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All questions of Chapter 18: Index numbers for CA Foundation Exam
Index nos. show _________ changes rather than absolute amounts of change.- a)relative
- b)percentage
- c)both
- d)none
Correct answer is option 'B'. Can you explain this answer?
Index nos. show _________ changes rather than absolute amounts of change.
a)
relative
b)
percentage
c)
both
d)
none
|
Dhruv Mehra answered |
If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That's your percentage! To use the calculator, enter two numbers to calculate the percentage the first is of the second by clicking Calculate Percentage.
If the 1970 index with base 1965 is 200 and 1965 index with base 1960 is 150, the index 1970 on base 1960 will be :- a)700
- b)300
- c)500
- d)600
Correct answer is option 'B'. Can you explain this answer?
If the 1970 index with base 1965 is 200 and 1965 index with base 1960 is 150, the index 1970 on base 1960 will be :
a)
700
b)
300
c)
500
d)
600
|
Freedom Institute answered |
Then 1965 index with base 1960 is 150
=> 1960 index = 100
the 1970 index with base 1965 is 200
=> 1965 index = 100
When 1965 index = 100 then 1970 index = 200
When 1965 index = 1 then 1970 index = 200/100
When 1965 index = 150 then 1970 index = (200/100) * 150 = 300
so 1970 index = 300 When 1960 index = 100
Hence the index 1970 on the base 1960 will be 300
From the following data
Q. The price index number for the year 1934 is :- a)140
- b)145
- c)147
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
From the following data
Q. The price index number for the year 1934 is :
a)
140
b)
145
c)
147
d)
None of these.
|
Naroj Boda answered |
ANSWER :- d
Solution :- Price Index = ΣP(Current area)/ΣP(Base Area) * 100
= (42/31)*100
= 135.48
From the following data with 1966 as base year
Q. The price per unit of commodity A in 1966 is- a)Rs. 5
- b)Rs. 6
- c)Rs. 4
- d)Rs. 12
Correct answer is option 'A'. Can you explain this answer?
From the following data with 1966 as base year
Q. The price per unit of commodity A in 1966 is
a)
Rs. 5
b)
Rs. 6
c)
Rs. 4
d)
Rs. 12
|
Shehna'z Lullabies answered |
Since they have given the base year as "1966" and they have given the data for "1966" it becomes easy .
according to the formula we will divide 500/100
according to the formula we will divide 500/100
In 1996 the average price of a commodity was 20% more than in 1995 but 20% less than in 1994; and more over it was 50% more than in 1997 to price relatives using 1995 as base (1995 price relative 100) Reduce the data is:- a)150, 100, 120, 80 for (1994 - 97)
- b)135, 100, 125, 87, for (1994 - 97)
- c)140, 100, 120, 80 for (1994 - 97)
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
In 1996 the average price of a commodity was 20% more than in 1995 but 20% less than in 1994; and more over it was 50% more than in 1997 to price relatives using 1995 as base (1995 price relative 100) Reduce the data is:
a)
150, 100, 120, 80 for (1994 - 97)
b)
135, 100, 125, 87, for (1994 - 97)
c)
140, 100, 120, 80 for (1994 - 97)
d)
None of these
|
|
Freedom Institute answered |
Let say 1975 Price = 100
1976 price = 100 + (20/100)100 = 120
20% less than 1974 = 120
=> 1974 Price * ( 1 - 0.2) = 120
=> 1974 Price = 150
50% more than 1977 = 120
=> 1977 price * ( 1 + 0.5) = 120
=> 1977 price = 80
1974 = 150
1975 = 100
1976 = 120
1977 = 80
Consumer price index number goes up from 110 to 200 and the Salary of a worker is also raised from Rs. 325 to Rs. 500. Therefore, in real terms he has not gain, to maintain his previous standard of living he should get an additional amount is :- a)Rs. 85
- b)Rs.90.91
- c)Rs. 98.25
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Consumer price index number goes up from 110 to 200 and the Salary of a worker is also raised from Rs. 325 to Rs. 500. Therefore, in real terms he has not gain, to maintain his previous standard of living he should get an additional amount is :
a)
Rs. 85
b)
Rs.90.91
c)
Rs. 98.25
d)
None of these
|
Alok Jayant answered |
Expenditure =325/110*100=295.4545
500/200*100=250
difference between them = 45.4545
additional amt= 45.4545*2
The quantity Index number using Fisher’s formula satisfies :
- a)Unit Test
- b)Factor Reversal Test.
