Question: If the average of three batches of 55, 60, 45 students respectively is 50, 55 and 60 then what is th...

Question

If the average of three batches of 55, 60, 45 students respectively is 50, 55 and 60 then what is the average marks of all the students?
(a) 53.33
(b) 54.68
(c) 55
(d) None of these

Answer 1

Solution

To solve this problem first we have to get the total marks that students scored for each individual batch, we can find this simply by multiplying the average marks of the batch with the number of students in that batch. We will find this for all three batches and then add all of them to get the total marks for all three batches. Then we will add the number of students in each batch to get the total number of students. To get the average we will divide the obtained total marks by the total number of students.

Complete step by step answer:
We are given three batches of students in which the number of students are 55, 60 and 45 and average marks of these three batches is 50, 55 and 60 respectively.
So to solve this we have to know first that how can we calculate average,
According to the given question we can calculate the average as,
= $\dfrac{total\,marks\,of\,all\,students\,in\,all\,three\,batches}{total\,number\,of\,students\,in\,all\,batches}$
Hence we have to first calculate the total number of marks, we can do this by multiplying the average marks of the batch with its respective number of students and then add them all to get total marks.
We can solve this as,
Batch 1: $55\times 50=2750$
Batch 2: $60\times 55=3300$
Batch 3: $45\times 60=2700$
Now adding all we get,
$2750+3300+2700=8750$
And total number of students are given as,
55 + 60 + 45 = 160
Hence we get average as,
Average = $\dfrac{8750}{160}=54.6875=54.68$
Hence we get option (b) as the correct answer.

Note:
You need to be careful while solving this question. Many students commit many common mistakes while solving this for example some students may just add the total average marks and then divide it by total number of students and then they will get the wrong answer and may mark the none of these as the correct answer. You should read the question carefully before solving it.