Aptitude Discussion

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 |

**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 $Z$

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

\(=81.5\)