- c)Circular Test.
- d)Time Reversal Test.
Correct answer is option 'B,D'. Can you explain this answer?
The quantity Index number using Fisher’s formula satisfies :
a)
Unit Test
b)
Factor Reversal Test.
c)
Circular Test.
d)
Time Reversal Test.
|
Srsps answered |
Correct Answer :- d
Explanation : The time reversal test requires that the index for the later period based on the earlier period should be the reciprocal of that for the earlier period based on the later period; one of the desirable features of the “Fisher Ideal” price and volume indexes.
Fisher’s method satisfies both the time reversal test and factor reversal test. Hence it is called the ideal index number. Another test of the adequacy of the index number formula is what is known as ‘circular test’.
Fisher’s method satisfies both the time reversal test and factor reversal test. Hence it is called the ideal index number. Another test of the adequacy of the index number formula is what is known as ‘circular test’.
If the index number of prices at a place in 1994 is 250 with 1984 as base year, then the prices have increased on average- a)250%
- b)150%
- c)350%
- d)None of these.
Correct answer is option 'B'. Can you explain this answer?
If the index number of prices at a place in 1994 is 250 with 1984 as base year, then the prices have increased on average
a)
250%
b)
150%
c)
350%
d)
None of these.
|
Sameer Rane answered |
Index number is a specialized average designed to measure the change in the level of an activity or item, either with respect to time or geographic location or some other characteristic. It is described either as a ratio or a percentage. For example, when we say that consumer price index for 1998 is 175 compared to 1991, it means that consumer prices have risen by 75% over these seven years.
The consumer price Index for April 1985 was 125. The food price index was 120 and other items index was 135. The percentage of the total weight of the index is- a)66.67
- b)68.28
- c)90.25
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The consumer price Index for April 1985 was 125. The food price index was 120 and other items index was 135. The percentage of the total weight of the index is
a)
66.67
b)
68.28
c)
90.25
d)
None of these
|
Atchaya Atchayaraja answered |
13500-12500=135x-120x
1000/15=x
Therefore the value of X IS 66.67.
1000/15=x
Therefore the value of X IS 66.67.
If ∑ Pnqn= 249, ∑ Poqo = 150, Paasche’s Index Number = 150 and Drobiseh and Bowely’s Index number = 145. Then the Fisher’s Ideal Index Number is- a)75
- b)60
- c)145.97
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
If ∑ Pnq
n
= 249, ∑ Poqo = 150, Paasche’s Index Number = 150 and Drobiseh and Bowely’s Index number = 145. Then the Fisher’s Ideal Index Number isa)
75
b)
60
c)
145.97
d)
None of these
|
|
Rishika Goud answered |
Bowley index number=la+pa/2
145=La+150/2
La+150= 290
La=290_150
La =140
(Fishers index number)2= la×pa
(FIN)2=150×140
=21000
=144.913
145=La+150/2
La+150= 290
La=290_150
La =140
(Fishers index number)2= la×pa
(FIN)2=150×140
=21000
=144.913
Suppose a business excutive was earning Rs. 2,050 in the base period, what should be his salary in the current period if his standard of living is to remain the same ? Given ∑w = 25 and ∑IW = 3544:- a)Rs. 2096
- b)Rs. 2906
- c)Rs. 2106
- d)Rs. 2306
Correct answer is option 'B'. Can you explain this answer?
Suppose a business excutive was earning Rs. 2,050 in the base period, what should be his salary in the current period if his standard of living is to remain the same ? Given ∑w = 25 and ∑IW = 3544:
a)
Rs. 2096
b)
Rs. 2906
c)
Rs. 2106
d)
Rs. 2306
|
Rabiya Athar answered |
First he was earning RS 2050 in the base period whose price index number is 100 as we know. Then in the current year the consumer price index become 141.76 by dividing 3544 by 25. Then we can say that 2050---100 and x---141.7 then we calculate the value x=2050*141.7/100
With the base year 1960 as the base the C. L. I. In 1972 stood at 250 x was getting a monthly Salary of Rs. 500 in 1960 and Rs. 750 in 1972. In 1972 to maintain his standard of living in 1960 x have received as extra allowances is- a)Rs. 600/-
- b)Rs. 500/-
- c)Rs. 300/-
- d)none of these.
