2016 · Q86
The average score of class X is 83. The average score of class Y is 76. The average score of class Z is 85. The average score of class X and Y is 79 and average score of class Y and Z is 81. What is the average score of X, Y and Z ?
Elementary MathematicsStatistics
- A81.5
- B80.5
- C79.0
- D78.0
Explanation
From 83nₓ+76n_y = 79(nₓ+n_y) we get nₓ:n_y = 3:4, and from 76n_y+85n_z = 81(n_y+n_z) we get n_y:n_z = 4:5. The combined average is (3×83+4×76+5×85)/12 = 978/12 = 81.5 (option A).