Question

The average of A, B is 2.5, B, C is 4 and average of C, A is 3.5. The average of A, B and C is equal to

• A. 7.5
• B. $\frac{10}{3}$
  
• C. 4.5
• D. 3.5

Answer 1

The correct option is B $\frac{10}{3}$


Given that the average of A, B is 2.5, average of B, C is 4 and average of C, A is 3.5.
Now,
Average = $\frac{\text{Sum of obserrvations}}{\text{Total number of observations}}$
$\therefore \frac{A+B}{2}=2.5$
$\Rightarrow A+B=5$ ........(i)
and, $\frac{B+C}{2}=4$
$\Rightarrow B+C=8$ ........(ii)
and, $\frac{C+A}{2}=3.5$
$\Rightarrow C+A=7$ ........(iii)
Adding (i), (ii) and (iii), we get
$\Rightarrow (A+B)+(B+C)+(C+A)=5+8+7$
$\Rightarrow 2(A+B+C)=20$
$\Rightarrow A+B+C=10$
$\therefore$ Average of A, B, C =$\frac{A+B+C}{3}$
=$\frac{10}{3}$
Hence, the correct answer is option (b).