Correct answer is option 'B'. Can you explain this answer?
With the base year 1960 as the base the C. L. I. In 1972 stood at 250 x was getting a monthly Salary of Rs. 500 in 1960 and Rs. 750 in 1972. In 1972 to maintain his standard of living in 1960 x have received as extra allowances is
a)
Rs. 600/-
b)
Rs. 500/-
c)
Rs. 300/-
d)
none of these.
|
Shubha .k answered |
The price of a commodity increases from Rs. 5 per unit in 1990 to Rs. 7.50 per unit in 1995 and the quantity consumed decreases from 120 units in 1990 to 90 units in 1995. The price and quantity in 1995 are 150% and 75% respectively of the corresponding price and quantity in 1990. Therefore, the product of the price ratio and quantity ratio is :- a)1.8
- b)1.125
- c)1.75
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The price of a commodity increases from Rs. 5 per unit in 1990 to Rs. 7.50 per unit in 1995 and the quantity consumed decreases from 120 units in 1990 to 90 units in 1995. The price and quantity in 1995 are 150% and 75% respectively of the corresponding price and quantity in 1990. Therefore, the product of the price ratio and quantity ratio is :
a)
1.8
b)
1.125
c)
1.75
d)
None of these
|
|
Freedom Institute answered |
Let us first find out the product of price and quantity in 1995 after the changes.
So,
Product of price and quantity 
Now, we will find the product of price and quantity in 1990.
So,
Product of price and quantity 
Now we have to find the required ratio, so
Ratio 
If the prices of all commodities in a place have increased 1.25 times in comparison to the base period, the index number of prices of that place now is- a)125
- b)150
- c)225
- d)None of these.
Correct answer is option 'C'. Can you explain this answer?
If the prices of all commodities in a place have increased 1.25 times in comparison to the base period, the index number of prices of that place now is
a)
125
b)
150
c)
225
d)
None of these.
|
Raghavendra Choudhury answered |
Calculation of Index Number of Prices:
The index number of prices is a measure of the average price level of goods and services in a particular place or country. It is calculated by comparing the prices of goods and services in the current period with a base period.
Given that the prices of all commodities in a place have increased 1.25 times in comparison to the base period, we need to calculate the index number of prices for the current period.
Formula:
Index Number of Prices = (Price in the Current Period / Price in the Base Period) x 100
Calculation:
Let's assume that the price of a commodity in the base period was Rs. 100.
As per the given condition, the price of the same commodity in the current period is Rs. 125 (1.25 times the base period price).
Using the formula mentioned above, we can calculate the index number of prices as follows:
Index Number of Prices = (Price in the Current Period / Price in the Base Period) x 100
= (125 / 100) x 100
= 125
Therefore, the correct option is (c) 225.
Conclusion:
Hence, we can conclude that the index number of prices for the current period when the prices of all commodities in a place have increased 1.25 times in comparison to the base period is 125.
The index number of prices is a measure of the average price level of goods and services in a particular place or country. It is calculated by comparing the prices of goods and services in the current period with a base period.
Given that the prices of all commodities in a place have increased 1.25 times in comparison to the base period, we need to calculate the index number of prices for the current period.
Formula:
Index Number of Prices = (Price in the Current Period / Price in the Base Period) x 100
Calculation:
Let's assume that the price of a commodity in the base period was Rs. 100.
As per the given condition, the price of the same commodity in the current period is Rs. 125 (1.25 times the base period price).
Using the formula mentioned above, we can calculate the index number of prices as follows:
Index Number of Prices = (Price in the Current Period / Price in the Base Period) x 100
= (125 / 100) x 100
= 125
Therefore, the correct option is (c) 225.
Conclusion:
Hence, we can conclude that the index number of prices for the current period when the prices of all commodities in a place have increased 1.25 times in comparison to the base period is 125.
