Question: Three Science classes A, B and C take a life Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of classes A and B is 79 and average score of classes B and C is 81. Then, the average score of classes A, B and C is
Options:
A) 80
B) 80.5
C) 81.5
D) 81
Show Answer
Answer:
Correct Answer: C
Solution:
- Let the number of students In classes A, B and C be a, b and c respectively.
$ \therefore $ Total score of class A = 83a
Total score of class B = 76b
Total score of class C = 85c
According to the question,
$ \frac{83a+76b}{a+b}=79 $ [ $ \because $ average of A and B = 79]
$ \Rightarrow $ $ 4a=3b $
$ \Rightarrow $ $ a=\frac{3b}{4} $
(i)
Again, average of B and C = 81
$ \Rightarrow $ $ \frac{76b+85c}{b+c}=81 $
$ \Rightarrow $ $ 5b=4c $
$ \Rightarrow $ $ c=\frac{5b}{4} $ … (ii)
$ \therefore $ Average of A, B and C $ =\frac{83a+76b+85c}{a+b+c} $
$ =\frac{83\times \frac{3b}{4}+76b+85\times \frac{5b}{4}}{\frac{3b}{4}+b+\frac{5b}{4}} $
$ =\frac{249b+304b+425b}{3b+4b+5b}=\frac{978b}{12b}=81.5 $
BETA
