Index Number Long Questions (Question 4)


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)
I= P 1 P 0 ×100 I= P 2008 P 2006 ×100 125= x 0.80 ×100 x=RM1.00 y= 2.80 2.00 ×100 y=140 150= 0.60 z ×100 z=RM0.40
(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
Composite index for cost of making biscuits  in the year 2008 based on the year 2006,  I ¯ I ¯ = IW W I ¯ = ( 125 )( 80 )+( 140 )( 120 )+( 150 )( 100 )+( 80 )( 60 ) 80+120+100+60 I ¯ = 46600 360 I ¯ =129.44
(b)(ii)
I ¯ = P 2008 P 2006 ×100 129.44= P 2008 585 ×100  Cost of making biscuit in the year 2008 based on the year 2006=RM757.22.
(c)
year 2006  +29.44%  year 2008  +40%  year 2010 Expected composite index for the year 2010 based on the year 2006,   I ¯ =129.44× 140 100 =181.22