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, A, B, C 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
Material	2011	2014	Price index in the year 2014 based on the year 2011	Proportion
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)

\begin{array}{l} I = \frac{P_{1}}{P_{0}} \times 100 \\ I = \frac{P_{2014}}{P_{2011}} \times 100 \\ 120 = \frac{7.20}{x} \times 100 \\ x = 6.00 \\ y = \frac{5.50}{5.00} \times 100 \\ y = 110 \end{array}

(b)

\begin{array}{l} Composite index for bag in the year \\ 2014 based on the year 2011, \\ \bar{I} = \frac{\sum I W}{\sum W} \\ \bar{I} = \frac{(120) (7) + (115) (3) + (110) (6) + (125) (8)}{7 + 3 + 6 + 8} \\ \bar{I} = \frac{840 + 345 + 660 + 1000}{24} \\ \bar{I} = 118.54 \end{array}

(c)

\begin{array}{l} \bar{I} = \frac{P_{2014}}{P_{2011}} \times 100 \\ 118.54 = \frac{115}{P_{2011}} \times 100 \\ P_{2011} = 97.01 \end{array}

(d)

\begin{array}{l} Composite index for the bag in the year \\ 2015 based on the year 2011, \\ \bar{I} = \frac{\sum I W}{\sum W} \\ = \frac{(120 \times 0.9) (7) + (115 \times 1.05) (3) + (110 \times 1.05) (6) + 1000}{24} \\ = \frac{756 + 362.25 + 693 + 1000}{24} \\ = 117.14 \end{array}

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