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 = R M 2.70
(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 ¯ = I W W 118.5 = ( 80 ) ( 2 ) + ( 120 ) ( 3 ) + ( 135 ) ( m ) + ( 116 ) ( 4 ) 2 + 3 + m + 4 118.5 = 984 + 135 m 9 + m 1066.5 + 118.5 m = 984 + 135 m 16.5 m = 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 = R M 414.75.
(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



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 = R M 1.00 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 ¯ = I W 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 = R M 757.22.
(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

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