Multiple choice

The average of marks obtained by 120 condidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates who passed the examination was

  1. 100

  2. 110

  3. 120

  4. 150
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A Correct answer
Explanation

Let x be the number of passed candidates. Then 120 - x is the number of failed candidates. Total marks = 120 * 35 = 4200. Sum of marks = 39x + 15(120 - x) = 4200. 39x + 1800 - 15x = 4200. 24x = 2400. x = 100.

AI explanation

Using the method of alligation, the ratio of passed to failed candidates is 39 minus 15 = 24 for the failed side and 39 minus 35 = 4 for the passed side. The ratio is 20:24, which simplifies to 5:6. Out of the total 11 parts, passed students represent 5 parts and failed students represent 6 parts. The number of passed candidates is 120 times 5/11, which equals 100.

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