Weighted Average Questions : CAT 2016 Online Preparation
Question 4 the day : August 12, 2003
The question for the day is from the topic Averages. It is a question on weighted averages.
Question
Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average for all the three classes?
 81
 81.5
 82
 84.5
Correct Answer is 81.5. Choice (2) is right.
Explanatory Answer
Average score of class X is 83 and that of class Y is 76 and the combined average of X and Y is 79.
By rule of alligation ratio of students in X : Y is given by
Similarly, average score of class Y is 76 and that of class Z is 85 and the combined average is 81.
By rule of alligation ratio of students in Y : Z is
X : Y : Z = 3 : 4 : 5
Total average for X, Y and Z =
=
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