Multiple choice

The average marks obtained by 180 students in an examination are 50. If the average marks obtained by students who have passed are 80 and that obtained by students who have failed are 40, then what is the number of students who have failed the examination?

  1. 90

  2. 135

  3. 100

  4. 45
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let F be the number of failed students and P be the number of passed students. P + F = 180. Total marks = 180 * 50 = 9000. 80P + 40F = 9000. Substitute P = 180 - F: 80(180 - F) + 40F = 9000 => 14400 - 40F = 9000 => 40F = 5400 => F = 135.

AI explanation

Using the method of alligation, the ratio of passed to failed students is the difference between the overall average and the failed average, to the difference between the passed average and the overall average. This gives a ratio of 50 minus 40 to 80 minus 50, resulting in 10 to 30, or 1 to 3. Since the total number of students is 180, the number of failed students is 3 divided by 4 of 180, which is 135.

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