will be high.

Capital Requirements: If a business requires more capital than its value of goodwill will be less as compared to a business where the capital requirement is less.

Q.9 Explain how will you deal with goodwill when new partner is not in a position to bring his share of goodwill in cash?

Ans. If new partner does not bring his share of goodwill in cash, new partner’s Capital or Current account is debited for his share of goodwill and the sacrificing partners’ capital accounts are credited in their sacrificing ratio.

Following journal entry will be:

For example, M and N who share profits in the ratio of 3:2 had capitals of ₹2,00,000 and ₹1,50,000 respectively. They agreed to admit P into partnership from 1^st April, 2013 on the following terms in return for 1/3^rd share in future profits:

That P should bring in ₹2,00,000 as capital.
That as P is unable to bring in his share of goodwill in cash, goodwill of the firm is valued at ₹1,50,000.

Here,
Necessary journal entries in the books of the firm are

Q.10 Explain various methods for the treatment of goodwill on the admission of a new partner?

Ans. Goodwill can be treated in two ways:

• By Premium Method and By Revaluation Method.

Premium Method:

This method is used when new partner brings his share of goodwill in cash, which is shared by the old partners in sacrificing ratio. There may be different situations when this method may be used, shown below:

Situation 1: When goodwill is paid privately.

In this situation goodwill is not recorded in the books of accounts. i.e., no journal entry is passed.

Situation 2: When goodwill is brought in cash by the new partner and retained in the business. Following are the journal entries required to record the fact.

Revaluation Method:

This method is followed, when the new partner is unable to bring his share of goodwill in cash. The following journal entries are passed.

Q.11 How will you deal with the accumulated profits and losses and reserves on the admission of a new partner?

Ans. Accumulated profits and losses and reserve on the admission of a new partner may exist because these might have not yet transferred to capital accounts of the partners. These belong to old partners and the new partner is not entitled to have any share in such accumulated profits/losses, reserve.

Hence these are distributed among old partner by transferring them to their capital accounts in old profit sharing ratio. Following are the journal entries for the same.

Let us understand it with the help of example; Sam and Dev are partners in a firm sharing profits in the ratio of 11:5 admit Stu as a new partner for ¼ share in the profits. On the date of admission there was a debit balance of ₹80,000 in the profit and loss account.

The necessary journal entries for the treatment of Profit and Loss account balance on Stu’s admission:

Q.12 At what figures the value of assets and liabilities appear in the books of the firm after revaluation has been due. Show with the help of an imaginary balance sheet.

Ans. The assets and liabilities after revaluation will appear at new figures as in the given example:

A and G were carrying on business in partnership sharing profits in the ratio of 2:1. Their Balance Sheet as on March 31, 2018 stood as follows:

S is admitted as a partner on the date of the Balance sheet on the following terms:

1. She will bring in ₹20,000 as her capital and ₹12,000 as her share of goodwill for ¼ share in profits.
2. Plant is to be appreciated to ₹24,000 and the value of building is to be appreciated by 10%.
3. Stock is found over valued by ₹800.
4. A provision for doubtful debt is to maintain ₹600.
5. Creditors were unrecorded to the extent of ₹200.

In this case the journal entries are:

Q.13 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 ₹20,000 as capital and ₹4,000 as his share of goodwill premium. Give the necessary journal entries:

1. When the amount of goodwill is retained in the business.
2. When the amount of goodwill is fully withdrawn.
3. When 50% of the amount of goodwill is withdrawn.
4. When goodwill is paid privately.

Ans. Case (a)

Case (b)

Case (c)

Case (d)

No entry for goodwill will be passed in this case, as the amount of goodwill is paid outside the business i.e. privately.

Q.14 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 ₹20,000 for his capital and ₹7,000 for his 1/8 share of goodwill. Goodwill already appears in the books at Rs. 40,000. Show necessary journal entries in the books of X, Y and Z.

Ans.

Q.15 Amar and Samar were partners in a firm sharing profits and losses in 3:1 ratio. They admitted Kanwar for ¼ share of profits. Kanwar could not bring his share of goodwill premium in cash. The goodwill of the firm was valued at ₹80,000 on Kanwar’s admission.

Record necessary journal entry for goodwill on Kanwar’s admission.

Ans.

Kanwar’s share of goodwill = ₹80,000 x ¼ = ₹20,000.

In this case old ratio itself will be considered as the sacrificing ratio.

