Averages, weighted average problems and solutions : Ascent - CAT XAT SNAP Coaching classes, tests, study material

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?

1. 81
2. 81.5
3. 82
4. 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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