\

10.3.5 Index Number Long Questions (Question 5)


Question 5:
Table below shows the prices, the price indices and the proportion of four materials, ABC and D used in the production of a type of bag.

Material
Price (RM) for the year
Price index in the year 2014 based on the year 2011
Proportion
2011
2014
A
x
7.20
120
7
B
8.00
9.20
115
3
C
5.00
5.50
y
6
D
3.00
3.75
125
8
(a) Calculate the value of x and of y. [2 Marks]

(b)   Find the composite index for the bag in the year 2014 based on the year 2011. [3 Marks]

(c) Given the cost for the production of the bag in the year 2014 is RM 115, find the corresponding cost in the year 2011. [2 Marks]

(d)   From the year 2014 to year 2015, the price indices of material B and C increase by 5%, material A decrease by 10% and material D remains unchanged.
  Calculate the composite index in the year 2015 based on the year 2011. [3 Marks]



Solution:
(a)
I=P1P0×100I=P2014P2011×100120=7.20x×100x=6.00y=5.505.00×100y=110

(b)
Composite index for bag in the year2014 based on the year 2011,ˉI=IWWˉI=(120)(7)+(115)(3)+(110)(6)+(125)(8)7+3+6+8ˉI=840+345+660+100024ˉI=118.54

(c)
ˉI=P2014P2011×100118.54=115P2011×100P2011=97.01

(d)
<Composite index for the bag in the year2015 based on the year 2011,ˉI=IWW=(120×0.9)(7)+(115×1.05)(3)+(110×1.05)(6)+100024=756+362.25+693+100024=117.14


Leave a Comment