Multiple choice

There are 100 students in three departments [X, Y and Z] of a college. Average marks of all the student is 82.7. Average marks of X and Z is 83. Average marks of Y are 82, then find number of students in Y?

  1. 51

  2. 78

  3. 47

  4. 30

  5. 39
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D Correct answer
Explanation

Let nX, nY, nZ be students in each. nX+nY+nZ = 100. Total marks = 82.7 * 100 = 8270. (nX+nZ)*83 + nY*82 = 8270. Since nX+nZ = 100 - nY, we have (100-nY)*83 + 82nY = 8270. 8300 - 83nY + 82nY = 8270. nY = 30.

AI explanation

The total marks of all 100 students is 100 multiplied by 82.7, which equals 8270. Let the number of students in department Y be Y. The total marks of X and Z combined is (100 minus Y) multiplied by 83, and the total marks of Y is Y multiplied by 82. Setting up the equation, 8300 minus 83Y plus 82Y equals 8270. Solving for Y gives 8300 minus 8270 equals Y, so the number of students in Y is 30.

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