Question

A pupil’s marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half the number of pupils in the class. The number of pupils in the class is _________.
A. 10
B. 20
C. 40
D. 73

Answer 1

Hint: Assuming the number of pupils to be x and with the given condition we can get that the increase is half times the number of pupils in the class and we can also get the increase by finding the difference between the marks and further equating them we get the value of x.

Complete step by step solution:
So now let the number of pupils be x
Due to incorrect entry of marks the average has increased by half the number of pupils
It is nothing but the increase half times the number of pupils
Therefore increase = $\dfrac{1}{2}x$ ……….(1)
But here with the given marks the increase in marks can be given by their difference
That is , increase $ = 83 - 63 = 20$ ……..(2)
Hence by equating 1 and 2 we get
$
   \Rightarrow \dfrac{x}{2} = 20 \\
   \Rightarrow x = 40 \\
 $
Therefore the number of pupils in the class is 40

Therefore the correct answer is option C.

Note :
In colloquial language, an average is a single number taken as representative of a list of numbers. Different concepts of average are used in different contexts. Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged. In statistics, mean, mode and median are all known as measures of central tendency and in colloquial usage any of these might be called an average value.