Multiple choice

The average marks of 120 students are 35. If the average of passed students was 39 and failed students was 15, then find the number of students who have passed

  1. 80

  2. 100

  3. 120

  4. 140
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P be passed students and F be failed students. P + F = 120. 39P + 15F = 35 * 120 = 4200. Substitute F = 120 - P: 39P + 15(120 - P) = 4200 => 24P + 1800 = 4200 => 24P = 2400 => P = 100.

AI explanation

Using the method of alligation, the ratio of passed to failed students is calculated from the differences between their averages and the overall average. The difference for passing students is 39 minus 35 to give 4, and the difference for failing students is 35 minus 15 to give 20. This yields a passing to failing ratio of 4 to 20, or 1 to 5, meaning 1 out of every 6 students passed. Multiplying this 1/6 fraction by the total of 120 students shows that 100 students passed.

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