The average weight of a class of 20 students is 45kgs. A new student whose weight is 40kg replaces an old student of this class. Hence, the average weight of the whole class decreases by 1kg. The weight of the replaced student is:
A. 55 kg
B. 50kg
C. 60kg
D. None of these
Answer
279.9k+ views
Hint: To solve this question we will first calculate the total weight of 20 boys by using the formula, $\text{average weight=}\dfrac{\text{total weight}}{\text{number of boys}}$. After calculating the weight of those 20 students, we will again calculate the new weight of the students of the class. And then by subtracting, we will find the weight of that student.
Complete step by step answer:
Given that the average weight of a class of 20 students is 45kg. A new student whose weight is 40kg replaces an old student of this class. Hence, the average weight of the whole class decreases by 1kg and we have to find the weight of that student. As we know that we can calculate the average weight of the class by the formula:
$\text{average weight=}\dfrac{\text{total weight}}{\text{number of boys}}$
Total number of students = 20
Their average weight first = 45kg
Hence, $45=\dfrac{\text{total weight}}{20}$
So, the total weight of the class = 900kg.
Now if the weight of the new student who joined the class = 40kg,
Let us consider the weight of the student who left the class = $xkg$ .
So, now the new total net weight = $900+40-xkg=940-xkg$.
And the average weight is now 44kg, so,
$\begin{align}
& 44=\dfrac{940-x}{20} \\
& \Rightarrow 940-x=880 \\
& \Rightarrow x=940-880 \\
& \Rightarrow x=60 \\
\end{align}$
So, the weight of that student was 60kg.
So, the correct answer is “Option C”.
Note: While solving this type of questions, you have to be careful about the total weight and all the other calculations. And if it is asked to find the average weight or total number of students, then we can calculate all that without using another formula, we will use this same formula for calculating them too.
Complete step by step answer:
Given that the average weight of a class of 20 students is 45kg. A new student whose weight is 40kg replaces an old student of this class. Hence, the average weight of the whole class decreases by 1kg and we have to find the weight of that student. As we know that we can calculate the average weight of the class by the formula:
$\text{average weight=}\dfrac{\text{total weight}}{\text{number of boys}}$
Total number of students = 20
Their average weight first = 45kg
Hence, $45=\dfrac{\text{total weight}}{20}$
So, the total weight of the class = 900kg.
Now if the weight of the new student who joined the class = 40kg,
Let us consider the weight of the student who left the class = $xkg$ .
So, now the new total net weight = $900+40-xkg=940-xkg$.
And the average weight is now 44kg, so,
$\begin{align}
& 44=\dfrac{940-x}{20} \\
& \Rightarrow 940-x=880 \\
& \Rightarrow x=940-880 \\
& \Rightarrow x=60 \\
\end{align}$
So, the weight of that student was 60kg.
So, the correct answer is “Option C”.
Note: While solving this type of questions, you have to be careful about the total weight and all the other calculations. And if it is asked to find the average weight or total number of students, then we can calculate all that without using another formula, we will use this same formula for calculating them too.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write an application to the principal requesting five class 10 english CBSE
