 # Index Number Long Questions (Question 2)

Question 2:
Diagram below is a bar chart indicating the weekly cost of the items A, B, C, D and E  for the year 2000. Table below shows the prices and the price indices for the items.

 Items Price in 2000 Price in 2006 Price Index in 2006 based on 2000 A x RM 1.75 140 B RM 2.00 RM 2.50 125 C RM 4.00 RM4.80 y D RM 6.00 z 125 E RM 2.50 2.75 110

(a) Find the value of
(i) x
(ii) y
(iii) z

(b) Calculate the composite index for items in the year 2006 based on the year 2000.

(c) The total monthly cost of the items in the year 2000 is RM456. Calculate the
corresponding total monthly cost for the year 2006.

(d) The cost of the items increases by 15 % from the year 2006 to the year 2009.
Find the composite index for the year 2009 based on the year 2000.

Solution:
(a)(i)
$\begin{array}{l}I=\frac{{P}_{1}}{{P}_{0}}×100\\ I=\frac{{P}_{2006}}{{P}_{2000}}×100\\ 140=\frac{1.75}{x}×100\\ x=\text{RM}1.25\end{array}$
(a)(ii)
$\begin{array}{l}I=\frac{{P}_{2006}}{{P}_{2000}}×100\\ y=\frac{4.80}{4.00}×100\\ y=120\end{array}$
(a)(iii)
$\begin{array}{l}I=\frac{{P}_{2006}}{{P}_{2000}}×100\\ 125=\frac{z}{6.00}×100\\ z=\text{RM7}\text{.50}\end{array}$
(b)
 Items Price Index in 2006 based on 2000 Weightage (from the diagram above) A 140 15 B 125 30 C 120 24 D 125 33 E 110 12

(c)

(d)