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?

• Solution:
  
  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
  
• 9 years agoHelpfull: Yes(26) No(5)
• X = 83
  Y =76
  Z =85
  so to find the average of x,y,z
  (x+y+z)/3=244/3
  ans is 81.33
• 9 years agoHelpfull: Yes(8) No(7)
• 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
• 9 years agoHelpfull: Yes(2) No(0)
• 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
• 9 years agoHelpfull: Yes(1) No(0)
• No fo student in class X = x
  
  Total score of student in Class X = 83x
  
  No of students in Class Y= y
  
  Total score of student in Class Y = 76y
  
  No of students in Class Z = z
  
  Total score of students in Class Z = 85z
  
  Average score of class X and Y = 79
  
  83x + 76y = 79
  
  x + y
  
  83x + 76y = 79(x + y)
  
  83x - 79x = 79y - 76y
  
  4x = 3y
  
  x = 3y/4
  
  Similarly we we should with classes Y and Z
  
  76y + 85z = 81y + 81z
  
  z = 5y/4
  
  Average of three classes =
  
  83x + 76y + 85z = 83 (3y/4) + 76y + 85 (5y/4)
  
  x + y + z (3y/4) + y + (5y/4)
  
  249/4 + 304/4 + 425/4 = 249 + 304 + 425 = 978 / 12 = 81.50
  --------------------------------- ----------------------
  3/4 + 4y/4 + 5/4 12
• 5 years agoHelpfull: Yes(1) No(0)
• 81.5
  http://www.lofoya.com/aptitude/average/three-math-classes-x-y-and-z-take-an-algebra-test-the-average-score-in.php
• 9 years agoHelpfull: Yes(0) No(0)
• X=83
  Y=76
  Z=85
  In question,he asked that average so (X+Y+Z)/3
  We know the values of X,Y &Z.
• 9 years agoHelpfull: Yes(0) No(0)