Question

Choose the correct option from the provided options to the following question:
Calculate the price index for the following by using price relative method.

Material	Cement	Timber	Steel	Bricks
Price in $1969$(in Rs)	$5$	$9.5$	$35$	$12$
Price in $1970$(in Rs)	$8$	$14.3$	$42$	$24$

A. $152.34$
B. $135.5$
C. $157.5$
D. $154.25$

Answer 1

For each material, take the price in the first year as a variable representation and the price in the second ear as another representation. Then calculate the relative price by calculating the ratio of the price in first year to the ratio of the price in second year and then multiply it with hundred to get the relativity. Find the total relative price. Then substitute the total relative price in the formula of the calculation of price relative, where frequency is needed as well.

Complete step-by-step solution:
Let us take the price in $1969$ as ${P_0}$
Let us take the price in $1970$ as ${P_1}$
Number of total Materials, i.e. frequency is $N$
$N = 4$
Let us take each material one by one;
Cement:
Price in $1969$ (in Rs) {P_0}$$$$ = $5$
Price in $1970$ (in Rs) {P_1}$$$$ = $8$
Price relative \dfrac{{{P_1}}}{{{P_0}}} \times 100$$$$ = $\dfrac{8}{5} \times 100 = 160.00$
Timber:
Price in $1969$ (in Rs) {P_0}$$$$ = $9.5$
Price in $1970$ (in Rs) {P_1}$$$$ = $14.3$
Price relative \dfrac{{{P_1}}}{{{P_0}}} \times 100$$$$ = $\dfrac{{9.5}}{{14.3}} \times 100 = 150.52$
Steel:
Price in $1969$ (in Rs) {P_0}$$$$ = $35$
Price in $1970$ (in Rs) {P_1}$$$$ = $42$
Price relative \dfrac{{{P_1}}}{{{P_0}}} \times 100$$$$ = $\dfrac{{35}}{{42}} \times 100 = 120.00$
Bricks:
Price in $1969$ (in Rs) {P_0}$$$$ = $12$
Price in $1970$ (in Rs) {P_1}$$$$ = $24$
Price relative \dfrac{{{P_1}}}{{{P_0}}} \times 100$$$$ = $\dfrac{{12}}{{24}} \times 100 = 200.00$
Total Price relative of all the materials = $$$$160.00 + 150.52 + 120.00 + 200.00
$\Rightarrow$Total $= 630.52$
Now, to find the relative price, i.e., ${P_{01}}$, we have;
${P_{01}} = \dfrac{{\dfrac{{{P_1}}}{{{P_0}}} \times 100}}{N}$
Substituting the values, we get;
$\Rightarrow {P_{01}} = \dfrac{{630.52}}{4}$
Dividing the term with the denominator, we get;
$\Rightarrow {P_{01}} = 157.5$
Hence, the price index for $1970$ by taking $1969$ as the base year$= 157.5$

$\therefore$ The correct option is C.

Note: We can observe that a price index is a normalized average of price relatives for a given class of goods or services in a given region, during a given interval of time. It is a statistic designed to help to compare how these price relatives, taken as a whole, differ between time periods or geographical locations. Price indices have several potential uses. For particularly broad indices, the index can be said to measure the economy’s general price level or a cost of living. More narrow price indices can help producers with business plans and pricing. Something, they can be useful in helping to guide investment. The frequency of the given statistical data is the number of materials used in each case. Here, the solution is entirely formula-based. You have to substitute the values acquired in the formula.