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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 |
Solution
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
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