Question

The Price Index Number for year 2004, with respect to year 2000 as base year. is known to be 130. Find the missing numbers in the following table if ∑p₀ = 320

Commodity	A	B	C	D	E	F
Price (in ₹) in 2000	40	50	30	x	60	100
Price (in ₹) in 2000	50	70	30	85	y	115

Answer 1

We first tabulate the given data.

Commodities	Price in 2000 (Base year) p0	Price in 2005 (Current year) p1
A	40	50
B	50	70
C	30	30
D	x	85
E	60	y
F	100	115

From the above table, we have

∑p₀ = 280 + x, ∑p₁ = 350 + y

But it is given that ∑p₀ = 320, so that

280 + x = 320

∴ x = 40

Further. using the formula

p₀ = `(sump_1)/(sump_0) xx 100`

We have, 130 = `(350 + y)/320 xx 100`

∴ `(130 xx 320)/100` = 350 + y

∴ 416 = 350 + y

∴ y = 66

Hence, x = 40 and y = 66