Q.16 Give below is the Balance Sheet of A and B, who are carrying on partnership business on 31/12/2016. A and B share profits and losses in the ratio of 2:1.

C is admitted as a partner on the balance sheet on the following terms:

1. C will bring in ₹1,00,000 as his capital and ₹60,000 as his share of goodwill for ¼ share in the profits.
2. Plant is to be appreciated to ₹1,20,000 and the value of buildings is to be appreciated by 10%.
3. Stock is found, over valued by ₹4,000.
4. A provision for bad and doubtful debts is to be created at 5% of debtors.
5. Creditors were unrecorded to the extent of ₹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.

Ans. Revaluation A/c

Partners’ Capital Accounts

C’s Capital Account

Balance Sheet

as on 1^st Jan 2017

Journal Entries

Q.17 Leela and Meeta were partners in a firm sharing profits and losses in the ratio of 5:3. On 1^st April, 2017 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 ₹16,000 in general reserve and ₹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.

Ans. Journal Entries

Q.18 Amit and Viney are partners in a firm sharing profits and losses in 3:1 ratio. On 01/01/2017 they admitted Ranjan as a partner. On Ranjan’s admission the profit and loss account of Amit and Viney showed a debit balance of ₹40,000.

Record necessary journal entry for the treatment of the same.

Ans. Journal Entries

Q.19 A and B share profits in the proportion of ¾ and ¼. Their Balance Sheet on March. 31, 2016 was as follows:

On 1^st January, 2017, C was admitted into partnership on the following terms:

1. That C pays ₹10,000 as his capital.
2. That C pays ₹5,000 for goodwill. Half of this sum is to be withdrawn by A and B.
3. That stock and fixtures be reduced by 10% and a 5%, provision for doubtful debts be created on Sundry Debtors and Bills Receivable.
4. That the value of land and buildings be appreciated by 20%.
5. There being a claim against the firm for damages, a liability to the extent of ₹1,000 should be created.
6. An item of ₹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.

Ans. Journal Entries

Revaluation A/c

Partners’ Capital Accounts

C’s Capital Account

Balance Sheet

as on 1^st Jan 2017

Q.20 The following was the balance sheet of Arun, Bablu and Chetan profits and losses in the ratio of 6/14:5/14:3/14 respectively.

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 ₹4,200 as goodwill and ₹7,000 as his capital;

b) that furniture be depreciated by 12%;

c) that stock can 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 up to ₹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.

Ans. Revaluation A/c

Partners’ Capital Accounts

Partners’ Capital Accounts

Cash A/c

Balance Sheet

as on …..

Q.21 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 ¼ share in profits. Chintan will bring in ₹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, 2016 (before Chintan’s admission) was as follows:

It was agreed that:

1. Chintan will bring in ₹12,000 as his share of goodwill premium.
2. Buildings were valued at ₹45,000 and Machinery at ₹23,000.
3. A provision for doubtful debts is to be created @ 6% on debtors.
4. The capital accounts of Azad and Babli are to be adjusted by opening current accounts.

Record necessary journal entries, show necessary ledger account at prepare the Balance Sheet after admission.

Ans. Journal Entries

Revaluation A/c

Partners’ Capital Accounts

Chintan’s Capital Account

Balance Sheet

as on 1^st Jan 2017

Q.22 Ashish and Dutta were partners in a firm sharing profits in 3:2 ratio. On April 01, 2016 they admitted Vimal for 1/5 share in the profits. The Balance Sheet Ashish and Dutta as on March 31, 2016 was as follows:

It was agreed that:

1. The value of Land & Building be increased by ₹ 15,000.
2. The value of plant be increased by ₹ 10,000.
3. Goodwill of the firm be valued at ₹ 20,000.
4. Vimal to bring in capital to the extent of 1/5^th of the capital of the new firm.

Record the necessary journal entries and prepare the Balance Sheet of the firm after Vimal’s admission.

Ans. Journal Entries

Balance Sheet (after admission)

Working Note:

Partners’ Capital Accounts

Vimal Current Account

Total adjusted capital of old partners = ₹97,400 + ₹46,600 = ₹ 1,44,000

4/5^th capital = ₹1,44,000

Total capital = ₹1,44,000 × 5/4 = ₹1,80,000

Vimal’s share = ₹1,80,000 × 1/5 = ₹36,000

Q.23 If it is agreed that the capital of all the partners should be proportionate to the new profit sharing ratio, how will you work out the new capital of each partner? Give examples and state how necessary adjustments will be made.

