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Q.

There are two sections A and B of a class, consisting of 36 and 44 students’ respectively.

If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.

 A.

30.00 kg

 B.

35.00 kg

 C.

37.25 kg

 D.

42.50 kg

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Solution:
Option(C) is correct

Total weight of $(36+44=80)$ Students $= (36 \times 40+44 \times 35)$ kg = 2980 kg

Therefore average weight of the whole class $= \left(\dfrac{2980}{80}\right)$ kg

Therefore average weight = 37.25kg

Edit: For an alternative solution, check comment by Sravan Reddy.


(5) Comment(s)


Umang Uniya
 ()

it is very easy in all cases i.e

36*40+44*35/36+44=37.25



Suprajha
 ()

If we add both the averages and divide it by 2 then also we get the same answer.

$=\dfrac{40+35}{2}=37.5$


Ritu
 ()

You got lucky in this case. But this will not work in every case as this is a wrong technique.

You need to consider weighted averages for the correct solution.


Sravan Reddy
 ()

Other way of solving (finally boils down to simplifying the calculation):

=> Assume that the 40 kg batch of 36 are also 35kg. So, average is straight forward 35. Now extra weight is the additional 5 kg from those 36 students - 180kg. So divide that 180 among $44+36 = 80$ students

=> So answer is $35 + \dfrac{180}{80} = 37.25$

P.S. It is similar to simplifying the equation of $\dfrac{(36*40)+(44*35)}{80}$ as $\dfrac{(36*5)+(36*35)+(44*35)}{80} = \dfrac{36*5}{80}+35$.

But this way of thinking gets us the answer in less than 20 sec by mind calculation :)



Manish Singh
 ()

We divided it by 80. because 2980 is the total weight of whole class (section $A$ and $B$).

We need to calculate the average of the whole class. and the sum of the students of section $A$ and $B$ is $34+ 46=80.$