Question: " 6 articles A,B,C,D,E and F are sold at a different price. B is costlier than only 2 items and C is not one of them. D is cheaper than A and is costlier than F, which is costlier than E. Cost of D is the average of cost of A and C. Cost of how many articles is more than F but less than C?"
Doubt:
"How is the information of average beneficial for us? How do I judge the relative position of A,D and C from here? Some guidance about the same will be most certainly welcome."
Lets list out the information we have: \begin{gather} C > B > X_1 > X_2, X_1, X_2 \text{ are unknown}\\ A > D > F > E\\ D = \frac{A+C}{2} \end{gather} Now if $B$ is greater than D then there will be 3 articles less than it, which is not allowed so we must have $B > F > E$. Now from the average, we know that because $A > D$, $D > C$ so that the average works. We now have the full order $A > D > C > B > F > E$.
Hope this helps!