# 11.3.2 Index Number Long Questions (Question 3 & 4)

Question 3:
Table shows the prices, the price indices and weightage for four types of stationery A, B, C and D.

 Stationery Price(RM) per unit Price index for the year 2009 based on the year 2008 Weightage Year 2008 Year 2009 A 2.50 2.00 x 2 B 3.50 4.20 120 3 C 2.00 y 135 m D z 5.80 116 4

(a) Find the value of
(i) x, (ii) y, (iii)    z.
(b) The composite index for the price of the stationery in the year 2009 based on the year
2008 is 118.5. Calculate the value of m.
(c) The total expenditure for the stationery in the year 2008 is RM350. Calculate the
corresponding total expenditure in the year 2009.
(d) The price index for B in the year 2010 based on the year 2008 is 132. Calculate the
price index for B in the year 2010 based on the year 2009.

Solution:
(a)(i)
$\begin{array}{l}I=\frac{{P}_{1}}{{P}_{0}}×100\\ x=\frac{{P}_{2009}}{{P}_{2008}}×100\\ x=\frac{2}{2.5}×100\\ x=80\end{array}$
(a)(ii)
$\begin{array}{l}135=\frac{{P}_{2009}}{2}×100\\ 135=\frac{y}{2}×100\\ y=RM2.70\end{array}$
(a)(iii)
$\begin{array}{l}116=\frac{5.80}{{P}_{2008}}×100\\ 116=\frac{5.80}{z}×100\\ z=\text{RM5}\end{array}$
(b)

(c)

(d)

Question 4:
Table below shows the prices and the price indices for the four ingredients P, Q, R and S, used in making biscuits of a particular kind.

 Ingredients Price per kg ( RM ) Price index for the year 2008 based on the year 2006 Year 2006 Year 2008 P 0.80 x 125 Q 2.00 2.8 y R z 0.60 150 S 0.50 0.40 80

Diagram below is a pie chart which represents the relative amount of the ingredients PQR and S, used in making biscuits.

(a) Find the value of x, y and z.
(b)(i) Calculate the composite index for cost of making these biscuits in the year 2008
based on the year 2006.
(ii) Hence, calculate the corresponding cost of making these biscuits in the year 2008 if
the cost in the year 2006 was RM 585.
(c) The cost of making these biscuits is expected to increase by 40 % from the year 2008 to
the year 2010. Find the expected composite index for the year 2010 based on the year
2006.

Solution:
(a)
$\begin{array}{l}I=\frac{{P}_{1}}{{P}_{0}}×100\\ I=\frac{{P}_{2008}}{{P}_{2006}}×100\\ 125=\frac{x}{0.80}×100\\ x=RM1.00\\ \\ y=\frac{2.80}{2.00}×100\\ y=140\\ \\ 150=\frac{0.60}{z}×100\\ z=\text{RM0}\text{.40}\end{array}$
(b)(i)
 Ingredients Price index for the year 2008 based on the year 2006 Weightage P 125 80 Q 140 120 R 150 100 S 80 60

Sector P = 360o– 120o – 100o – 60o = 80o

(b)(ii)

(c)