Consider the following table in respect of students of 4 schools who appeared in a test:<br><br> <table> <thead><tr><th>School</th><th>Number of<br>students</th><th>Average marks in<br>the test</th></tr></thead> <tbody> <tr><td>I</td><td>60</td><td>60</td></tr> <tr><td>II</td><td>50</td><td>80</td></tr> <tr><td>III</td><td>50</td><td>40</td></tr> <tr><td>IV</td><td>X</td><td>50</td></tr> </tbody> </table><br><br> If the average marks of the students of <strong>ALL</strong> four schools are 58, then how many students appeared from School-IV?
- A. 38
- B. 40 ✓
- C. 42
- D. 44
Correct Answer: B. 40
Explanation
Total sum of marks = 60(60) + 50(80) + 50(40) + X(50) = 3600 + 4000 + 2000 + 50X = 9600 + 50X. Total students = 160 + X. Setting the overall average to 58: \frac{9600 + 50X}{160 + X} = 58 \implies 9600 + 50X = 9280 + 58X \implies 8X = 320 \implies X = 40.
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