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प्रश्न
The consumer price index for June 2005 was 125. The food index was 120 and that of other items 135. What is the percentage of the total weight given to food?
उत्तर
|
Items |
Index |
Weights |
WI |
|
Food |
120 |
W1 |
120 W1 |
|
Other Items |
135 |
W2 |
135 W2 |
| ∑W = 100 | ∑WI = 120W1 + 135W2 |
Let the total weight = 100
W1 denotes the weight of food
W2 denotes the weight of food other items
So, W1 + W2 = 100 (i)
CPI = 125
CPI = `(sumWR)/(sumW)`
125 = `(120W_1 + 135W_2)/100`
12500 = 120 W1 + 135 W2 (ii)
Subtracting equations (ii) from (i)
|
13500 |
= | 135 | + | 135 |
| W1 | W2 | |||
| 12500 | = | 120 | + | 135 |
| W1 | W2 | |||
| - | - | - | ||
| 1000 | = | 15 | ||
| W1 |
So, `W_1 = 1000/15 = 66.67`
Substituting the value of W1 in the equation (i)
W1 + W2 = 100
Or, 66.67 + W2 = 100
W2 = 33.33
The percentage of total weights given to food is 66.67% and other items are 33.33%.
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संबंधित प्रश्न
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What does a consumer price index for industrial workers measure?
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The monthly per capita expenditure incurred by workers for an industrial centre during 1980 and 2005 on the following items are given below. The weights of these items are 75,10, 5, 6, and 4 respectively. Prepare a weighted index number for the cost of living for 2005 with 1980 as the base.
|
Items |
Price in 1980 |
Price in 2005 |
|
Food |
100 |
200 |
|
Clothing |
20 |
25 |
|
Fuel and Lighting |
15 |
20 |
|
House rent |
30 |
40 |
|
Misc. |
35 |
65 |
Try to list the important items of consumption in your family.
If the salary of a person in the base year is Rs 4,000 per annum and the current year salary is Rs 6,000, by how much should his salary be raised to maintain the same standard of living if the CPI is 400?
An enquiry into the budgets of the middle-class families in a certain city gave the following information:
|
Expenses on items |
Food 35% |
Fuel 10% |
Clothing 20% |
Rent 15% |
Misc. 20% |
|
Price (in Rs) in 2004 |
1500 |
250 |
750 |
300 |
400 |
|
Price (in Rs) in 1995 |
1400 |
200 |
500 |
200 |
250 |
What is the cost of living index of during the year 2004 as compared with 1995?
Given the following data-
| Year | CPI of industrial workers (1982 = 100) | CPI of agricultural labourers (1986-87 = 100) | WPI (1993-94 = 100) |
| 1995-96 | 313 | 234 | 121.6 |
| 1996-97 | 342 | 256 | 127.2 |
| 1997-98 | 366 | 264 | 132.8 |
| 1998-99 | 414 | 293 | 140.7 |
| 1999-00 | 428 | 306 | 145.3 |
| 2000-01 | 444 | 306 | 155.7 |
| 2001-02 | 463 | 309 | 161.3 |
| 2002-03 | 482 | 319 | 166.8 |
| 2003-04 | 500 | 331 | 175.9 |
Given the following data-
| Year | CPI of industrial workers (1982 = 100) | CPI of agricultural labourers (1986-87 = 100) | WPI (1993-94 = 100) |
| 1995-96 | 313 | 234 | 121.6 |
| 1996-97 | 342 | 256 | 127.2 |
| 1997-98 | 366 | 264 | 132.8 |
| 1998-99 | 414 | 293 | 140.7 |
| 1999-00 | 428 | 306 | 145.3 |
| 2000-01 | 444 | 306 | 155.7 |
| 2001-02 | 463 | 309 | 161.3 |
| 2002-03 | 482 | 319 | 166.8 |
| 2003-04 | 500 | 331 | 175.9 |
