Solutions of DK Goel Class 12 Chapter 2 Change in Profit Sharing Ratio among the Existing Partners [2025-26]
Table of Contents
Sacrificing and Gaining Ratio:
Question No. 1 to 2
Question 1(a)
X and Y were partners in a firm sharing …….. gain or sacrifice due to change in ratio.
(b) A and B were in partnerhip sharing ….. gain or sacrifice due to change in ratio.
Question 2 (a)
A, B and C were in partnership sharing …… gain or sacrifice due to change in ratio.
(b) Mahesh, Naresh and Om were partners …… due to change in ratio.
Solutions of DK Goel Class 12 Chapter 2 Change in Profit Sharing Ratio among the Existing Partners [2025-26]
Valuation of Goowill – Averaage Profit Method
Question No. 3 to 9
Question 3:
The goodwill of a firm is ……… Calculate the amount of goodwill.
Solution
Profits after adjustment:
2019-20 = 2,00,000
2020-21 = -3,00,000
2021-22 = 4,50,000 – 50,000 = 4,00,000
2022-23 = 3,50,000 + 90,000 = 4,40,000
2023-24 = 2,60,000
Average Profit = \(\frac{2,00,000 – 3,00,000 + 4,00,000 + 4,40,000 +2,60,000}{5}\) = \(\frac{10,00,000}{5}\) = 2,00,000
Goodwill = Average Profit \(\times\) Number of years’ purchase
\(\quad\)\(\quad\)\(\quad\)\(\;\) = 2,00,000\(\times\) 4 = ₹ 8,00,000
Question 4:
X purchased the business of Y …… Calculate the amount of goodwill.
Solution
Profits after adjustment:
31st March 2021 = 1,00,000 + 50,000 = 1,50,000
31st March 2022 = -1,50,000 + 80,000 + 60,000 = -10,000
31st March 2023 = 1,50,000 + (40,000 \(\times\) 2 ) – 6,000 = 2,24,000
31st March 2024 = 2,00,000 – 8,000 = 1,92,000
Average Profit = \(\frac{1,50,000 – 10,000 + 2,24,000 + 1,92,000}{4}\) = \(\frac{5,56,000}{4}\) = 1,39,000
Goodwill = Average Profit \(\times\) Number of years’ purchase
\(\quad\)\(\quad\)\(\quad\)\(\;\) = 1,39,000\(\times\) 100% = ₹ 1,39,000
Question 5:
A, B and C are partners in a firm ……. Calculate the amount of goodwill.
Solution
Average Profit of the previous four years = \(\frac{1,20,000 + 1,50,000 + 1,10,000 + 2,00,000}{4}\) = \(\frac{5,80,000}{4}\) = 1,45,000
Average Profit of the previous five years = \(\frac{1,30,000 + 1,20,000 + 1,50,000 + 1,10,000 + 2,00,000}{5}\) = \(\frac{7,10,000}{5}\) = 1,42,000
Average profit of the last 4 years is higher.
Goodwill = Average Profit of the previous four years \(\times\) Number of years’ purchase
\(\quad\)\(\quad\)\(\quad\)\(\;\) = 1,45,000\(\times\) 3 = ₹ 4,35,000
Question 6:
A, B and C are partners sharing profits and losses …… Calculate the amount of goodwill.
Solution
Profits after adjustment:
31st March 2019 = 60,000
31st March 2020 = 1,50,000
31st March 2021 = – 20,000
31st March 2022 = 2,00,000
31st March 2023 = 1,85,000 + 40,000 – 5,000 = 2,20,000
Average Profit = \(\frac{60,000 + 1,50,000 – 20,000 + 2,00,000 + 2,20,000}{5}\) = \(\frac{6,10,000}{5}\) = 1,22,000
Goodwill = Average Profit \(\times\) Number of years’ purchase
\(\quad\)\(\quad\)\(\quad\)\(\;\) = 1,22,000\(\times\) 3 = ₹ 3,66,000
Question 7:
The profits earned by a firm during the last four …… to the profits for 2021, 2022, 2023 and 2024.
Solution
Calculation of weighted Average Profit
| Years | Profit | Weight | Product |
| 2021 2022 2023 2024 | 80,000 1,00,000 1,10,000 1,50,000 | 1 2 3 4 | 80,000 2,00,000 3,30,000 6,00,000 |
| Total | 10 | 12,10,000 |
Weighted Average Profit = \(\frac{Total Weighted Average Profit}{Total Weights}\)
\(\quad \quad \quad \quad \quad \quad \quad\quad\quad\) = \(\frac{12,10,000}{10}\) = 1,21,000
Goodwill = Weighted Average Proift \(\times\) 3 years of purchase
\(\quad \quad\quad \quad\) = 1,21,000 \(\times\) 3 = ₹ 3,63,000
Question 8:
Following information is available about the business ….. 2022:-1; 2023:-2; 2024:-3.
