Answer
418.2k+ views
Hint: We will use the formula for average to calculate the total weight of the 8 boys. We will calculate the sum of weights of the 7 boys. The weight of the \[{8^{th}}\] boy will be the difference between the total weight and the sum of weights of the 7 boys. We will subtract the 2 quantities to obtain the weight of the \[{8^{th}}\] boy.
Formulas used:
The formula for the average weight of \[n\] people:
Average Weight \[ = \] Total weight of \[n\] people \[ \div n\].
Complete step-by-step answer:
We know that the average weight of 8 boys is 57 Kg. We will substitute 57 for average weight and 8 for \[n\] in the formula for the average weight:
\[ \Rightarrow 57 = \]Total weight of 8 people \[ \div 8\]
On cross multiplying 8 with 57, we get
\[ \Rightarrow 57 \times 8 = \]Total weight of 8 people
\[ \Rightarrow 45{\rm{6}} = \] Total weight of 8 people
We have calculated that the total weight of 8 people is 456 Kg. Out of the 8 people, we know the weight of 7 people. We will assume that the weight of the \[{8^{th}}\] boy is \[x\] kg. So, the total weight of 8 people will be:
\[x + 64 + 42 + 29 + 39 + 80 + 52 + 55\]
We know that the total weight is 465 Kg. On equating the above expression with 465, we get
\[ \Rightarrow 456 = x + 64 + 42 + 29 + 39 + 80 + 52 + 55\]
Adding the like terms, we get
\[ \Rightarrow 456 = x + 361\]
Subtracting 361 from both sides, we get
\[ \Rightarrow 456 - 361 = x + 361 - 361\]
\[ \Rightarrow 95 = x\]
We can conclude that the weight of the \[{8^{th}}\] student is 95 Kg.
$\therefore $ Option B is the correct option.
Note: The average which is also known as the arithmetic mean is often used as the representative of a large number of quantities. It is assumed to be the central value of the data. Here the weight is given in Kg so we need to keep the weight in the same unit and not change it throughout.
Formulas used:
The formula for the average weight of \[n\] people:
Average Weight \[ = \] Total weight of \[n\] people \[ \div n\].
Complete step-by-step answer:
We know that the average weight of 8 boys is 57 Kg. We will substitute 57 for average weight and 8 for \[n\] in the formula for the average weight:
\[ \Rightarrow 57 = \]Total weight of 8 people \[ \div 8\]
On cross multiplying 8 with 57, we get
\[ \Rightarrow 57 \times 8 = \]Total weight of 8 people
\[ \Rightarrow 45{\rm{6}} = \] Total weight of 8 people
We have calculated that the total weight of 8 people is 456 Kg. Out of the 8 people, we know the weight of 7 people. We will assume that the weight of the \[{8^{th}}\] boy is \[x\] kg. So, the total weight of 8 people will be:
\[x + 64 + 42 + 29 + 39 + 80 + 52 + 55\]
We know that the total weight is 465 Kg. On equating the above expression with 465, we get
\[ \Rightarrow 456 = x + 64 + 42 + 29 + 39 + 80 + 52 + 55\]
Adding the like terms, we get
\[ \Rightarrow 456 = x + 361\]
Subtracting 361 from both sides, we get
\[ \Rightarrow 456 - 361 = x + 361 - 361\]
\[ \Rightarrow 95 = x\]
We can conclude that the weight of the \[{8^{th}}\] student is 95 Kg.
$\therefore $ Option B is the correct option.
Note: The average which is also known as the arithmetic mean is often used as the representative of a large number of quantities. It is assumed to be the central value of the data. Here the weight is given in Kg so we need to keep the weight in the same unit and not change it throughout.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)