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 ¯ = IW W 125= ( 125 )( 30 )+( x )( 20 )+( 115 )( 10 )+( 135 )( 40 ) 30+20+10+40 125= 10300+20x 100 12500=10300+20x x=110
(b)(ii)
Lets price of the toy in the year 2004 is  P 2004 P 2004 × 125 100 =75 P 2004 =RM60