Question

Find values x and y if the Price Index Number by Simple Aggregate Method by taking 2001 as base year is 120, given ${\displaystyle \sum {\text{p}}_1}$ = 300.

Commodity	A	B	C	D
Price (in ₹) in 2001	90	x	90	30
Price (in ₹) in 2004	95	60	y	35

Answer 1

Commodity	Price (in ₹) in 2001: p0	Price (in ₹) in 2004: p1
A	90	95
B	x	60
C	90	y
D	30	35
Total	x + 210	y + 190

From the table, ${\displaystyle \sum {\text{p}}_0}$ = x + 210, ${\displaystyle \sum {\text{p}}_1}$ = y + 190

Given that ${\displaystyle \sum {\text{p}}_1}$ = 300

∴ y + 190 = 300

∴ y = 300 – 19

∴ y = 110

Price Index Number (P₀₁) = ${\displaystyle \frac{\sum {\text{p}}_1}{\sum {\text{p}}_0}\times 100}$

120 = ${\displaystyle \frac{300}{x+210}\times 100}$

∴ x + 210 = ${\displaystyle \frac{300\times 100}{120}}$

∴ x + 210 = 250

∴ x = 250 – 210

∴ x = 40

∴ x = 40 and y = 110