Question

Construct an index number by Price Relatives Method using 2004 as base year:

Goods	A	B	C	D
2004 Price (₹)	8	10	15	20
2017 Price (₹)	10	12	18	22
2018 Price (₹)	12	14	20	25

Answer 1

Goods	2004 Price (P0)	2017 Price (P1)	2018 Price (P2)	Price relatives of 2017 in relation to 2004 $\left(\frac{{\mathit{P}}_{\mathbf{1}}}{{\mathit{P}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}\right)$	Price relatives of 2018 in relation to 2004 $\left(\frac{{\mathit{P}}_{\mathbf{2}}}{{\mathit{P}}_{\mathbf{0}}}\mathbf{\times }\mathbf{100}\right)$
A	8	10	12	$\frac{10}{8}\times 100=125$	$\frac{12}{8}\times 100=150$
B	10	12	14	$\frac{12}{10}\times 100=120$	$\frac{14}{10}\times 100=140$
C	15	18	20	$\frac{18}{15}\times 100=120$	$\frac{20}{15}\times 100=133.33$
D	20	22	25	$\frac{22}{20}\times 100=110$	$\frac{25}{20}\times 100=125$
N = 4				$\mathrm{\Sigma }\left(\frac{P_1}{P_0}\times 100\right)=475$	$\mathrm{\Sigma }\left(\frac{P_2}{P_0}\times 100\right)=548.33$

$$\begin{gathered} P_{01}=\frac{\mathrm{\Sigma }\left({\displaystyle \frac{P_1}{P_0}}\times 100\right)}{N}=\frac{475}{4}=118.75 \\ {P}_{02}=\frac{\mathrm{\Sigma }\left({\displaystyle \frac{P_2}{P_0}}\times 100\right)}{N}=\frac{548.33}{4}=137.08 \end{gathered}$$