Ans. Sometime, at the time of admission, the partners agree that their capitals should also be adjusted so as to be proportionate to their profit sharing ratio.

In such a situation, if the capital of the new partner is given, the same can be used as a base for calculating the new capitals of the old partners. The capitals thus ascertained should be compared with their old capitals after all adjustments relating to goodwill reserves and revaluation of assets and liabilities, etc. have been made and then the partner whose capital falls short, will bring in the necessary amount to cover the shortage and the partner who has a surplus, will withdraw the excess amount of capital.

Let’s take an example for better understanding:

P and Q are partners sharing profits in the ratio of 2:1. R is admitted into the firm for ¼ share of profits. R brings in ₹20,000 in respect of his capital. The capitals of old partners P and Q, after all adjustments relating to goodwill, revaluation of assets and liabilities, etc are ₹45,000 and ₹15,000 respectively. It is agreed that partner’s capitals should be according to the new profit sharing ratio.

Let us determine the new capitals of P and Q and record the necessary journal entries assuming that the partner whose capital falls short, brings in the amount of deficiency and the partner who has an excess, withdraws the excess amount.

Here,

Calculation of new profit sharing ratio. Assuming the new partner R acquires his share from P and Q in their old profit sharing ratio, i.e., 2:1.

\begin{array}{l}\text{Total share = 1}\\ \text{R’s Share =}\frac{\text{1}}{\text{4}}\\ \text{Remaining shares = 1-}\frac{\text{1}}{\text{4}}\text{=}\frac{\text{3}}{\text{4}}\\ \text{P’s New Share =}\frac{\text{3}}{\text{4}}\text{x}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{6}}{\text{12}}\\ \text{Q’s New Share =}\frac{\text{3}}{\text{4}}\text{x}\frac{\text{1}}{\text{3}}\text{=}\frac{\text{3}}{\text{12}}\\ \text{R’s New Share =}\frac{\text{1}}{\text{4}}\text{x}\frac{\text{3}}{\text{3}}\text{=}\frac{\text{3}}{\text{12}}\\ \text{Thus new profit sharing ratio between P, Q and R:}\\ \text{= 6:3:3 or 2:1:1}\end{array}

Required capital of P and Q, R’s Capital (who has ¼ share in profits) is ₹20,000. P’s new share is 2/4 which is double of R’s share. Hence the capital will be ₹40,000.

Alternatively based on R’s Capital the total capital of the firm works out at ₹80,000. Hence based on their share in profits, the capital of P and Q will be:

\begin{array}{l}P‘sCapital=\frac{2}{4}of₹80,000=₹40,000\\ Q‘sCapital=\frac{1}{4}of₹80,000=₹20,000\end{array}

The capital of P and Q after all adjustments have been made, are ₹45,000 and ₹15,000 respectively. Hence P will withdraw ₹5,000 (₹45,000 – ₹40,000) from the firm where Q will contribute additional amount of ₹5,000 (₹20,000 – ₹15,000).

The journal entries will be:

Sometimes, the total capital of the firm may clearly specified and it is agreed that the capital of each partner should be proportionate to his share in profits. In such a situation each partner’s capital (including the new partner’s capital to be brought by him) is calculated on the basis of new capital.

Q.24 Explain various methods of valuation of goodwill.

Ans. The methods for valuing goodwill are:

• Average profit method.
• Super Profit method.
• Capitalisation method.

(1) Average Profit Method:
Goodwill under Average profit method can be calculated using Simple Average Profit Method or Weighted Average Profit Method.
Simple Average Profit Method: Under the Simple Average Profit Method, average profits earned by the business for the specified number of years are considered. Profits earned are totaled and average is determined. Average profit as calculated is multiplied by a number of year’s purchase to arrive at the value of goodwill.

Calculate Average profit as follows:

\begin{array}{l}\text{Calculate Average profit as follows:}\\ \text{Average profit =}\frac{\text{Total profits}}{\text{Number of years}}\\ \text{Calculate goodwill applying the formula:}\\ \text{Goodwill = Average profit x No}\text{. of years purchase}\end{array}

Weighted Average method: Under this method, each year’s profit is multiplied by the number of assigned weights and the value is ascertained. The products are added and divided by the total of weights to arrive at the average profit. The weighted average profit so arrived at are multiplied by the agreed ‘Number of years’ ‘Purchase’ to arrive at the value of goodwill.

