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Official PYQ · 2025Set 1 · Q3MCQ1 mark

GATE CS 2025 Set 1 Q3 — General Aptitude

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The average marks obtained by a class in an examination were calculated as 30.830.8. However, while checking the marks entered, the teacher found that the marks of one student were entered incorrectly as 2424 instead of 4242. After correcting the marks, the average becomes 31.431.4. How many students does the class have?

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Answer: C

Let NN be the total number of students in the class.

The initial average marks of the class is 30.830.8. Therefore, the initial sum of marks is:

Initial Sum=30.8×N\text{Initial Sum} = 30.8 \times N

One student's marks were incorrectly entered as 2424 instead of 4242. The correction increases the total sum of marks by:

Increase in Sum=42−24=18\text{Increase in Sum} = 42 - 24 = 18

The correct sum of marks is:

Correct Sum=30.8×N+18\text{Correct Sum} = 30.8 \times N + 18

We are given that the correct average is 31.431.4. Thus:

30.8×N+18N=31.4\frac{30.8 \times N + 18}{N} = 31.4

Solving for NN:

30.8×N+18=31.4×N30.8 \times N + 18 = 31.4 \times N31.4×N−30.8×N=1831.4 \times N - 30.8 \times N = 180.6×N=180.6 \times N = 18N=180.6=30N = \frac{18}{0.6} = 30

Thus, the class has 30 students, which corresponds to option (C).

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