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)
I= P 1 P 0 ×100 x= P 2009 P 2008 ×100 x= 2 2.5 ×100 x=80
(a)(ii)
135= P 2009 2 ×100 135= y 2 ×100 y=RM2.70
(a)(iii)
116= 5.80 P 2008 ×100 116= 5.80 z ×100 z=RM5
(b)
Composite index for items in the year 2009 based on the year 2008,  I ¯ =118.5 I ¯ = IW W 118.5= ( 80 )( 2 )+( 120 )( 3 )+( 135 )( m )+( 116 )( 4 ) 2+3+m+4 118.5= 984+135m 9+m 1066.5+118.5m=984+135m 16.5m=82.5 m=5
(c)
I ¯ = P 2009 P 2008 ×100 118.5= P 2009 350 ×100 Total expenditure in the year 2009,  P 2009 =RM414.75.
(d)
For stationery B, It is given  P 2010 P 2008 ×100=132  P 2010 P 2008 = 132 100 and  P 2009 P 2008 ×100=120  P 2009 P 2008 = 120 100 Price index for stationery B in the year 2010 based on the year 2009, I 10/09 = P 2010 P 2009 ×100 I 10/09 = P 2010 P 2008 × P 2008 P 2009 ×100 I 10/09 = 132 100 × 100 120 ×100 I 10/09 =110