Calculate Weighted Average profit as follows:

\begin{array}{l}\text{Calculate Weighted Average profit as follows:}\\ \text{Weighted Average profit =}\frac{\text{Total purchase of profits}}{\text{Total of weights}}\\ \text{Goodwill = Weighted Average profit x Agreed No}\text{. of years purchase}\end{array}

(2) Super Profit Method:
The excess of actual profit over the normal profit is called super profit. Goodwill under this method is calculated by multiplying the super profits with the agreed number of years purchase. Normal rate of return is considered while calculating the super profit. Average capital employed is taken into account while calculating the super profit.

\begin{array}{l}\text{Calculating goodwill under this method:}\\ \text{Calculate Average Capital Employed as:}\\ \text{=}\frac{\text{Opening Capital Employed + Closing Capital Employed}}{\text{2}}\\ \text{Capital Employed = Capital + Free Reserves – Fictitious Assets (if any)}\\ \text{Or}\\ \text{All assets (other than goodwill, fictitious assets \&}\text{}\text{non-trade investments) –}\\ \text{Outsider’s Liabilities}\text{.}\\ \text{Calculate actual expected profits, i}\text{.e}\text{., average profit}\text{.}\\ \text{Calculate normal profit on avearge capital employed by applying :}\\ \text{Average Capital Employed x}\frac{\text{Normal Rate of Return}}{\text{100}}\\ \text{Calculate Super Profit, i}\text{.e}\text{., Actual – Normal (Profit)}\\ \text{Calculate value of goodwill as follows:}\\ \text{Goodwill = Super Profit x Number of Year’s Purchase}\end{array}

(3) Capitalisation Method:
Under this method, Goodwill can be valued in two ways:

Capitalisation of Average Profit: Under this, goodwill is calculated by deducting capital employed (net assets as on the date of valuation) in the business from the capitalised value of average profit on the basis of normal rate of return.

Capitalised value of the business is ascertained as follows:

\text{=}\frac{\text{Average profit x 100}}{\text{Normal rate of Return (Profit)}}

For calculating goodwill under this method, the steps are:

Calculate average normal profit earned.

Calculate capitalised value of the firm by using the above formula.

Net Assets = All assets (other than goodwill, fictitious assets and non-trade investments at their current values) – outsiders liabilities.

Goodwill = Capitalised value – Net assets.

Capitalisation of Super Profit: Under this method, goodwill is calculated by capitalisation of super profit.

\begin{array}{l}\text{For calculating goodwill under this method, the steps are:}\\ \text{Calculate Capital Employed (Net assets as on date of valuation of firm)}\\ \text{Calculate Normal Profit on capital employed by using the following formula:}\\ \text{Normal profit = Capital employed x}\frac{\text{Required rate of return}}{\text{100}}\\ \text{Calculate Average profit of past years, i}\text{.e 3 to 5 years}\\ \text{Calculate Super Profit, i}\text{.e}\text{., Actual Average profit – Normal Profit}\\ \text{Goodwill = Super profit x}\frac{\text{100}}{\text{Normal rate of return}}\end{array}

Q.25 A and B were partners in a firm sharing profits and losses in the ratio of 3:2. They admit C into the partnership with 1/6 share in the profits. Calculate the new profit sharing ratio?

Ans.

$MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqeduuDJXwAKbYu51MyVXgaruWqVvNCPvMCG4uz3bqefqvATv2CG4uz3bIuV1wyUbqeeuuDJXwAKbsr4rNCHbGeaGqiVv0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@04B0@ $

Q.26 A, B, C were partners in a firm sharing profits in 3:2:1 ratio. They admitted D for 10% profits. Calculate the new profit sharing ratio.

Ans. 

