Calculate the weighted index number of the following data using the price relative method:

Item	$A$	$B$	$C$	$D$	$E$
Base year(Quantity)	$24$	$14$	$8$	$4$	$8$
Base year(Price)	$2$	$4$	$6$	$10$	$5$
Current year(Price)	$3$	$5$	$9$	$12$	$5$

 

The price relatives and weights of some products are given below.

Find the value of $x$ if the index for the set is $115$.

The price relatives and weights of some products are given below.

$\begin{array}{|ccccc|}\hline Products& A& B& C& D\\ Price relatives& 120& 110& 105& 115\\ Weights& x+1& x-1& x-2& x+2\\ \hline\end{array}$

Write the formula used for finding Index. Find the value of $x$ if the index for the set is $115$.