Averages
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Q.

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?

 A.

81

 B.

81.5

 C.

82

 D.

84.5

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Solution:
Option(B) is correct

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 $Z$

\(=\dfrac{3\times 83+4\times 76+5\times 85}{3+4+5}\)

\(=81.5\)


(1) Comment(s)


Ripudaman Kochhar
 ()

we can do

Average of all three classes =

(83 + 76 + 85) / 3 = 81.33