B, P and L are partners in a firm sharing profits in the ratio 4:3:2. B retires, P and L decided to share profits in the future in the ratio of 5 : 3. Gaining ratio will be :

21:11

The correct answer is option 2- 21:11.

Gained share = New share - Old share.
Old ratio = 4:3:2 (B, P and L)
B retires
New ratio = 5:3 (P and L)

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

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

Gaining Ratio = 21/72 : 11/72
                      = 21:11