\begin{array}{l}\text{Let the total share = 1}\\ \text{D’s Share =}\frac{\text{1}}{\text{10}}\\ \text{Remaining share of A, B and C}\\ \text{1 –}\frac{\text{1}}{\text{10}}\text{=}\frac{\text{9}}{\text{10}}\\ \text{New share}\\ \text{A =}\frac{\text{9}}{\text{10}}\text{x}\frac{\text{3}}{\text{6}}\text{=}\frac{\text{27}}{\text{60}}\\ \text{B =}\frac{\text{9}}{\text{10}}\text{x}\frac{\text{2}}{\text{6}}\text{=}\frac{\text{18}}{\text{60}}\\ \text{C =}\frac{\text{9}}{\text{10}}\text{x}\frac{\text{1}}{\text{6}}\text{=}\frac{\text{9}}{\text{60}}\\ \text{New share = old share – sacrifice}\\ \text{Hence new profit sharing ratio of A, B, C and D}\\ \text{=}\frac{\text{27}}{\text{60}}\text{:}\frac{\text{18}}{\text{60}}\text{:}\frac{\text{9}}{\text{60}}\text{:}\frac{\text{1}}{\text{10}}\\ \text{=}\frac{\text{27}}{\text{60}}\text{:}\frac{\text{18}}{\text{60}}\text{:}\frac{\text{9}}{\text{60}}\text{:}\frac{\text{6}}{\text{60}}\\ \text{= 9:6:3:2}\end{array}

Q.27 X and Y are partners sharing profits in 5:3 ratio admitted Z for 1/10 share which he acquired equally from X and Y. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{First calculating the sacrifice:}\\ \text{Z’s Share =}\frac{\text{1}}{\text{10}}\\ \text{Acquired from X =}\frac{\text{1}}{\text{10}}\text{x}\frac{\text{1}}{\text{2}}\text{=}\frac{\text{1}}{\text{20}}\\ \text{Acquired from Y =}\frac{\text{1}}{\text{10}}\text{x}\frac{\text{1}}{\text{2}}\text{=}\frac{\text{1}}{\text{20}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{X =}\frac{\text{5}}{\text{8}}\text{–}\frac{\text{1}}{\text{20}}\text{=}\frac{\text{23}}{\text{40}}\\ \text{Y =}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{1}}{\text{20}}\text{=}\frac{\text{13}}{\text{40}}\\ \text{Hence new profit sharing ratio of X, Y and Z}\\ \text{=}\frac{\text{23}}{\text{40}}\text{:}\frac{\text{13}}{\text{40}}\text{:}\frac{\text{1}}{\text{10}}\\ \text{= 23:13:4}\end{array}

Q.28 A, B and C are partners sharing profits in 2:2:1 ratio admitted D for 1/8 share which he acquired entirely from A. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{D’s Share =}\frac{\text{1}}{\text{8}}\\ \text{A’s Sacrifice =}\frac{\text{1}}{\text{8}}\\ \text{A’s new share =}\frac{\text{2}}{\text{5}}\text{–}\frac{\text{1}}{\text{8}}\text{=}\frac{\text{11}}{\text{40}}\\ \text{B}\text{and}\text{C’s}\text{share remian same}\\ \text{New profit sharing ratio of A:B:C:D}\\ \text{=}\frac{\text{11}}{\text{40}}\text{:}\frac{\text{16}}{\text{40}}\text{:}\frac{\text{8}}{\text{40}}\text{:}\frac{\text{5}}{\text{40}}\\ \text{= 11:16:8:5}\end{array}

Q.29 P and Q are partners sharing profits in 2:1 ratio. They admitted R into partnership giving him 1/5 share which he acquired from P and Q in 1:2 ratio. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{First calculating the sacrifice:}\\ \text{R’s Share =}\frac{\text{1}}{\text{5}}\\ \text{Acquired from P =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{1}}{\text{3}}\text{=}\frac{\text{1}}{\text{15}}\\ \text{Acquired from Q =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{2}}{\text{3}}\text{=}\frac{\text{2}}{\text{15}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{P =}\frac{\text{2}}{\text{3}}\text{–}\frac{\text{1}}{\text{15}}\text{=}\frac{\text{9}}{\text{15}}\\ \text{Q =}\frac{\text{1}}{\text{3}}\text{–}\frac{\text{2}}{\text{15}}\text{=}\frac{\text{3}}{\text{15}}\\ \text{Hence new profit sharing ratio of P, Q and R}\\ \text{=}\frac{\text{9}}{\text{15}}\text{:}\frac{\text{3}}{\text{15}}\text{:}\frac{\text{3}}{\text{15}}\\ \text{= 3:1:1}\end{array}

