The old profit and loss sharing ratio between A, B and C are 5:3:2 the...
Explanation:
The old profit sharing ratio between A, B, and C is given as 5:3:2. Let the total profit earned be x.
Therefore, the share of A, B, and C would be 5x/10, 3x/10, and 2x/10 respectively.
New Profit Sharing Ratio:
It is given that the new profit sharing ratio between B and C shall be the same as the existing ratio between A and B.
Let the new profit sharing ratio between A and B be a:b.
Then, the new profit sharing ratio between A, B, and C would be a:b:(2/(3+2) * b) = a:b:2b/5.
We know that the total profit earned is x.
Therefore, the share of A, B, and C in the new ratio would be ax/(a+b+2b/5), bx/(a+b+2b/5), and (2b/5)x/(a+b+2b/5) respectively.
As per the given condition, the new profit sharing ratio between B and C should be the same as the existing ratio between A and B.
Therefore, bx/(a+b+2b/5) = 3x/10.
Solving for b/a, we get b/a = 3/4.
Therefore, the new profit sharing ratio between A, B, and C would be a:b:(2b/5) = a:3a/4:2a/5 = 20a:15a:8a.
Simplifying, we get the new profit sharing ratio between A, B, and C as 20:15:8.