GATE CSE 2025 | Set 1 | GA | Question: 3

Question

The average marks obtained by a class in an examination were calculated as $30.8$. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as $24$ instead of $42$. After correcting the marks, the average becomes $31.4$. How many students does the class have?

• A. $25$
• B. $28$
• C. $30$
• D. $32$

Comments

Let X be the sum of marks of all candidates initially, and n be the no.of students.
X / n = 30.8 -----> X = n * 30.8  ----(1)
One of the students marks was mistaken , so increase 18 more marks to make 24 to 42
(X + 18) / n = 31.4 ------>  X = (n *31.4) - 18 -----(2)

Equate (1) and (2)
n * 30.8 = (n*31.4) - 18
n * 0.6 = 18
n = 30

Answer 1

C) 30 

let there be N students and total of all students except that one student whose marks are wrong be X 
(X+24)/N = 30.8 
X = 30.8N - 24  --(Eq. 1)

After correcting, 
(X+42)/N = 31.4
X = 31.4N - 42 --(Eq. 2)

by equation 1 & 2, we get N = 30
 

Answer 2

total increase = 42−24 = 18
           average increase = 31.4−30.8 = 0.6
           Since average = total / number of students
           therefore increase in average = increase in total / number of students

           0.6=18/n = n =18/0.6
           n = 30

Answer 3

\[\text{Let total students} = N\]
\[\text{Marks of students: } x_1, x_2, x_3, \ldots, x_N\]
Incorrect data
\[
\textbf{Incorrect Average} = 30.8,\qquad x_1 = 24
\]

\[
30.8N = 24 + (x_2 + x_3 + \cdots + x_N)
\]

\[
x_2 + x_3 + \cdots + x_N = 30.8N - 24 \qquad (1)
\]

Correct data
\[
\textbf{Correct Average} = 31.4,\qquad x_1 = 42
\]

\[
31.4N = 42 + (x_2 + x_3 + \cdots + x_N)
\]

\[
x_2 + x_3 + \cdots + x_N = 31.4N - 42 \qquad (2)
\]

Equating
\[
30.8N - 24 = 31.4N - 42
\]

\[
31.4N - 30.8N = 42 - 24
\]

\[
0.6N = 18
\]

\[
N = \frac{18}{0.6} = 30
\]

\[
\boxed{N = 30}
\]
 

Answer 4

Incorrect total marks = 30.8n

Actual total marks = Incorrect total + (Correct mark − Wrong mark)

Correct total=30.8n+(42−24)

Correct total=30.8n+18

(30.8n+18​) / n =31.4

 

hence n = 30

Answer 5

Option-C

Answer 6

Given avg of first ->from above 

after replacing value averages increases if u see by option verification= no of students *avg gives total sum ;

if total sum divides no of students gives that second averages then that average is satisfied;

do option verfication ;

orrrrrrrrrrrrrrr second method 

increases in number vs increases in averages 

how much increase value divides by average increase after gives no of students;

change in average=change in sum  and no change in no of students so it is constant ;

0.6=18/no of students do  cancellation according to equation