The correct answer is $\boxed{\text{C}}$.
Jagdish and Brij’s initial profit sharing ratio is 3:2. This means that Jagdish gets 3 parts of the profit for every 2 parts that Brij gets. When Ramesh is admitted, the new profit sharing ratio must add up to 1. To do this, we can multiply Jagdish’s original share by $\frac{3}{3+2+1}=\frac{3}{6}=\frac{1}{2}$, Brij’s original share by $\frac{2}{6}=\frac{1}{3}$, and Ramesh’s share by $\frac{1}{6}$. This gives us the new profit sharing ratio of $\boxed{\frac{1}{2}:\frac{1}{3}:\frac{1}{6}=3:2:3}$.
Option A is incorrect because it does not add up to 1. Option B is incorrect because it does not reflect the original profit sharing ratio of Jagdish and Brij. Option D is incorrect because it does not reflect the new profit sharing ratio of Jagdish, Brij, and Ramesh.