Question

Solve the following problem :

Find x if the Price Index Number using Simple Aggregate Method is 200.

Commodity	P	Q	R	S	T
Base Year Price	20	12	22	23	13
Current Year Price	30	x	38	51	19

Answer 1

Commodity	Base Year Price p0	Current Year Price p1
P	20	30
Q	12	x
R	22	38
S	23	51
T	13	19
Total	90	x + 138

From the table, ${\displaystyle \sum {\text{p}}_0=90,\sum {\text{p}}_1=x+138}$

P₀₁ = ${\displaystyle \frac{\sum {\text{p}}_1}{\sum {\text{p}}_0}\times 100}$

∴ 200 = ${\displaystyle \frac{x+138}{90}\times 100}$

∴ ${\displaystyle \frac{x+138}{90}}$ = 2

∴ x + 138 = 180
∴ x = 180 – 138
∴ x = 42.