In a firm, A, B and C shares the profit in the ratio 5:3:2. B died. In which ratio A and C are gaining after the death of B?

5:2

The correct answer is option 2- 5:2.

Old ratio= 5:3:2 (A, B and C)
New Ratio of A & C = 5:2 (When nothing is mentioned, old ratio is considered to be new at retirement)
Gaining Ratio = New ratio - Old ratio
A's Gain = 5/7 - 5/10
             = (50-35)/70
             = 15/70

B's Gain = 2/7 - 2/10
              = (20-14)/70
              = 6/70

Gaining ratio = 15/70 : 6/70
                    = 15:6
                    = 5:2