GATE2025_CS1_Q3

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?

✅ Final Answer:

The correct answer is option (C) 30.

🔹 Short Answer:

The number of students can be found by dividing the change in the total sum of marks by the change in the average. The total sum increased by 42 - 24 = 18. The average increased by 31.4 - 30.8 = 0.6. Therefore, the number of students is 18 / 0.6 = 30.

🔸 Long Answer:

This problem can be solved using the basic formula for an arithmetic mean (average) and some simple algebra. Let's break down the solution step-by-step.

Step 1: Define variables

• Let n be the total number of students in the class.
• Let S_initial be the initial (incorrect) sum of marks for all students.
• Let S_correct be the final (correct) sum of marks for all students.

Step 2: Formulate equations from the given data

From the problem statement, we have:

1. Initial (Incorrect) Average: The average was 30.8.
   Initial Average = S_initial / n = 30.8   ⟹   S_initial = 30.8 * n
2. Final (Correct) Average: The corrected average is 31.4.
   Correct Average = S_correct / n = 31.4   ⟹   S_correct = 31.4 * n

Step 3: Relate the incorrect and correct sums

The error was that one student's marks were entered as 24 instead of 42. To get the correct sum, we must subtract the wrong value and add the correct value to the initial sum.

S_correct = S_initial - 24 + 42
S_correct = S_initial + 18

Step 4: Solve for 'n'

Now we have a system of equations. We can substitute the expressions for S_initial and S_correct in terms of n into the relationship we found in Step 3.

Substitute S_correct = 31.4 * n and S_initial = 30.8 * n into the equation S_correct = S_initial + 18:

31.4 * n = (30.8 * n) + 18

Now, we solve for n:

31.4n - 30.8n = 18
0.6n = 18
n = 18 / 0.6
n = 180 / 6
n = 30

Therefore, there are 30 students in the class.

Bibliography:
- Aggarwal, R. S. (2021). Quantitative Aptitude for Competitive Examinations. S. Chand Publishing. (Chapter on Averages).

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