Old ratio of Praveena and Dhanya = 7:3 that is \(\frac{7}{10}:\frac{3}{10}\)
New ratio of Paveena, Dhanya and Malini = 5:2:3 that is, \(\frac{5}{10};\frac{2}{10};\frac{3}{10}\)
Share sacrificed = Old share - New share
Praveena \(=\frac { 7 }{ 10 } -\frac { 5 }{ 10 } =\frac { 7-5 }{ 10 } =\frac { 2 }{ 10 } \)
Dhanya \(=\frac { 3 }{ 10 } -\frac { 2 }{ 10 } =\frac { 3-2 }{ 10 } =\frac { 1 }{ 10 } \)
Sacrificing ratio ofPraveena and Dhanya is \(\frac { 2 }{ 10 } :\frac { 1 }{ 10 } \) that is 2:1

Computation of sacrificing ratio and new profit sharing ratio
Old ratio of Ambika, Dharani and Padma \(5:3:2\quad or\quad \frac { 5 }{ 10 } :\frac { 3 }{ 10 } :\frac { 2 }{ 10 } \)
Ramya's share of profit = 25% or \(\frac { 25 }{ 100 } or\frac { 1 }{ 4 } \)
Let the total share be 1 
Remaining share \(=1-\frac { 1 }{ 4 } =\frac { 4-1 }{ 4 } =\frac { 3 }{ 4 } \)
New share of old partners = Remaining share \(\times\) Old share
Ambika \(=\frac { 3 }{ 4 } \times \frac { 5 }{ 10 } =\frac { 15 }{ 40 } \)
Dharani \(=\frac { 3 }{ 4 } \times \frac { 3 }{ 10 } =\frac { 9 }{ 40 } \)
Padma \(=\frac { 3 }{ 4 } \times \frac { 2 }{ 10 } =\frac { 6 }{ 40 } \)
Share of new partner
Ramya \(=\frac { 1 }{ 4 } \)
In order to equalise the denominator, multiply and divide Ramya's share by 10 
Rarnyas share \(=\frac { 1 }{ 4 } \times \frac { 10 }{ 10 } =\frac { 10 }{ 40 } \)
New profit sharing ratio of Ambika, Dharani, Padma and Ramya \(=\frac { 15 }{ 40 } :\frac { 9 }{ 40 } :\frac { 6 }{ 40 } :\frac { 10 }{ 40 } \), that is 15: 9: 6: 10

Computation of sacrificing ratio and new profit sharing ratio
Siva's share = \(\frac{1}{5}\)
Proportion of share sacrificed = 1 : 1 (equally) i.e.\(\frac{1}{2}:\frac{1}{2}\)
Share scarified = New partner's share x Proportion of share sacrificed
Selvam \(=\frac { 1 }{ 5 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 10 } \)
Senthil \(=\frac { 1 }{ 5 } \times \frac { 1 }{ 2 } =\frac { 1 }{ 10 } \)
Sacrificing ratio of Selvam and Senthil is \(\frac { 1 }{ 10 } :\frac { 1 }{ 10 } \) that is 1:1
New share of old partner = Old share - Share sacrificed
Selvam \(=\frac { 2 }{ 5 } -\frac { 1 }{ 10 } =\frac { 4-1 }{ 10 } =\frac { 3 }{ 10 } \)
Senthil \(=\frac { 3 }{ 5 } -\frac { 1 }{ 10 } =\frac { 6-1 }{ 10 } =\frac { 5 }{ 10 } \)
Share of new partner
Siva = \(\frac{1}{5}\)
In order to equate, monthly and divide Siva's share by 2
\(=\frac { 1 }{ 5 } \times \frac { 2 }{ 2 } =\frac { 2 }{ 10 } \)
New profit sharing ratio of Selvam, Senthil and Siva \(=\frac { 3 }{ 10 } :\frac { 5 }{ 10 } :\frac { 2 }{ 10 } \), that is 3:5:2

Computation of sacrificing ratio and new profit sharing ratio
Old share = 5:3 that is prema \(\frac{5}{8}\) amd Chandra \(\frac{3}{8}\)
Share scarified =Old share x Proportion of share sacrificed
Prema \(=\frac { 5 }{ 8 } \times \frac { 1 }{ 8 } =\frac { 5 }{ 64 } \)
Chandra \(=\frac { 3 }{ 8 } \times \frac { 1 }{ 8 } =\frac { 3 }{ 64 } \)
Sacrificing ratio of Prema and Chandra is \(\frac{5}{64}\)and \(\frac{3}{64}\) that is 5:3
New share = Old share - Share sacrificed
Prema \(=\frac { 5 }{ 8 } -\frac { 5 }{ 64 } =\frac { 40-5 }{ 64 } =\frac { 35 }{ 64 } \)
Chandra \(=\frac { 3 }{ 8 } -\frac { 3 }{ 64 } =\frac { 24-3 }{ 64 } =\frac { 21 }{ 64 } \)
Share of new partner = Sum of shares sacrificed by Prema and Chandra
Hema \(=\frac { 5 }{ 24 } +\frac { 3 }{ 64 } =\frac { 5+3 }{ 64 } =\frac { 8 }{ 64 } \)
New profit sharing ratio of Prema, Chandra and Hema \(=\frac { 35 }{ 64 } :\frac { 21 }{ 64 } :\frac { 8 }{ 64 } \), that is 35:21:8

Computation of sacrificing ratio and new profit sharing ratio
Share sacrificed \(=\frac{1}{14}:\frac{1}{14}\)
Sacrificing ratio of Vimala and Kamala is 1 : 1
Old ratio is 4: 3 that is \(\frac { 4 }{ 7 } :\frac { 3 }{ 7 } \)
New share of old partner = Old share - Share sacrificed
Vimala \(=\frac { 4 }{ 7 } -\frac { 1 }{ 14 } =\frac { 8-1 }{ 14 } =\frac { 7 }{ 14 } \)
Kamala \(=\frac { 3 }{ 7 } -\frac { 1 }{ 14 } =\frac { 6-1 }{ 14 } =\frac { 5 }{ 14 } \)
Share of new partner:
Vinitha = Sum of shares sacrificed by old partners
\(=\frac { 1 }{ 14 } +\frac { 1 }{ 14 } =\frac { 2 }{ 14 } \)
New profit sharing ratio of Vimala, Kamala and Vinitha is \(\frac { 7 }{ 14 } :\frac { 5 }{ 14 } :\frac { 2 }{ 14 } \) or 7:5:2