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प्रश्न
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 |
उत्तर
| 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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| I | 22 | 46 |
| II | 38 | 36 |
| III | 20 | 28 |
| IV | 18 | 44 |
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| I | 20 | 42 | 22 | 45 |
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| Price in 2005 (in ₹) | 10 | 25 | 14 | 20 | 30 |
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| Watch | 900 | 1,475 |
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| Prive | Quantity | Price | Quantity | |
| A | 10 | 10 | 20 | 10 |
| B | 8 | 20 | 22 | 15 |
| C | 2 | x | 8 | 10 |
| D | 9 | 10 | 16 | 10 |
| E | 5 | 6 | 3 | 10 |
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| A. Price Index | (a) `(sump_1q_1)/(sump_0q_0) xx 100` |
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| C. Quantity Index | (c) `(sump_1q_1)/(sump_0q_1) xx 100` |
| D. Paasche's Index | (d) `(sump_1)/(sump_0) xx 100` |
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| Commodity | A | B | C | D | E | F |
| Price (in ₹) in 2000 | 40 | 50 | 30 | x | 60 | 100 |
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An index number measuring the general changes in the prices of goods over a period of time.
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| 1) | Price Index | a) | `(sump_1q_1)/(sump_0q_0) xx 100` |
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| 3) | Quantity Index | c) | `(sump_1q_1)/(sump_0q_1) xx 100` |
| 4) | Paasche's Index | d) | `(sump_1)/(sump_0) xx 100` |
