Question

The average weight of \[5\] boys in the class is \[40\] kg. The average weight of \[35\] girls is \[50\] kg. What is the average weight of the whole class?

Answer 1

Hint: We will first find the total weight of \[5\] boys using the concept of average. Then we will find the total weight of \[35\] girls using the same concept. Then we will add the total weight of \[5\] boys and total weight of \[35\] girls to find the total weight of the whole class and total number of students will become \[\left( {5{\text{ boys}} + 35{\text{ girls}}} \right)\] i.e., \[40\]. Then using the definition of average, we will calculate the average weight of the whole class.

Complete step by step answer:
As we know, \[{\text{average}} = \dfrac{{{\text{sum of all values}}}}{{{\text{total number of values}}}}\]
So, we can write in this case,
\[ \Rightarrow \] Average weight of the boys in the class \[ = \dfrac{{{\text{Total weight of 5 boys}}}}{5}\]
Average weight of \[5\] boys is given in the question as \[40\] kg. Putting this value, we get
\[ \Rightarrow 40{\text{ kg}} = \dfrac{{{\text{Total weight of }}5{\text{ boys}}}}{5}\]
On cross multiplication and on rearranging, we get
\[ \Rightarrow {\text{Total weight of }}5{\text{ boys}} = {\text{5}} \times 40{\text{ kg}}\]
\[ \Rightarrow {\text{Total weight of }}5{\text{ boys}} = 200{\text{ kg}}\]
Now,
\[ \Rightarrow \] Average weight of the girls in the class \[ = \dfrac{{{\text{Total weight of 35 girls}}}}{{35}}\]
Average weight of \[35\] girls is given in the question as \[50\] kg. Putting this value, we get
\[ \Rightarrow 50{\text{ kg}} = \dfrac{{{\text{Total weight of 3}}5{\text{ girls}}}}{{35}}\]
On cross multiplication and on rearranging, we get
\[ \Rightarrow {\text{Total weight of 3}}5{\text{ girls}} = 3{\text{5}} \times 50{\text{ kg}}\]
\[ \Rightarrow {\text{Total weight of 3}}5{\text{ girls}} = 1750{\text{ kg}}\]
Therefore, Total weight of the whole class \[ = \] Total weight of \[5\] boys \[{\text{ + }}\] Total weight of \[{\text{3}}5\] girls
\[ \Rightarrow \] Total weight of the whole class \[ = 200{\text{ kg}} + 1750{\text{ kg}}\]
\[ = 1950{\text{ kg}}\]
Total number of students is \[\left( {5{\text{ boys}} + 35{\text{ girls}}} \right)\] i.e., \[40\].
Average weight of the whole class \[ = \] \[\dfrac{{{\text{Total weight of the class}}}}{{{\text{Total number of students in the class}}}}\]
\[ \Rightarrow \] Average weight of the whole class \[ = \dfrac{{1950}}{{40}}\]
\[ = 48.75{\text{ kg}}\]
Therefore, the average weight of the whole class is \[48.75{\text{ kg}}\].

Note:
An average is a single number taken as representative of a non- empty list of numbers. All items count equally in determining their average value and their positions in the list are irrelevant. Also, note that if all numbers of a list are multiplied by the same positive number, then its average changes by the same factor.