Trade payables turnover ratio = \(\frac { Net\quad credit\quad purchases }{ Average\quad trade\quad payables } \)
Average trade payables = \(\frac { Opening\quad trade\quad payables+Closing\quad trade\quad payables }{ 2 } \)
= \(\frac { (20,000+4,000)+(10,000+6,000) }{ 2 } \)
= \(\frac { 40,000 }{ 2 } \) = Rs.20,000
Average payment period (in days) = \(\frac { Number\quad of\quad days\quad in\quad a\quad year }{ Trade\quad payables\quad turn\quad over\quad ratio } \)
=\(\frac { 365 }{ 5 } \)  = 70 days
∴ Trade payables turnover ratio (in days) = \(\frac { 1,00,000 }{ 20,000 } \) = 5 times.

(i) Gross profit ratio =\(\frac { Gross\quad profit }{ Revenue\quad from\quad operations } \) \(\times\) 100
Cost of revenue from operations = Purchases of stock-in-trade + Change in inventory + Direct expenses
= 8,500 - 500 + 0 = Rs.8,000
Gross profit = Revenue from operations - Cost of revenue from operations
= 10,000 - 8,000 = Rs.2,000
∴ Gross profit ratio =\(\frac { 2,000 }{ 8,000 } \) \(\times\) 100 = 25%
(ii) Net profit ratio =\(\frac { Net\quad profit\quad after\quad tax }{ Revenue\quad from\quad operations } \) \(\times\) 100
=\(\frac { 800 }{ 10,000 } \) \(\times\) 100 = 8%
(iii) Operating cost ratio =\(\\ \frac { Operating\quad cost }{ Revenue\quad from\quad operations } \) \(\times\) 100
Operating cost = Cost of revenue from operations + Operating expenses
Operating expenses Other expenses = Rs.1,200
Operating cost = 8,000 + 1,200 = Rs.9,200
∴ Operating cost ratio =\(\frac { 9,200 }{ 10,000 } \) \(\times\) 100 = 92%
(iv) Operating profit ratio = \(\frac { Operating\quad profit }{ Revenue\quad from\quad operations } \) \(\times\) 100
Operating profit = Revenue from operations - Operating Cost
= 10,000 - 9,200 = Rs.800
∴ Operating profit ratio = \(\frac { 800 }{ 10,000 } \) \(\times\) 100 = 8%

Solution:

(i) New partner sharing ratio:
Let the total profit be 1
New partner Kamala's share \(=\frac{1}{5}\)
Remaining share of Sheela and Neela \(=1-\frac{1}{5}=\frac{5-1}{5}=\frac{4}{5}\)
New share of Sheela = Remaining share x Sheela's old share
Sheela \(=\frac{4}{5}\times\frac{4}{7}=\frac{16}{35}\)
Neela \(=\frac{4}{5}\times\frac{3}{7}=\frac{12}{35}\)
Share of new partner:
Kamala \(=\frac{1}{5}\)
In order to equalize the denominator, multiply and divide Kamala's share by 7.
Kamala's share \(=\frac{1}{5}\times\frac{1}{7}=\frac{7}{35}\)
New profit sharing ratio of Sheela, Neela and Kamala \(=\frac{16}{35}:\frac{12}{32}=\frac{7}{35}\) that 16:12:7
ii. Sacrificing ratio:
Sacrifice = Old share - New share
Sheela's sacrifice \(=\frac { 4 }{ 7 } -\frac { 16 }{ 35 } =\frac { 15-12 }{ 35 } =\frac { 4 }{ 35 } \)
Neela's sacrifice \(=\frac { 3 }{ 7 } -\frac { 12 }{ 35 } =\frac { 15-12 }{ 35 } =\frac { 3 }{ 35 } \)
Sacrificing ratio \(=\frac { 4 }{ 35 } :\frac { 3 }{ 35 } =4:3\)

Average profit \(=\frac{Total\ profit}{Number\ of\ years}\)
\(=\frac{20,000+25,000+24,000+23,000}{4}\)
\(\frac{92,000}{4}\)
Average profit =Rs.23,000
Average profit before adjusting fair remuneration of the partner = Rs.23,000
Less:
Fair remuneration of partners  =3,000
                                                         _____
Average profit                              =20,000
                                                         _____
Goodwill = Average profit x Number of years of purchase
=20,000x3= Rs. 60,000