Multiple choice

In an examination, the average marks of 180 students is 70. If average marks of passed students is 85 and average marks of failed students is 25 then find out the ratio between the passed and failed students in the examination ?

  1. 3 : 1

  2. 2 : 1

  3. 3 : 2

  4. 3 : 4

  5. None of these
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A Correct answer
Explanation

Using allegation method: Let passed students = P, failed students = F. Total students = 180, so P + F = 180. Average of all is 70, so total marks = 180 × 70 = 12600. Also: 85P + 25F = 12600. Substituting F = 180 - P: 85P + 25(180 - P) = 12600, which gives 60P = 8100, so P = 135 and F = 45. Ratio P:F = 135:45 = 3:1. The claimed answer 3:1 is correct.

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