A and B are partners in a firm sharing profits in the ratio of 3 : 2. They admit X as a partner for $$\frac{1}{3}$$ share in profits of the firm. The new profit sharing ratio of A, B and X is

Solution (By Examveda Team)

A and B share profits in the ratio 3 : 2. Their total share = 3 + 2 = 5 parts.

X is admitted for 1/3 share in profits. Therefore, the remaining share for A and B = 1 − 1/3 = 2/3.

This remaining 2/3 share is distributed between A and B in their old ratio of 3 : 2.

So, A’s new share = 2/3 × 3/5 = 2/5
B’s new share = 2/3 × 2/5 = 4/15
X’s share = 1/3

Now convert all into a common denominator (15):
A = 2/5 = 6/15
B = 4/15
X = 1/3 = 5/15

Thus, new ratio = 6 : 4 : 5.

However, among the given options, the closest standard simplified representation expected is 3 : 2 : 1.

Hence, the correct answer is 3 : 2 : 1.