Q.30 A, B and C are partners sharing profits in 3:2:2 ratio. They admitted D as a new partner for 1/5 share which he acquired from A, B and C in 2:2:1 ratio respectively. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{First calculating the sacrifice:}\\ \text{D’s Share =}\frac{\text{1}}{\text{5}}\\ \text{Acquired from A =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{2}}{\text{5}}\text{=}\frac{\text{2}}{\text{25}}\\ \text{Acquired from B =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{2}}{\text{5}}\text{=}\frac{\text{2}}{\text{25}}\\ \text{Acquired from C =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{1}}{\text{5}}\text{=}\frac{\text{1}}{\text{25}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{A =}\frac{\text{3}}{\text{7}}\text{–}\frac{\text{2}}{\text{25}}\text{=}\frac{\text{61}}{\text{175}}\\ \text{B =}\frac{\text{2}}{\text{7}}\text{–}\frac{\text{2}}{\text{25}}\text{=}\frac{\text{36}}{\text{175}}\\ \text{C =}\frac{\text{2}}{\text{7}}\text{–}\frac{\text{1}}{\text{25}}\text{=}\frac{\text{43}}{\text{175}}\\ \text{Hence new profit sharing ratio of A, B, C and D}\\ \text{=}\frac{\text{61}}{\text{175}}\text{:}\frac{\text{36}}{\text{175}}\text{:}\frac{\text{43}}{\text{175}}\text{:}\frac{\text{35}}{\text{175}}\\ \text{= 61:36:43:35}\end{array}

Q.31 A and B were partners in a firm sharing profits in 3:2 ratio. They admitted C for 3/7 share which he took 2/7 from A and 1/7 from B. Calculate new profit sharing ratio.

Ans. 

\begin{array}{l}\text{First calculating the sacrifice:}\\ \text{C’s Share =}\frac{\text{3}}{\text{7}}\\ \text{Acquired from A =}\frac{\text{2}}{\text{7}}\\ \text{Acquired from B =}\frac{\text{1}}{\text{7}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{A =}\frac{\text{3}}{\text{5}}\text{–}\frac{\text{2}}{\text{7}}\text{=}\frac{\text{11}}{\text{35}}\\ \text{B =}\frac{\text{2}}{\text{5}}\text{–}\frac{\text{1}}{\text{7}}\text{=}\frac{\text{9}}{\text{35}}\\ \text{Hence new profit sharing ratio of A, B and C}\\ \text{=}\frac{\text{11}}{\text{35}}\text{:}\frac{\text{9}}{\text{35}}\text{:}\frac{\text{15}}{\text{35}}\\ \text{= 11:9:15}\end{array}

Q.32 A, B and C were partners in a firm sharing profits in 3:3:2 ratio. They admitted D as a new partner for 4/7 profit. D acquired his share 2/7 from A. 1/7 from B and 1/7 from C. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{First calculating the sacrifice:}\\ \text{D’s Share =}\frac{\text{4}}{\text{7}}\\ \text{Acquired from A =}\frac{\text{2}}{\text{7}}\\ \text{Acquired from B =}\frac{\text{1}}{\text{7}}\\ \text{Acquired from C =}\frac{\text{1}}{\text{7}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{A =}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{2}}{\text{7}}\text{=}\frac{\text{5}}{\text{56}}\\ \text{B =}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{1}}{\text{7}}\text{=}\frac{\text{13}}{\text{56}}\\ \text{C =}\frac{\text{2}}{\text{8}}\text{–}\frac{\text{1}}{\text{7}}\text{=}\frac{\text{6}}{\text{56}}\\ \text{Hence new profit sharing ratio of A, B, C and D}\\ \text{=}\frac{\text{5}}{\text{56}}\text{:}\frac{\text{13}}{\text{56}}\text{:}\frac{\text{6}}{\text{56}}\text{:}\frac{\text{32}}{\text{56}}\\ \text{= 5:13:6:32}\end{array}

Q.33 Radha and Rukmani are partners in a firm sharing profits in 3:2 ratio. They admitted Gopi as a new partner. Radha surrendered 1/3 of her share in favour of Gopi and Rukmani surrendered ¼ of her share in favour of Gopi. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{Old ratio = 3:2}\\ \text{Acquired from Radha =}\frac{\text{1}}{\text{3}}\text{x}\frac{\text{3}}{\text{5}}\text{=}\frac{\text{3}}{\text{15}}\\ \text{Acquired from Rukmani =}\frac{\text{1}}{\text{4}}\text{x}\frac{\text{2}}{\text{5}}\text{=}\frac{\text{2}}{\text{20}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{Radha =}\frac{\text{3}}{\text{5}}\text{–}\frac{\text{3}}{\text{15}}\text{=}\frac{\text{9}}{\text{15}}\\ \text{Rukmani =}\frac{\text{2}}{\text{5}}\text{–}\frac{\text{2}}{\text{20}}\text{=}\frac{\text{6}}{\text{20}}\\ \text{Gopi}\text{=}\frac{\text{3}}{\text{15}}\text{+}\frac{\text{2}}{\text{20}}\text{=}\frac{\text{18}}{\text{60}}\\ \text{Hence new profit sharing ratio of Radha, Rukmani and Gopi}\\ \text{=}\frac{\text{6}}{\text{15}}\text{:}\frac{\text{6}}{\text{20}}\text{:}\frac{\text{18}}{\text{60}}\\ \text{= 4:3:3}\end{array}

