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Question
Find x from following data if the Value Index Number is 200.
| Commodity | Base Year | Current Year | ||
| 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 |
Solution
| Commodity | Bae yer | Current Year | ||||
| Price p0 |
Quantity q0 |
Price p1 |
Quantity q1 |
p0q0 | p1q1 | |
| A | 10 | 10 | 20 | 10 | 100 | 200 |
| B | 8 | 20 | 22 | 15 | 160 | 330 |
| C | 2 | x | 8 | 10 | 2x | 80 |
| D | 9 | 10 | 16 | 10 | 90 | 160 |
| E | 5 | 6 | 3 | 10 | 30 | 30 |
| Total | 380 + 2x | 800 | ||||
Form the table, `sum"p"_0"q"_0` = 380 + 2x, `sum"p"_1"q"_1` = 800
Value Index Number (V01) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_0) xx 100`
∴ 200 = `800/(380 + 2x) xx 100`
∴ 380 + 2x = `800/200 xx 100`
∴ 380 + 2x = 400
∴ 2x = 20
∴ x = 10
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