A and B are partners sharing profit and losses in 3 : 2. C is admitted in the firm for $${\frac{1}{5}^{{\text{th}}}}$$ share and he brings Rs. 10,000 as capital. What will be adjusted capital of B?

The correct answer is B. Rs. 12,000.

Initially, A and B have capitals of Rs. 3x and Rs. 2x respectively. When C is admitted, the new profit sharing ratio is 3:2:1. So, the capitals of A, B and C should be in the ratio of 3:2:1.

Let C’s capital be Rs. y. Then,
3x + 2x + y = 6y
y = 5x
C brings Rs. 10,000 as capital. So, x = 2000.
B’s adjusted capital = Rs. (2 * 2000) = Rs. 4000.
So, the adjusted capital of B is Rs. 12,000.

Explanation of each option:

Option A: Rs. 10,000. This is the capital that C brings in. However, this is not the adjusted capital of B.
Option B: Rs. 12,000. This is the correct answer.
Option C: Rs. 14,000. This is the capital that B would have if the profit sharing ratio was 3:3:2. However, the profit sharing ratio is 3:2:1.
Option D: Rs. 16,000. This is the capital that B would have if the profit sharing ratio was 2:2:2. However, the profit sharing ratio is 3:2:1.