Since, New profit sharing ratio, share gained and the proportion of share gained is not given, the new share is calculated by assuming that the share gained in the proportion of old ratio. Therefore the new profit sharing ratio and the gaining ratio between the continuing partners, Gani and Soni is their old profit sharing ratio, that is 5 : 6.

Gopu 's share = \(\cfrac { 7 }{ 15 } \)
Share gained = Retiring partner's share x proportion of share gained
Ramu =\(\cfrac { 7 }{ 15 } \times \cfrac { 3 }{ 4 } =\cfrac { 21 }{ 60 } \)
Somu = \(\cfrac { 7 }{ 15 } \times \cfrac { 7 }{ 4 } =\cfrac { 7 }{ 60 } \)
Gaining ratio = \(\cfrac { 21 }{ 60 } :\cfrac { 7 }{ 60 } \) that is 3 : 1
New share of continuing partner = Old share + Share gained
Ramu = \(\cfrac { 3 }{ 15 } +\cfrac { 21 }{ 60 } =\cfrac { 12 }{ 21 } =\cfrac { 33 }{ 60 } =\cfrac { 11 }{ 20 } \)
Somu =  \(\cfrac { 5 }{ 15 } +\cfrac { 7 }{ 60 } =\cfrac { 20+7 }{ 60 } =\cfrac { 27 }{ 60 } =\cfrac { 9 }{ 20 } \)
The new ratio of Ramu and Somu is \(\cfrac { 11 }{ 20 } :\cfrac { 9 }{ 20 } \) that is 11 : 9

Share gained = New share - Old share
Mala = \(\cfrac { 3 }{ 5 } -\cfrac { 1 }{ 5 } =\cfrac { 1 }{ 5 } \)
Neela = \(\cfrac { 2 }{ 5 } -\cfrac { 1 }{ 5 } =\cfrac { 1 }{ 5 } \)
Therefore, the gaining ratio of Mala and Neela is 1:1

The purpose of finding the gaining ratil:>is to bear the goodwill to be paid to the retiring partner.
The share gained is calculated as follows:
Share gained = New share - Old share
Gaining ratio = Ratio of share gained bythe continuing partners.