Rana, Sana and Kamana are partners, sharing profits in the ratio 4:3:2. Rana retires; Sana and Kamana decided to share profits in the future in the ratio of 5:3. The Gaining Ratio of Sana and Kamana will be

21:11

The correct answer is Option 1 - 21:11.

Old ratio = 4:3:2 (Rana, Sana and Kamana)
Rana retires
New ratio = 5:3 (Sana and Kamana)

Gaining share = New share - old share

Gain of Sana = 5/8 - 3/9
                   = (45-24) / 72
                   = 21/72

Gain of Kamana = 3/8 - 2/9
                        = (27-16) / 72
                        = 11/72

Gaining ratio = 21/72 : 11/72
                    = 21:11