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
X :
Y
79
/
\
83
76
3 :
4
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
Y
: Z
81
/
\
76
85
4
: 5
X : Y : Z = 3 : 4 : 5
Total average for X, Y and Z = ( 3*83+4*76+5*85) /
(3+4+5)
=
(249 + 304 + 425) / 12 = 81.5
