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10.3.2 Index Number Long Questions (Question 2)

Question 2:
Table shows the prices, the price indices and weightage for four types of stationery A, B, C and D.


(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=P1P0×100x=P2009P2008×100x=22.5×100x=80

(a)(ii)
135=P20092×100135=y2×100y=RM2.70

(a)(iii)
116=5.80P2008×100116=5.80z×100z=RM5


(b)
Composite index for items in the year 2009 based on the year 2008, ¯I=118.5¯I=IWW118.5=(80)(2)+(120)(3)+(135)(m)+(116)(4)2+3+m+4118.5=984+135m9+m1066.5+118.5m=984+135m16.5m=82.5m=5

(c)
¯I=P2009P2008×100118.5=P2009350×100Total expenditure in the year 2009, P2009=RM414.75.

(d)
For stationery B,It is given P2010P2008×100=132 P2010P2008=132100and P2009P2008×100=120 P2009P2008=120100Price index for stationery B in the year 2010 based on the year 2009,I10/09=P2010P2009×100I10/09=P2010P2008×P2008P2009×100I10/09=132100×100120×100I10/09=110


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