Question

In a class the average weight of \[40\] students is \[35.5kg\]. If along with the class teacher all of them weigh on an average of \[36kg\]. Then what is the weight of the class teacher in kilograms?

A. \[54kg\]

B. \[55.5kg\]

C. \[56kg\]

D. \[55kg\]

Answer 1

Hint: Here we use the concept of average which is the sum of all quantities divided by the number of quantities and we find average in both situations with the teacher and without the teacher. We use the sum of weight of all students obtained from the first situation and subtract it from the sum of the weight of students along with the teacher from the second situation.

*  Average is defined as the mean of all observations which is given by the sum of all observations divided by the total number of observations.

Complete step-by-step answer:

Given total number of students is \[40\]

Let us assume sum of weight of all students be \[x\]

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

\[35.5 = \dfrac{x}{{40}}\]

Cross multiplying the value from denominator of RHS to LHS

$  x = 35.5 \times 40 $

$  x = 1420kg $

So sum of weight of all students is \[1420kg\]

Now we assume weight of the class teacher be \[y\]

Now sum of all students along with the class teacher will be \[(1420 + y)kg\]

We are given the new average is \[36kg\] 

Total number of observations is \[40 + 1 = 41\] as class teacher is added to the list.

Now, substituting the values in formula for average

\[36 = \dfrac{{1420 + y}}{{41}}\]

Cross multiplying the denominator of RHS to LHS

$  1420 + y = 36 \times 41 $

$  1420 + y = 1476 $

Take constants to one side of the equation

$  y = 1476 - 1420 $

$  y = 56kg $

Therefore, the weight of the class teacher is \[56kg\].

So, option C is correct.

Note: Students are likely to make the mistake of not writing SI units along with the value obtained at the end. Also, if by chance weights are in different units, always convert all the values to the same unit. Some important conversions are

$  1kg = 1000 grams $

 $ 1kg = 2.204 pounds $