Profit sharing ratio of A, B and C is $$\frac{1}{2},\,\frac{3}{{10}}$$ and $$\frac{1}{5}$$ respectively C dies. What will be profit haring ratio between A and B?

The correct answer is $\boxed{\text{B. 2 : 1}}$.

The initial profit sharing ratio of A, B, and C is $\frac{1}{2}:\frac{3}{10}:\frac{1}{5} = 10:6:4$. If C dies, then A and B will share the profits in the ratio of $10+6:6 = 16:6 = 2:1$.

Here is a brief explanation of each option:

• Option A: $3:1$. This is the ratio of the initial profit shares of A and C. However, C dies, so this ratio is no longer valid.
• Option B: $2:1$. This is the correct answer. It is the ratio of the initial profit shares of A and B, plus the share that A will inherit from C.
• Option C: $3:2$. This is the ratio of the initial profit shares of A and B, plus the share that B will inherit from C. However, B does not inherit any shares from C, since C dies.
• Option D: $5:3$. This is not a valid profit sharing ratio.