CBSE Class 12 Accountancy: Reconstitution of a Partnership Firm – Admission of a Partner NCERT Solutions

The old profit sharing ratio of Singh, Gupta, and Khan is 3:2:3. The total shares are 3+2+3 = 8.

Old shares are: Singh = $3/8$, Gupta = $2/8$, Khan = $3/8$.

Calculate the sacrifice made by each old partner:

Singh's sacrifice = $1/3$ of his share = $1/3\; \backslash times\; 3/8\; =\; 3/24$

Gupta's sacrifice = $1/4$ of his share = $1/4\; \backslash times\; 2/8\; =\; 2/32$

Khan's sacrifice = $1/5$ of his share = $1/5\; \backslash times\; 3/8\; =\; 3/40$

Now, calculate the new share of each old partner by subtracting their sacrifice from their old share:

Singh's new share = Old share - Sacrifice = $3/8\; -\; 3/24$

To subtract, find a common denominator, which is 24: $\backslash frac\{3\; \backslash times\; 3\}\{8\; \backslash times\; 3\}\; -\; \backslash frac\{3\}\{24\}\; =\; \backslash frac\{9\}\{24\}\; -\; \backslash frac\{3\}\{24\}\; =\; \backslash frac\{6\}\{24\}$

Gupta's new share = Old share - Sacrifice = $2/8\; -\; 2/32$

To subtract, find a common denominator, which is 32: $\backslash frac\{2\; \backslash times\; 4\}\{8\; \backslash times\; 4\}\; -\; \backslash frac\{2\}\{32\}\; =\; \backslash frac\{8\}\{32\}\; -\; \backslash frac\{2\}\{32\}\; =\; \backslash frac\{6\}\{32\}$

Khan's new share = Old share - Sacrifice = $3/8\; -\; 3/40$

To subtract, find a common denominator, which is 40: $\backslash frac\{3\; \backslash times\; 5\}\{8\; \backslash times\; 5\}\; -\; \backslash frac\{3\}\{40\}\; =\; \backslash frac\{15\}\{40\}\; -\; \backslash frac\{3\}\{40\}\; =\; \backslash frac\{12\}\{40\}$

Jain's share is the sum of the sacrifices made by Singh, Gupta, and Khan:

Jain's share = Singh's sacrifice + Gupta's sacrifice + Khan's sacrifice = $3/24\; +\; 2/32\; +\; 3/40$

To add these fractions, find a common denominator for 24, 32, and 40. The least common multiple (LCM) is 480.

$\backslash frac\{3\; \backslash times\; 20\}\{24\; \backslash times\; 20\}\; +\; \backslash frac\{2\; \backslash times\; 15\}\{32\; \backslash times\; 15\}\; +\; \backslash frac\{3\; \backslash times\; 12\}\{40\; \backslash times\; 12\}\; =\; \backslash frac\{60\}\{480\}\; +\; \backslash frac\{30\}\{480\}\; +\; \backslash frac\{36\}\{480\}\; =\; \backslash frac\{60\; +\; 30\; +\; 36\}\{480\}\; =\; \backslash frac\{126\}\{480\}$

The new profit sharing ratio is Singh : Gupta : Khan : Jain, which is $\backslash frac\{6\}\{24\}:\backslash frac\{6\}\{32\}:\backslash frac\{12\}\{40\}:\backslash frac\{126\}\{480\}$.

To simplify this ratio, convert all fractions to have a common denominator of 480:

Singh's share = $\backslash frac\{6\; \backslash times\; 20\}\{24\; \backslash times\; 20\}\; =\; \backslash frac\{120\}\{480\}$

Gupta's share = $\backslash frac\{6\; \backslash times\; 15\}\{32\; \backslash times\; 15\}\; =\; \backslash frac\{90\}\{480\}$

Khan's share = $\backslash frac\{12\; \backslash times\; 12\}\{40\; \backslash times\; 12\}\; =\; \backslash frac\{144\}\{480\}$

Jain's share = $\backslash frac\{126\}\{480\}$

The new profit sharing ratio is 120:90:144:126.

This ratio can be simplified by dividing each part by their greatest common divisor, which is 6.

120 ÷ 6 = 20

90 ÷ 6 = 15

144 ÷ 6 = 24

126 ÷ 6 = 21

Therefore, the new profit sharing ratio is 20:15:24:21.

The old profit sharing ratio of Sandeep and Navdeep is 5:3. The total shares are 5+3 = 8.

Old shares are: Sandeep = $5/8$, Navdeep = $3/8$.

The new profit sharing ratio of Sandeep, Navdeep, and C is 4:2:1. The total shares are 4+2+1 = 7.

New shares are: Sandeep = $4/7$, Navdeep = $2/7$, C = $1/7$.

The sacrificing ratio is calculated as: Old Ratio - New Ratio.

