In a class the average weight of 40 students is . If along with the class teacher all of them weigh on an average of . Then what is the weight of the class teacher in kilograms?

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54 kg

55.5 kg

56 kg

answer is C.

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Detailed Solution

Concept- Here, we apply the idea of average, which is defined as the total of all quantities divided by the total number of quantities. We may determine average in both teacher- and student-assisted learning scenarios. We deduct the total weight of students and the teacher from the second situation from the total weight of all students acquired from the first situation. The definition of average is "the mean of all observations," which is obtained by dividing the total number of observations by the sum of all observations.
Given total number of students is 40
Let us assume sum of weight of all students be

Since, average = sum of all observations / total number of observations
Therefore, Average weight here is sum of weight of all students/total number of students
Substituting the values we get

Cross multiplying the value from denominator of RHS to LHS

So, sum of weight of all students is

Now, we assume weight of the class teacher be

Now, sum of all students along with the class teacher will be

We are given the new average is

Total number of observations is

as class teacher is added to the list.
Now, substituting the values in formula for average

Cross multiplying the denominator of RHS to LHS

Take constants to one side of the equation

Therefore, the weight of the class teacher is

.
So, the correct answer is 3) 56 kg

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