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If the average marks of three batches of and students respectively is and then the average marks of all students is

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None of these

answer is A.

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Detailed Solution

Concept:
In this question, we are given the average marks

and

of the three batches with number of students

and

. We have to find the average marks of total students. First find the sum of marks of each batch using the formula

. Now, use the same formula again for the average of total marks of all the students.
As we know that,

It implies that the sum of marks of each batch will be the product of average marks and the number of students.
Now, in three batches number of students

and

have average marks

and

respectively.
Therefore, using equation (2)
For batch 1, sum of marks

For batch 2, sum of marks

For batch 3, sum of marks

Now, for the average of total marks
Total number of marks of batch 1, 2, 3

Total number of students of all the batches

From equation (1) ,
The average of total number of marks of batch 1, 2, and 3

Hence, the correct answer is option 1) 54.68

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