Question

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
A.53.33
B.54.68
C.55
D.None of these

Answer 1

Hint: First we will find the total marks scored by each student in each of the three batches, then we will add them to get the total marks scored by all students. After this, we will add the number of students in each batch and get the total number of students in all three batches. And finally to get the average marks scored by all students we divide the total marks by total number of students.

Complete step-by-step answer:
The average marks of 55, 60 and 45 students respectively is 50, 55, and 60, thus their total marks will be given by \[55 \times 50 = 2750\], \[60 \times 55 = 3300\] and \[45 \times 60 = 2700\] respectively. So the total marks scored by all the students across 3 batches will be \[2750 + 3300 + 2700 = 8750\].
Now, the total number of students in three batches is \[55 + 60 + 45 = 160\].
Now, we will divide the total marks scored by all students with the total number of students and get the average marks scored by each student.
Thus, the average marks scored by each student will be \[\dfrac{{8750}}{{160}} = 54.6875 = 54.68\].
Hence, option (B) will be the correct option.

Note: When we are finding the average from three different averages, we must find the total value and then divide it by total count of the value. Taking the average of the averages is incorrect as that would mean there are only 3 students which is wrong.