| 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 [SSC (CGL) Mains 2015] |
A) 80
B) 80.5
C) 81.5
D) 81
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 \[=\,\,\frac{83a+76b+85c}{a+b+c}\] |
| \[=\,\,\frac{83\times \frac{3b}{4}+76b+85\times \frac{5b}{4}}{\frac{3b}{4}+b+\frac{5b}{4}}\] |
| \[=\,\,\frac{249b+304b+425b}{3b+4b+5b}\,\,=\,\,\frac{978b}{12b}=81.5\] |
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