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

Given:

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.

To find:

Find N.

Solution:

Let Rn be the sum of N natural numbers.

Given, the average obtained by each student = 21

As, each of the student  missed a different number while adding

(Rn - x) / (N-1) = 21  

Rn - x = 21 × (N-1)

Therefore, the sum of Average obtained  by all students,

N (Rn ) - ( x1 + x2 + x3 + ........+ xn) = N × 21 × (N - 1)

as, each of them missed a different number, so sum of all different numbers will be Rn

N (Rn) - (Rn)  =  N × 21 × (N - 1)

Rn * (N - 1) = N × 21 × (N - 1)

Rn = N × 21

N × (N + 1) / 2 = N × 21  

N + 1 = 21 × 2

N = 42 - 1

∴ N = 41