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Question
The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below
| Commodity | A | B | C | D | E | F |
| Price in the year 2000 (₹) | 50 | x | 30 | 70 | 116 | 20 |
| Price in the year 2010 (₹) | 60 | 24 | y | 80 | 120 | 28 |
Solution
| Base price (₹) in 2000 P0 |
Price(₹) in 2010 P1 |
|
| A | 50 | 60 |
| B | x | 24 |
| C | 30 | y |
| D | 70 | 80 |
| E | 116 | 120 |
| F | 20 | 28 |
| ∑P0 = 286 + x | ∑P1 = 312 + y |
Given ∑P0 = 300
⇒ x = 300 - 286 = 14
Index number P01 = 116
P01 = `( ∑P_1)/( ∑P_0) xx 100`
116 = `(312 + y)/(300) xx 100`
⇒ 116 x 3 = 312 + y
⇒ y = 36
∴ x = 14, y = 36
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