Index Number Long Questions (Question 1)


Question 1:

Table below shows the price indices and percentage of usage of four items, P , Q , R and S , which are the main ingredients in the production of a type of toy.

Item
Price index for the year 2007 based on the year 2004
Percentage of usage
(%)
P
125
30
Q
x
20
R
115
10
S
135
40

(a)  Calculate
      (i) the price of S in the year 2004 if its price in the year 2007 is RM43.20 ,
      (ii) the price index of P in the year 2007 based on the year 2002 if its price index in
           the year 2004 based on the year 2002 is 110.
(b)   The composite index of the cost of toy production for the year 2007 based on the
        year 2004 is 125.
        Calculate
       (i) the value of  x ,
       (ii) the price of the toy in the year 2004 if the corresponding price in the year 2007 is
            RM75.

Solution:
(a)(i)
135 = 43.2 P 2004 × 100 P 2004 = 43.2 × 100 135 = 32 The price of  S  in the year 2004 is RM32
(a)(ii)
Given  P 2004 P 2002 × 100 = 110   P 2004 P 2002 = 110 100 and  P 2007 P 2004 × 100 = 125   P 2007 P 2004 = 125 100 Price index of  P  in the year 2007 based on the year 2002, I = P 2007 P 2002 × 100 I = P 2007 P 2004 × P 2004 P 2002 × 100 I = 125 100 × 110 100 × 100 I = 137.50
(b)(i)
Given composite index  I ¯ = 125 I ¯ = I W W 125 = ( 125 ) ( 30 ) + ( x ) ( 20 ) + ( 115 ) ( 10 ) + ( 135 ) ( 40 ) 30 + 20 + 10 + 40 125 = 10300 + 20 x 100 12500 = 10300 + 20 x x = 110
(b)(ii)
Lets price of the toy in the year 2004 is  P 2004 P 2004 × 125 100 = 75 P 2004 = R M 60

Question 2:
Diagram below is a bar chart indicating the weekly cost of the items A, B, C, D and E  for the year 2000. Table below shows the prices and the price indices for the items.


Items

Price in 2000

Price in 2006
Price Index in 2006 based on 2000
A
x
RM 1.75
140
B
RM 2.00
RM 2.50
125
C
RM 4.00
RM4.80
y
D
RM 6.00
z
125
E
RM 2.50
2.75
110

(a) Find the value of
    (i) x
    (ii) y
    (iii) z                                                                                                   

(b) Calculate the composite index for items in the year 2006 based on the year 2000.
                                                                                                                            
(c) The total monthly cost of the items in the year 2000 is RM456. Calculate the
      corresponding total monthly cost for the year 2006.
                                                                                                                            
(d) The cost of the items increases by 15 % from the year 2006 to the year 2009.
      Find the composite index for the year 2009 based on the year 2000.

Solution:
(a)(i)
I = P 1 P 0 × 100 I = P 2006 P 2000 × 100 140 = 1.75 x × 100 x = RM 1.25
(a)(ii)
I = P 2006 P 2000 × 100 y = 4.80 4.00 × 100 y = 120
(a)(iii)
I = P 2006 P 2000 × 100 125 = z 6.00 × 100 z = RM7 .50
(b)
Items
Price Index in 2006 based on 2000
Weightage
(from the diagram above)
A
140
15
B
125
30
C
120
24
D
125
33
E
110
12

Composite index for items in the year 2006 based on the year 2000,  I ¯ I ¯ = I W W I ¯ = ( 140 ) ( 15 ) + ( 125 ) ( 30 ) + ( 120 ) ( 24 ) + ( 125 ) ( 33 ) + ( 110 ) ( 12 ) 15 + 30 + 24 + 33 + 12 I ¯ = 14175 114 I ¯ = 124.34
(c)
I = P 1 P 0 × 100 Lets total monthly cost for the year 2006 is  P 2006 I = P 2006 P 2000 × 100 124.34 = P 2006 RM 456 × 100 P 2006 = RM 567
(d)
Lets composite index for the year 2009 based on year 2000 is  I ¯ 2009 I ¯ 2009 = 124.34 × 115 100 I ¯ 2009 = 143

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