If the average marks of three batches of $55$, $60$ and $45$ students respectively is $50$, $55$, $60$, then the average marks of all the students is:

To find the combined average marks of all students, we calculate the total marks scored across all batches and divide by the total number of students.
$$\text{Total Marks}=(55\times 50)+(60\times 55)+(45\times 60)$$

$$\text{Total Marks}=2750+3300+2700=8750$$

$$\text{Total Number of Students}=55+60+45=160$$

$$\text{Weighted Average}=\frac{\text{Total Marks}}{\text{Total Students}}=\frac{8750}{160}=\frac{875}{16}\approx 54.6875$$

Rounding off gives approximately $54.68$.