Question

There are N students in a class. Their class teacher gave them a task of finding the average of the first N natural numbers. Each of them missed a different number while adding. The average obtained by each student was 21. Find N.

Answer 1

Answer:

41

Step-by-step explanation:

there are N students....

average of first n natural is (N+1)/2...

given average =21..

therefore equate...N=41

Answer 2

Answer:

41

Step-by-step explanation:

Let Tn be the sum of N natural numbers.

Average obtained by each student = 21

⇒ (Tn - x)/(n-1)=21  (∵ Each of them missed a different number while adding)

⇒Tn - x = 21 * (n-1)

Sum of Average obtained  by all students :

     n (Tn ) - ( x1 + x2 +...+xn) =n * 21 * (n-1)

⇒   n (Tn) - (Tn)  =  n * 21 * (n-1)  (∵ Each of them missed a different number, so sum of all different numbers will be Tn)

⇒  Tn * (n-1) = n * 21 * (n-1)

⇒ Tn = n * 21

⇒ n * (n+1) / 2 = n * 21  

⇒ n +1 = 21 * 2

⇒ n = 42 -1

⇒ n = 41