# Index Number Long Questions (Question 3)

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)