Question

The average weight of all students in a class equals the number of students in the class.The increase in the average weight when a teacher of 21 kg is included.What is the strength of the class?

Answer 1

The strength of the class = 20

Correct question : The average weight (in kg) of all the students in a class equals the number of students in the class. The increase in the average weight when a teacher to 21 kg is included equals the decrease in average weight when a student of 19 kg is included. What is the strength of the class?

Given :

• The average weight (in kg) of all the students in a class equals the number of students in the class.

• The increase in the average weight when a teacher to 21 kg is included equals the decrease in average weight when a student of 19 kg is included.

To find :

The strength of the class

Solution :

Step 1 of 2 :

Form the equation to find strength of the class

Let the strength of the class = n

Then average weight of all the students in the class = n kg

∴ Total weight of all the students in the class

= n × n kg

= n² kg

By the given condition

$\displaystyle \sf{ \frac{ {n}^{2} + 21}{n + 1} - n = n - \frac{ {n}^{2} + 19}{n + 1}}$

Step 2 of 2 :

Calculate the strength of the class

$\displaystyle \sf{ \frac{ {n}^{2} + 21}{n + 1} - n = n - \frac{ {n}^{2} + 19}{n + 1}}$

$\displaystyle \sf{ \implies \frac{ {n}^{2} + 21}{n + 1} + \frac{ {n}^{2} + 19}{n + 1} = n + n}$

$\displaystyle \sf{ \implies \frac{ {n}^{2} + 21 + {n}^{2} + 19 }{n + 1} = 2 n}$

$\displaystyle \sf{ \implies \frac{ 2{n}^{2} + 40 }{n + 1} = 2 n}$

$\displaystyle \sf{ \implies 2 {n}^{2} + 2n = 2 {n}^{2} + 40 }$

$\displaystyle \sf{ \implies 2n = 40 }$

$\displaystyle \sf{ \implies n = \frac{40}{2} }$

$\displaystyle \sf{ \implies n = 20 }$

Hence the strength of the class = 20

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Answer 2

The given question is incomplete, it should be like this: " The average weight (in kg) of all the students in a class equals the number of students in the class. The increase in the average weight when a teacher to 21 kg is included equals the decrease in average weight when a student of 19 kg is included. What is the strength of the class?"

Let's consider the strength of the class = P

According the question,the average weight of all the students in the class will be  = P kg

Therefore total weight of all the students in the class will be:-

= P × P kg

= P² kg

In the question it was given :-

⇒ ($\frac{P^{2} +21}{P +1}$ ) - P=P- ( $\frac{P^{2}+19 }{P+1}$)

⇒($\frac{P^{2} +21}{P +1}$ ) +( $\frac{P^{2}+19 }{P+1}$)= 2P

⇒$\frac{P^{2}+21+P^{2} +19 }{P+1}$ =2P

⇒$\frac{2P^{2}+40 }{P+1}$ = 2P

⇒$( P+1)$×2P= $(2P^{2} + 40)$

⇒$2P^{2} +2P$=$2P^{2} +40$

⇒$2P = 40$

⇒P = $\frac{40}{2}$= 20

Therefore the strength of the class will be 20.

Ans :- The strength of the class will be 20.

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