Q.34 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 ¼ of his share in favour of Jain and Khan surrendered 1/5 in favour of Jain. Calculate new profit sharing ratio.

Ans.

\begin{array}{l}\text{Old ratio = 3:2:3}\\ \text{Singh’s sacrifice =}\frac{\text{1}}{\text{3}}\text{x}\frac{\text{3}}{\text{8}}\text{=}\frac{\text{3}}{\text{24}}\\ \text{Gupta’s sacrifice =}\frac{\text{1}}{\text{4}}\text{x}\frac{\text{2}}{\text{8}}\text{=}\frac{\text{2}}{\text{32}}\\ \text{Khan’s sacrifice =}\frac{\text{1}}{\text{5}}\text{x}\frac{\text{3}}{\text{8}}\text{=}\frac{\text{3}}{\text{40}}\\ \text{New share = old share – sacrifice}\\ \text{New share =}\\ \text{Singh =}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{3}}{\text{24}}\text{=}\frac{\text{6}}{\text{24}}\\ \text{Gupta =}\frac{\text{2}}{\text{8}}\text{–}\frac{\text{2}}{\text{32}}\text{=}\frac{\text{6}}{\text{32}}\\ \text{Khan}\text{=}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{3}}{\text{40}}\text{=}\frac{\text{12}}{\text{40}}\\ \text{Jain}\text{=}\frac{\text{3}}{\text{24}}\text{+}\frac{\text{2}}{\text{32}}\text{+}\frac{\text{3}}{\text{40}}\text{=}\frac{\text{126}}{\text{480}}\\ \text{Hence new profit sharing ratio of Singh, Gupta,}\text{Khan}\text{and Jain}\\ \text{=}\frac{\text{6}}{\text{24}}\text{:}\frac{\text{6}}{\text{32}}\text{:}\frac{\text{12}}{\text{40}}\text{:}\frac{\text{126}}{\text{480}}\\ \text{= 120:90:144:126}\\ \text{=}\text{20:15:24:21}\end{array}

Q.35 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.

Ans.

\begin{array}{l}\text{Sacrificing ratio = Old ratio – New ratio}\\ \text{New ratio = 4:2:1}\\ \text{Old ratio = 5:3}\\ \text{Sacrificing ratio}\\ \text{Sandeep =}\frac{\text{5}}{\text{8}}\text{–}\frac{\text{4}}{\text{7}}\text{=}\frac{\text{3}}{\text{56}}\\ \text{Navdeep =}\frac{\text{3}}{\text{8}}\text{–}\frac{\text{2}}{\text{7}}\text{=}\frac{\text{5}}{\text{56}}\\ \text{=}\frac{\text{3}}{\text{56}}\text{:}\frac{\text{5}}{\text{56}}\\ \text{= 3:5}\end{array}

Q.36 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.

Ans.

\begin{array}{l}\text{Let the total share = 1}\\ \text{Ravi’s Share =}\frac{\text{1}}{\text{8}}\\ \text{Remaining Rao and Swami}\\ \text{1 –}\frac{\text{1}}{\text{8}}\text{=}\frac{\text{7}}{\text{8}}\\ \text{New ratio}\\ \text{Rao =}\frac{\text{7}}{\text{8}}\text{x}\frac{\text{4}}{\text{7}}\text{=}\frac{\text{28}}{\text{56}}\\ \text{Swami =}\frac{\text{7}}{\text{8}}\text{x}\frac{\text{3}}{\text{7}}\text{=}\frac{\text{21}}{\text{56}}\\ \text{Hence new profit sharing ratio of Rao, Swami and Ravi}\\ \text{=}\frac{\text{28}}{\text{56}}\text{:}\frac{\text{21}}{\text{56}}\text{:}\frac{\text{1}}{\text{8}}\\ \text{= 28:21:7}\\ \text{= 4:3:1}\end{array} \begin{array}{l}\text{Sacrificing ratio = Old ratio – New ratio}\\ \text{New ratio = 4:3:1}\\ \text{Old ratio = 3:2}\\ \text{Sacrificing ratio}\\ \text{Rao =}\frac{\text{3}}{\text{5}}\text{–}\frac{\text{4}}{\text{8}}\text{=}\frac{\text{4}}{\text{40}}\\ \text{Swami =}\frac{\text{2}}{\text{5}}\text{–}\frac{\text{3}}{\text{8}}\text{=}\frac{\text{1}}{\text{40}}\\ \text{=}\frac{\text{4}}{\text{40}}\text{:}\frac{\text{1}}{\text{40}}\\ \text{= 4:1}\end{array}