Solution
Calculation of weighted Average Profit
| Years | Profit | Weight | Product |
| 2022 2023 2024 | 39,600 42,600 48,600 | 1 2 3 | 39,600 85,200 1,45,800 |
| Total | 6 | 2,70,600 |
Weighted Average Profit = \(\frac{Total Weighted Average Profit}{Total Weights}\)
\(\quad \quad \quad \quad \quad \quad \quad\quad\quad\) = \(\frac{2,70,600}{6}\) = 45,100
Goodwill = Weighted Average Proift \(\times\) 2 years of purchase
\(\quad \quad\quad \quad\) = 45,100 \(\times\) 2 = ₹ 90,200
Question 9:
Calculate the value of goodwill on …… 20% p.a. on diminishing balance method.
Solution
Calculation of weighted Average Profit
| Years | Profit | Weight | Product |
| 2019 2020 2021 2022 2023 | 40,000 1,86,500 (60,000) 1,29,000 2,10,200 | 1 2 3 4 5 | 40,000 3,73,000 (1,80,000) 5,16,000 10,51,000 |
| Total | 15 | 18,00,000 |
Weighted Average Profit = \(\frac{Total Weighted Average Profit}{Total Weights}\)
\(\quad \quad \quad \quad \quad \quad \quad\quad\quad\) = \(\frac{18,00,000}{15}\) = 1,20,000
Goodwill = Weighted Average Proift \(\times\) 3 years of purchase
\(\quad \quad\quad \quad\) = 1,20,000 \(\times\) 3 = ₹ 3,60,000
Solutions of DK Goel Class 12 Chapter 2 Change in Profit Sharing Ratio among the Existing Partners [2025-26]
Super Profit Method:
Questions No. 10 to 15
Question 10:
A firm earned profits of ₹ 80,000, ……. of average super profits of last four years.
Solution
Average Profit = \(\frac{80,000 + 1,00,000 + 1,20,000 + 1,80,000}{4}\) = \(\frac{4,80,000}{4}\) = 1,20,000
Normal Profit = Capital employed \(\times\) Normal Rate of Return
\(\quad \quad \quad \quad\) = 5,00,000 \(\times\) \(\frac{15}{100}\) = 75,000
Super Profit = Average Profit – Normal Profit = 1,20,000 – 75,000 = 45,000
Goodwill = Super Profit \(\times\) 3 years of purchase
\(\quad \quad \quad \quad\) = 45,000 \(\times\) 3 = 1,35,000
Question 11:
Capital invested in a firm is ……… Calculate goowill at five times the super profits.
Solution
Average Profit = 41,000 + 2,000 = 43,000
Normal Profit = Capital employed \(\times\) Normal Rate of Return
\(\quad \quad \quad \quad\) = 3,00,000 \(\times\) \(\frac{10}{100}\) = 30,000
Super Profit = Average Profit – Normal Profit = 43,000 – 30,000 = 13,000
Goodwill = Super Profit \(\times\) 5 years of purchase
\(\quad \quad \quad \quad\) = 13,000 \(\times\) 5 = 65,000
Question 12:
The Capital of the firm of Anuj and Benu is …… Calculate the goodwill of the firm.
Solution
Average Profit = \(\frac{2,80,000 + 3,80,000 + 4,20,000 – (60,000 \times 3 \times 2)}{3}\) = \(\frac{7,20,000}{3}\) = 2,40,000
Normal Profit = Capital employed \(\times\) Normal Rate of Return
\(\quad \quad \quad \quad\) = 10,00,000 \(\times\) \(\frac{15}{100}\) = 15,000
Super Profit = Average Profit – Normal Profit = 2,40,000 – 1,50,000 = 90,000
Goodwill = Super Profit \(\times\) 2 years of purchase
\(\quad \quad \quad \quad\) = 90,000 \(\times\) 2 = 1,80,000
Question 13:
Find out the capital employed from …….. 3 years purchased of Super Profits.
Solution
Average Profit = \(\frac{80,000 + 1,30,000 + 1,56,000}{3}\) = \(\frac{3,66,000}{3}\) = 1,22,000
Normal Profit = Capital employed \(\times\) Normal Rate of Return
Let Capital employed be ₹ x.
\(\quad \quad \quad \quad\) = x \(\times\) \(\frac{12}{100}\) = \(\frac{12x}{100}\)
Super Profit = Average Profit – Normal Profit = 1,22,000 – \(\frac{12x}{100}\)
Goodwill = Super Profit \(\times\) 3 years of purchase
1,50,000 = [1,22,000 – \(\frac{12x}{100}\) ]\(\times\) 3
\(\frac{1,50,000}{3}\) = 1,22,000 – \(\frac{12x}{100}\)
\(\frac{12x}{100}\) = 1,22,000 – 50,000 = 72,000
x = 72,000 \(\times \frac{100}{12}\) = 6,00,000
So, Capital employed = 6,00,000
Question 14:
A and B are partners. They admit C …… calculate C’s share of goodwill.
