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 score for all the three classes, taken together?

• According to the given condition
  (83x+76y)/(x+y) = 79
  on solving x = 3y/4
  similarly (76y+85z)/(y+z) = 81
  on solving z = 5y/4
  average score for all the three classes taken together = 83x+76y+85z/x+y+z
  
  on solving you will get 978y/12y=81.5
• 11 years agoHelpfull: Yes(15) No(1)
• 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+5×853+4+5)
  =(249+304+425)12=81.5
• 10 years agoHelpfull: Yes(4) No(0)
• 83+76+85=244÷3=81.33 =~ 81.5
• 7 years agoHelpfull: Yes(1) No(0)