Sandeep's sacrifice = Old share - New share = $5/8\; -\; 4/7$

To subtract these fractions, find a common denominator, which is 56:

$\backslash frac\{5\; \backslash times\; 7\}\{8\; \backslash times\; 7\}\; -\; \backslash frac\{4\; \backslash times\; 8\}\{7\; \backslash times\; 8\}\; =\; \backslash frac\{35\}\{56\}\; -\; \backslash frac\{32\}\{56\}\; =\; \backslash frac\{3\}\{56\}$

Navdeep's sacrifice = Old share - New share = $3/8\; -\; 2/7$

To subtract these fractions, find a common denominator, which is 56:

$\backslash frac\{3\; \backslash times\; 7\}\{8\; \backslash times\; 7\}\; -\; \backslash frac\{2\; \backslash times\; 8\}\{7\; \backslash times\; 8\}\; =\; \backslash frac\{21\}\{56\}\; -\; \backslash frac\{16\}\{56\}\; =\; \backslash frac\{5\}\{56\}$

The sacrificing ratio is the ratio of the sacrifices made by Sandeep and Navdeep.

Sacrificing Ratio = Sandeep's sacrifice : Navdeep's sacrifice = $\backslash frac\{3\}\{56\}:\backslash frac\{5\}\{56\}$

This simplifies to 3:5.

The old profit sharing ratio of Rao and Swami is 3:2. The total shares are 3+2 = 5.

Old shares are: Rao = $3/5$, Swami = $2/5$.

Ravi is admitted for a $1/8$ share in the profits.

The remaining share for the old partners (Rao and Swami) is $1\; -\; 1/8\; =\; 7/8$.

This remaining share of $7/8$ is to be shared between Rao and Swami in their new ratio of 4:3.

Calculate the new shares of Rao and Swami:

Rao's new share = Remaining share × Rao's new ratio part = $7/8\; \backslash times\; 4/7\; =\; 28/56$

Swami's new share = Remaining share × Swami's new ratio part = $7/8\; \backslash times\; 3/7\; =\; 21/56$

Ravi's share is given as $1/8$. To express this with a denominator of 56, multiply by 7/7:

Ravi's share = $1/8\; \backslash times\; 7/7\; =\; 7/56$

The new profit sharing ratio of Rao : Swami : Ravi is $28/56\; :\; 21/56\; :\; 7/56$.

This simplifies to 28:21:7. Dividing by their greatest common divisor, 7, we get the simplified new profit sharing ratio as 4:3:1.

Now, calculate the sacrificing ratio. Sacrificing ratio = Old Ratio - New Ratio.

Rao's sacrifice = Old share - New share = $3/5\; -\; 28/56$

To subtract, find a common denominator, which is 56:

$\backslash frac\{3\; \backslash times\; 56\}\{5\; \backslash times\; 56\}\; -\; \backslash frac\{28\; \backslash times\; 5\}\{56\; \backslash times\; 5\}\; =\; \backslash frac\{168\}\{280\}\; -\; \backslash frac\{140\}\{280\}\; =\; \backslash frac\{28\}\{280\}$

Swami's sacrifice = Old share - New share = $2/5\; -\; 21/56$

To subtract, find a common denominator, which is 280:

$\backslash frac\{2\; \backslash times\; 56\}\{5\; \backslash times\; 56\}\; -\; \backslash frac\{21\; \backslash times\; 5\}\{56\; \backslash times\; 5\}\; =\; \backslash frac\{112\}\{280\}\; -\; \backslash frac\{105\}\{280\}\; =\; \backslash frac\{7\}\{280\}$

The sacrificing ratio of Rao and Swami is $28/280\; :\; 7/280$.

This simplifies to 28:7. Dividing by their greatest common divisor, 7, we get the sacrificing ratio as 4:1.

To compute the value of goodwill using the average profit method, we first need to calculate the average profit over the last five years.

The profits for the last five years are: ₹40,000, ₹50,000, ₹60,000, ₹50,000, and ₹60,000.

Total profit = $40,000\; +\; 50,000\; +\; 60,000\; +\; 50,000\; +\; 60,000\; =\; 2,60,000$

Average profit = Total Profit / Number of years

Average profit = $2,60,000\; /\; 5\; =\; 52,000$

The problem states that goodwill is to be valued on the basis of four years' purchase of the average profits.

Goodwill = Average Profit × Number of years' purchase

Goodwill = $52,000\; \backslash times\; 4\; =\; 2,08,000$

Therefore, the value of goodwill is ₹2,08,000.

To calculate goodwill using the super profit method, we need to determine the normal profit and then the super profit.

Given:

Capital Employed = ₹2,00,000

Normal Rate of Return = 15%

Actual Profit (for the year 2002) = ₹48,000

First, calculate the Normal Profit:

Normal Profit = Capital Employed × Normal Rate of Return

Normal Profit = $2,00,000\; \backslash times\; \backslash frac\{15\}\{100\}\; =\; 30,000$

Next, calculate the Super Profit:

Super Profit = Actual Profit - Normal Profit

Super Profit = $48,000\; -\; 30,000\; =\; 18,000$

Finally, calculate the Goodwill based on 3 years' purchase of super profit:

Goodwill = Super Profit × Number of years' purchase

Goodwill = $18,000\; \backslash times\; 3\; =\; 54,000$

Therefore, the value of goodwill is ₹54,000.