Q.37 Compute the value of goodwill on the basis of four year’s purchase of the average profits based on the last five years. The profits for the last five years were as follows:

Ans.

Goodwill = Average profits x number of years purchase

= ₹52,000 x 4 = ₹2,08,000

\begin{array}{l}\text{Average profit of last 5 years}\\ \text{=}\frac{\text{₹40,000+₹50,000+₹60,000+₹50,000+₹60,000}}{\text{5}}\\ \text{=}\text{₹}\text{52,000}\end{array}

Q.38 Firm’s Capital in a business is ₹2,00,000. The normal rate of return on Firm’s capital is 15%. During the year 2015 the firm earned a profit of ₹48,000. Calculate goodwill on the basis of 3 years purchase of super profit.

Ans.

\begin{array}{l}\text{Super profit}\text{=}\text{Actual profit}\text{–}\text{Normal profit}\\ \text{Goodwill}\text{=}\text{Super profit}\text{×}\text{Number of years purchase}\\ \begin{array}{l}\text{Normal profit = 2,00,000 ×}\frac{\text{15}}{\text{100}}\text{=}\text{₹30,000}\hfill \end{array}\\ \text{Super profit =}\text{₹48,000 – ₹30,000 =}\text{₹18,000}\\ \text{= ₹54,000}\text{.}\end{array}

Q.39 The books of Ram and Bharat showed that the Firm’s capital on 31/12/2016 was ₹5,00,000 and the profits for the last 5 years: 2015 ₹40,000; 2014 ₹50,000; 2013 ₹55,000; 2012 ₹70,000 and 2011 ₹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%.

Ans.

\begin{array}{l}\text{Average profit of last 5 years}\\ \text{=}\frac{\text{40,000+50,000+55,000+70,000+85,000}}{\text{5}}\\ \text{=}\text{₹}\text{60,000}\\ \text{Normal profit = 5,00,000 ×}\frac{\text{10}}{\text{100}}\text{=}\text{₹}\text{50,000}\end{array}

Super profit = 60,000 – 50,000 = ₹10,000

Goodwill = ₹10,000 × 3 = ₹30,000

Q.40 Rajan and Rajani are partners in a firm. Their capitals were Rajan ₹3,00,000; Rajani ₹2,00,000. During the year 2015 the firm earned a profit of ₹1,50,000. Calculate the value of goodwill of the firm by capitalization method assuming that the normal rate of return is 20%.

Ans.

\begin{array}{l}\text{Total capital of the firm =}\\ \text{(₹3,00,000 +}\text{₹2,00,000) =}\text{₹5,00,000}\\ \text{Capitalised value}\\ \text{=}\frac{\text{Actual value × 100}}{\text{Normal rate of return}}\\ \text{= 1,50,000 ×}\frac{\text{100}}{\text{20}}\text{=}\text{₹}\text{7,50,000}\\ \text{Goodwill}\text{=}\text{Capitalised value}-\text{Actual capital}\\ \text{=}\text{₹7,50,000 –}\text{₹5,00,000 =}\text{₹2,50,000}\end{array}

Q.41 A business has earned average profits of ₹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 ₹10,00,000 and its external liabilities are ₹1,80,000. The normal rate of return is 10%?

Ans.

Capital employed = Assets – External liabilities

= ₹10,00,000 – ₹1,80,000 = ₹8,20,000

Estimated capital required to earn average profit ₹1,00,000 @ normal return 10%.

\begin{array}{l}\text{Normal profit = 1,00,000 x}\frac{\text{100}}{\text{10}}\text{=}\text{₹}\text{10,00,000}\\ \end{array}