question_answer

There are three classes A, B and C. The average of class A is 81. The average of class B is 74. The average of class C is 83. The average of class A and B is 77, and the average of class B and C is 79. Find the average of all three classes.

A)  74.4               

B)  79.5   

C)       81.2   

D)       78.5   

E)       72.5

Correct Answer: B

Solution :

By allegation method So, the ratio of students in Class A to B comes out to 3 : 4. And, the ratio of students in Class B to C is 4 : 5. Ratio of students in class A, B and C = 3 : 4 : 5 So, average of all the classes \[=\frac{(81\times 3+74\times 4+83\times 5)}{3+4+5}=\frac{243+296+415}{12}\] \[=\frac{954}{12}=79.5\]