Goodwill Settlement

Under the old ratio, B’s share was \(\frac{5}{15}\) and C’s share was \(\frac{3}{15}\). Under the new ratio of 2:1, B’s share is \(\frac{2}{3}=\frac{10}{15}\) and C’s share is \(\frac{1}{3}=\frac{5}{15}\). Therefore, B gains \(\frac{10}{15}-\frac{5}{15}=\frac{5}{15}\), while C gains \(\frac{5}{15}-\frac{3}{15}=\frac{2}{15}\). Hence, the gaining ratio is 5:2. Exam tip: calculate each continuing partner’s gain as new share minus old share before forming the ratio.

A negative result shows that the partner has sacrificed share. Such partner is not charged goodwill burden.

The total profit-sharing ratio is \(7+5+4=16\). C's share is \(\frac{4}{16}\). Therefore, C's share of goodwill is \(₹1,92,000 \times \frac{4}{16}=₹48,000\). The other amounts represent incorrect fractions of the total goodwill: 3/16, 5/16 and 7/16. Exam tip: To calculate a partner's share of goodwill, multiply total goodwill by that partner's fraction of the profit-sharing ratio.

The retiring partner share is ₹60000. In 7:5 the second partner burden is (60000 \times \frac{5}{12}=25000).

The retiring partner share is ₹44000. The first partner burden is (44000 \times \frac{3}{11}=12000).

B sacrifice is ( \frac{5}{15}-\frac{2}{7}=\frac{1}{21} ). Therefore compensation is (210000 \times \frac{1}{21}=10000).

A gain is ( \frac{7}{10}-\frac{5}{15}=\frac{11}{30} ). Therefore total burden is (225000 \times \frac{11}{30}=82500).

When old goodwill is written off, the partners’ capital or current accounts are debited in the old profit-sharing ratio. Partner B’s share is \(\frac{5}{4+5+2}=\frac{5}{11}\). Therefore, the amount debited to B’s account is \(₹1,87,000\times\frac{5}{11}=₹85,000\). Exam tip: Always use the sum of all ratio terms as the denominator; using 5 alone as the denominator gives an incorrect result.

When old goodwill is written off, each partner’s account is debited with their share according to the old profit-sharing ratio. Partner C’s share is \(\frac{7}{7+4+7}=\frac{7}{18}\). Therefore, the amount debited is \(₹1,62,000\times\frac{7}{18}=₹63,000\). ₹36,000 represents the 4/18 share and therefore is not C’s amount. Exam tip: Use the old ratio when writing off existing goodwill.

B debit for old goodwill is ₹24000 and credit for new goodwill is ₹60000. Net effect is ₹36000 credit.

C debit for old goodwill is ₹48000 and credit for new goodwill is ₹80000. Net effect is ₹32000 credit.

The direct answer is B, ₹36,000. The retiring partner’s goodwill claim is ₹99,000, and the gaining ratio of the continuing partners is 4:7. The total ratio is 4 + 7 = 11. Therefore the first gaining partner’s fraction of the goodwill is 4/11. His debit is ₹99,000 × 4/11. Since ₹99,000 ÷ 11 = ₹9,000, the amount is ₹9,000 × 4 = ₹36,000. Option B is correct. Option A, ₹27,000, equals 3/11 of ₹99,000 and does not use the first partner’s ratio of 4. Option C, ₹63,000, is the second partner’s amount, because ₹99,000 × 7/11 = ₹63,000. Option D, ₹99,000, is the whole goodwill claim, not the first partner’s share. In the direct method, gaining partners are debited and the retiring partner is credited with the amount due. Memory cue: divide the total goodwill according to the gaining ratio, then debit each gainer’s own portion.

Under the memorandum method, when goodwill is recorded, the old partners’ capital accounts are credited in the old profit-sharing ratio. Partner C’s share is 4/9. Therefore, the amount credited is ₹1,80,000 × 4/9 = ₹80,000. ₹60,000 represents a 3/9 share, not C’s share. Exam tip: Use the old ratio when goodwill is raised and the new ratio when it is written off.

The direct answer is C, ₹300,000. For weighted average profit, multiply each profit by its weight, add the weighted profits, and divide by the total of the weights. The products are ₹60,000 × 1 = ₹60,000, ₹90,000 × 2 = ₹180,000, and ₹120,000 × 3 = ₹360,000. Their total is ₹600,000. The total weight is 1 + 2 + 3 = 6. Weighted average profit = ₹600,000/6 = ₹100,000. Goodwill at three years’ purchase = ₹100,000 × 3 = ₹300,000. Option C is correct. Option A, ₹200,000, uses only two years’ purchase. Option B, ₹250,000, does not follow the stated weighted calculation. Option D, ₹360,000, is not three times the correct average; it is merely one possible distractor based on an incorrect computation. The important point is that higher weights give greater influence to the corresponding profits. Memory cue: multiply, add, divide by total weights, then multiply by years’ purchase.

The adjusted second year profit is ₹90000 and adjusted total profit is ₹290000. At 3 years purchase goodwill is ₹290000.

The adjusted third year profit is ₹75000 and average profit is ₹125000. At 2 years purchase goodwill is ₹250000.

Normal profit = ₹16,00,000 × 11% = ₹1,76,000. Therefore, super profit = average profit − normal profit = ₹2,15,000 − ₹1,76,000 = ₹39,000. Goodwill at four years’ purchase = ₹39,000 × 4 = ₹1,56,000, so option C is correct. Option A represents only one year’s super profit, not four years’ purchase. Exam tip: calculate normal profit first, subtract it from average profit, and then multiply the super profit by the number of years’ purchase.

Capitalized value is (330000 \times \frac{100}{15}=2200000). Goodwill is ₹2200000 minus ₹1800000 which is ₹400000.

Goodwill is (55000 \times 3.60478=198262.9) which is approximately ₹198263. Multiply super profit by the annuity factor.

The excess ₹66000 is his ( \frac{11}{30} ) share. Total hidden goodwill is (66000 \times \frac{30}{11}=180000).

The direct answer is C, ₹180000. The retiring partner’s adjusted capital is ₹240000, while the amount due is ₹294000. First find the excess amount: ₹294000 − ₹240000 = ₹54000. This excess represents the retiring partner’s share of hidden goodwill, namely 3/10 of the total goodwill. Let total hidden goodwill be G. Then \\(3/10\\) of G = ₹54000, so G = ₹54000 × 10/3 = ₹180000. Option C is correct. A, ₹54000, is only the retiring partner’s share of goodwill, not the total hidden goodwill. B, ₹126000, does not follow from the given fraction. D, ₹294000, is the total amount due, not goodwill. Memory cue: excess due ÷ partner’s fraction = total hidden goodwill.

Hidden goodwill is indicated by excess amount due. If there is no excess amount hidden goodwill is not calculated.

A deceased partner’s account may include several independent amounts due from the firm. Goodwill represents compensation for the partner’s share in the firm’s reputation and future earning capacity. Profit up to the date of death represents the partner’s share of profit earned during the part of the accounting period in which the partner was alive and associated with the firm. These arise for different reasons, so they are two separate entitlements. Choice A is correct.

The goodwill amount is calculated under the agreed goodwill method and adjusted through the partners’ capital or current accounts. Profit up to death is calculated using the appropriate time, sales, or estimated-profit basis. One item is not deducted from the other merely because both are credited to the deceased partner’s account. They must be calculated, recorded, and explained separately.

A negative result shows that new share is less than old share. It is treated as sacrifice and not gain.

In average profit method average profit is multiplied by years purchase. In super profit method normal profit is deducted first.