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Question
Find values x and y if the Price Index Number by Simple Aggregate Method by taking 2001 as base year is 120, given `sum"p"_1` = 300.
| Commodity | A | B | C | D |
| Price (in ₹) in 2001 | 90 | x | 90 | 30 |
| Price (in ₹) in 2004 | 95 | 60 | y | 35 |
Solution
| 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, `sum"p"_0` = x + 210, `sum"p"_1` = y + 190
Given that `sum"p"_1` = 300
∴ y + 190 = 300
∴ y = 300 – 19
∴ y = 110
Price Index Number (P01) = `(sum"p"_1)/(sum"p"_0) xx 100`
120 = `300/(x + 210) xx 100`
∴ x + 210 = `(300 xx 100)/120`
∴ x + 210 = 250
∴ x = 250 – 210
∴ x = 40
∴ x = 40 and y = 110
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