Multiple choice

The average mark of students of class ECE is 50 and the average mark of students of class CSE is 60. The overall average mark of students both classes is 56. Find the ratio of the number of students of classes ECE and CSE, respectively.

  1. 3 : 2

  2. 2 : 3

  3. 5 : 8

  4. 5 : 13

  5. None of these
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B Correct answer
Explanation

Let E and C be the number of students. (50E + 60C) / (E + C) = 56. 50E + 60C = 56E + 56C. 4C = 6E. E/C = 4/6 = 2/3.

AI explanation

Using the method of alligation, the ratio of the number of students in the two classes is the inverse ratio of the differences between their individual averages and the overall average. The difference between the overall average and the class CSE average is 56 minus 60, giving 4. The difference between the class ECE average and the overall average is 50 minus 56, giving 6. Therefore, the ratio of the number of students in class ECE to class CSE is 4 to 6, which simplifies to 2 is to 3.

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