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Let's assume the initial profit of the firm is x.
Initially, A and B share the profit in the ratio 1:2. So, A's share is (1/3) * x and B's share is (2/3) * x.
Now, they admit C into the partnership and decide to give him 1/3rd share of the future profits.
So, C's share is (1/3) * (1/3) * x = (1/9) * x.
The new ratio of the partners will be:
A : B : C = A's share : B's share : C's share
A : B : C = (1/3) * x : (2/3) * x : (1/9) * x
Simplifying the ratio, we get:
A : B : C = 3x : 6x : x
Dividing by x, we get:
A : B : C = 3 : 6 : 1
So, the new ratio of the partners is 3 : 6 : 1.
Therefore, the correct answer is B: It is 2:4:3