Solution
Average Profit = 2,00,000
Capital Employed = Partners’ capital + General Reserve + Profit & Loss (cr.) = 5,00,000 + 4,00,000 + 1,50,000 + 30,000 = 10,80,000
Normal Profit = Capital employed \(\times\) Normal rate of return = 10,80,000 \(\times\) 15% = 1,62,000
Super Profit = Average Proift – Normal Profit = 2,00,000 – 1,62,000 = 38,000
Goodwill = Super Profit \(\times \) 3 years purchase = 38,000 \(\times\) 3 = 1,14,000
C’s share in goodwill = 1,14,000 \(\times\) 1/4 = 28,500
Question 15:
On April 1st 2024, an existing firm …… find the average profits of the firm.
Solution
Goodwill = 64,000 and Number of year’s purchase = 4
Goodwill = Super Profit \(\times\) No. year’s purchase
Super Profit = 64,000/4 = 16,000
Normal Profit = Capital employed \(\times\) Normal Rate of Return
Capital employed = 3,80,000 + 90,000 = 4,70,000
Normal Profit = 4,70,000 \(\times\) 20% = 94,000
Supter Profit = Average Profit – Normal Profit
16,000 = Average Profit – 94,000
Average Profit = 16,000 + 94,000 = ₹ 1,10,000
Solutions of DK Goel Class 12 Chapter 2 Change in Profit Sharing Ratio among the Existing Partners [2025-26]
Capitlisation Method
Questions No. 16 to 19
Question 16:
The Average profits of a firm is ₹ 48,000. ……… Calculate goodwill from capitalisation of average proifts method.
Solution
Capitlsed value of Average Profit = Average Profit × \(\frac{100}{Normal Rate of Return}\)
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 48,000 × \(\frac{100}{12}\) = ₹ 4,00,000
Capital Employed = Assets – Outside Liabilities
\(\quad\quad\quad\quad\quad\quad\quad\quad\)= 8,00,000 – 5,00,000 = ₹ 3,00,000
Goodwill of the firm = Capital value of Average Profit – Capital Employed
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 4,00,000 – 3,00,000 = ₹ 1,00,000
Question 17:
Anupma, Purnima and Ruchika ara partners ……… goodwill by Capitalisation of Average Profit Method.
Solution
Capital Employed = Partner’s capitals + Parntners’ Current = 6,00,000 – 60,000 + 5,00,000 – 30,000 + 5,00,000 +10,000 = ₹ 15,20,000
Capitalised Value of Average Profit = Average Profit × \(\frac{100}{Normal Rate of Return}\)
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 2,40,000 × \(\frac{100}{12}\) = ₹ 20,00,000
Goodwill of the firm = Capital value of Average Profit – Capital Employed
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 20,00,000 – 15,20,000 = ₹ 4,80,000
Question 18:
Calculate the value of goodwill according ….. Super Profit Method in the previous Q. 16.
Solution
Capital Employed = Assets – Outside Liabilities = 8,00,000 – 5,00,000 = ₹ 3,00,000
Normal Profit = Capital Employed × \(\frac{Normal Rate of Return}{100}\)
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 3,00,000 × \(\frac{12}{100}\) = ₹ 36,000
Super Profit = Average Profit – Normal Profits = 48,000 – 36,000 = 12,000
Goodwill of the firm = Super Profit × \(\frac{100}{Normal Rate of Return}\)
\(\quad\quad\quad\quad\quad\quad\quad\quad\) = 12,000 × \(\frac{100}{12}\)= ₹ 1,00,000
Question 19:
The following information relates to a …….. (iv) Capitalisation of Super Profits ₹ 80,000.
Solution
(i) Average Profit = \(\frac{20,000 + 60,000 – 10,000 + 60,000 + 50,000 + 72,000}{6}\)
\(\quad\quad\quad\quad\) = \(\frac{2,52,000}{6}\) = 42,000
Goodwill of the firm = Average Profit × 4 years’s purchase
\(\quad\quad\quad\quad\) = 42,000 × 4 = 1,68,000
(ii) Normal Profit = Capital Employed × \(\frac{Normal Rate of Return }{100}\)
= 2,00,000 × \(\frac{15}{100}\) = 30,000
Super Profit = Average Profit – Normal Profit
= 42,000 – 30,000 = 12,000
Goodwill of the firm = Average Profit × 4 years’s purchase
\(\quad\quad\quad\quad\) = 12,000 × 4 = 48,000
(iii) Capitalised value of Average Profit = Average Profit × \(\frac{100}{Normal Rate of Return}\)
= 42,000 × \(\frac{100}{15}\) = 2,80,000
Goodwill of the firm = Capitalised Value of Average Profit – Capital employed
\(\quad\quad\quad\quad\) =2,80,000 – 2,00,000 = 80,000
(iv) Normal Profit = Capital Employed × \(\frac{Normal Rate of Return}{100}\)
= 2,00,000 × \(\frac{15}{100}\) = 30,000
Super Profit = Average Profit – Normal Profit = 12,000
Capitalised value of super profit = Super Profit × \(\frac{100}{Normal Rate of Return}\)
= 12,000× \(\frac{100}{15}\) 80,000
