11.3.1 Index Number Long Questions (Question 1 & 2)

Question 1:

Table below shows the price indices and percentage of usage of four items, P , Q , R and S , which are the main ingredients in the production of a type of toy.

 Item Price index for the year 2007 based on the year 2004 Percentage of usage (%) P 125 30 Q x 20 R 115 10 S 135 40

(a)  Calculate
(i) the price of S in the year 2004 if its price in the year 2007 is RM43.20 ,
(ii) the price index of P in the year 2007 based on the year 2002 if its price index in
the year 2004 based on the year 2002 is 110.
(b)   The composite index of the cost of toy production for the year 2007 based on the
year 2004 is 125.
Calculate
(i) the value of  x ,
(ii) the price of the toy in the year 2004 if the corresponding price in the year 2007 is
RM75.

Solution:
(a)(i)

(a)(ii)

(b)(i)

(b)(ii)

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)

1 thought on “11.3.1 Index Number Long Questions (Question 1 & 2)”

1. I need the longest table with x, y, z