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Question
The price of six different commodities for years 2009 and year 2011 are as follows:
| Commodities | A | B | C | D | E | F |
|
Price in 2009 (₹) |
35 | 80 | 25 | 30 | 80 | x |
| Price in 2011 (₹) | 50 | y | 45 | 70 | 120 | 105 |
The Index number for the year 2011 taking 2009 as the base year for the above data was calculated to be 125. Find the values of x andy if the total price in 2009 is ₹ 360.
Solution
| Commodities | Prices in 2009 | Prices in 2011 |
| A | 35 | 50 |
| B | 80 | y |
| C | 25 | 45 |
| D | 30 | 70 |
| E | 80 | 120 |
| F | x | 105 |
| `Σ"P"_0` = 360 | ΣP1 = 390 + y |
Since `Σ"P"_0` = 360
∴ x + 250 = 360
x = 110
`"P"_1/"P"_0 xx 100 = "P"_1`
`(390 + "y")/(360) xx 100 = 125`
390 + y = `(125 xx 360)/(100)`
390 + y = 450
y = 60
Hence, the value of x is ₹ 110 and the value y is ₹ 60
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