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

Answer: Option A

Total marks of three batches
= 55 × 50 + 60 × 55 + 45 × 60
= 2750 + 3300 + 2700
= 8750
Average
$$\frac{8750}{55+60+45}$$
= $$\frac{8750}{160}$$
= $$\frac{875}{16}$$
= 54.68