Question

Solve the following problem :

Find x if Paasche’s Price Index Number is 140 for the following data.

Commodity	Base Year		Current Year
	Price p0	Quantity q0	Price p1	Quantity q1
A	20	8	40	7
B	50	10	60	10
C	40	15	60	x
D	12	15	15	15

Answer 1

Commodity	Base Year		Current Year		p0q1	p1q1
	p0	q0	p1	q1
A	20	8	40	7	140	280
B	50	10	60	10	500	600
C	40	15	60	x	40x	60x
D	12	15	15	15	180	225
Total	–	–	–	–	40x + 820	60x + 1105

From the table,
`sum"p"_0"q"_1 = 40x + 820, sum"p"_1"q"_1 = 60x + 1,105`

Paasche’s Price Index Number:

P₀₁(P) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_1) xx 100`

∴ 140 = `(60x + 1105)/(40x + 820) xx 100`  ...[P₀₁(P) = 140]

∴ `(140)/(100) = (60x + 1,105)/(40x + 820)`

∴ `(7)/(5) = (60x + 1,105)/(40x + 820)`

∴ 280x + 5,740 = 300x + 5,525
∴ 300x – 280x = 5,740 – 5,525
∴ 20x = 215
∴ x = 10.75