The total value of retained imports into India in 1960 was Rs. 71.5 million per month. The corresponding total for 1967 was Rs. 87.6 million per month. The index of volume of retained inports in 1967 composed with 1960( =100) was 62.0. The price index for retained inputs for 1967 our 1960 as base is - a)198.61
- b)197.61
- c)198.25
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The total value of retained imports into India in 1960 was Rs. 71.5 million per month. The corresponding total for 1967 was Rs. 87.6 million per month. The index of volume of retained inports in 1967 composed with 1960( =100) was 62.0. The price index for retained inputs for 1967 our 1960 as base is
a)
198.61
b)
197.61
c)
198.25
d)
None of these
|
Vivek Vivek answered |
Here value means price×quantity .
quantity is considered as volume .
value index=price index×quantity index(without 100)
(87.6 million/71.5 million)×100 =price index ×(62/100)
price index =
quantity is considered as volume .
value index=price index×quantity index(without 100)
(87.6 million/71.5 million)×100 =price index ×(62/100)
price index =
The price of a commodity increases from Rs. 5 per unit in 1990 to Rs. 7.50 per unit in 1995 and the quantity consumed decreases from 120 units in 1990 to 90 units in 1995. The price and quantity in 1995 are 150% and 75% respectively of the corresponding price and quantity in 1990. Therefore, the product of the price ratio and quantity ratio is:- a)1.8
- b)1.125
- c)1.75
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The price of a commodity increases from Rs. 5 per unit in 1990 to Rs. 7.50 per unit in 1995 and the quantity consumed decreases from 120 units in 1990 to 90 units in 1995. The price and quantity in 1995 are 150% and 75% respectively of the corresponding price and quantity in 1990. Therefore, the product of the price ratio and quantity ratio is:
a)
1.8
b)
1.125
c)
1.75
d)
None of these
|
Ritika Iyer answered |
Given data:
Price in 1990 = Rs. 5 per unit
Price in 1995 = Rs. 7.50 per unit
Quantity in 1990 = 120 units
Quantity in 1995 = 90 units
Price ratio = (Price in 1995 / Price in 1990) * 100%
= (7.50 / 5) * 100%
= 150%
Quantity ratio = (Quantity in 1995 / Quantity in 1990) * 100%
= (90 / 120) * 100%
= 75%
Product of price ratio and quantity ratio = (150% * 75%) / 100%
= 1.125
Therefore, the correct answer is option B) 1.125.
Explanation:
In 1990, the price of the commodity was Rs. 5 per unit and the quantity consumed was 120 units. In 1995, the price increased to Rs. 7.50 per unit and the quantity consumed decreased to 90 units. This means that there was an increase in price and a decrease in quantity consumed over the time period of 1990 to 1995. To calculate the price ratio and quantity ratio, we divide the values of 1995 by the values of 1990 and multiply by 100% to get the percentage increase or decrease. The product of the price ratio and quantity ratio gives us the overall change in the commodity over the time period of 1990 to 1995. In this case, the product is 1.125, which means that there was an overall decrease in the commodity of 12.5%.
Price in 1990 = Rs. 5 per unit
Price in 1995 = Rs. 7.50 per unit
Quantity in 1990 = 120 units
Quantity in 1995 = 90 units
Price ratio = (Price in 1995 / Price in 1990) * 100%
= (7.50 / 5) * 100%
= 150%
Quantity ratio = (Quantity in 1995 / Quantity in 1990) * 100%
= (90 / 120) * 100%
= 75%
Product of price ratio and quantity ratio = (150% * 75%) / 100%
= 1.125
Therefore, the correct answer is option B) 1.125.
Explanation:
In 1990, the price of the commodity was Rs. 5 per unit and the quantity consumed was 120 units. In 1995, the price increased to Rs. 7.50 per unit and the quantity consumed decreased to 90 units. This means that there was an increase in price and a decrease in quantity consumed over the time period of 1990 to 1995. To calculate the price ratio and quantity ratio, we divide the values of 1995 by the values of 1990 and multiply by 100% to get the percentage increase or decrease. The product of the price ratio and quantity ratio gives us the overall change in the commodity over the time period of 1990 to 1995. In this case, the product is 1.125, which means that there was an overall decrease in the commodity of 12.5%.
The cost of living Index (C.L.I.) is always :- a)Weighted index
- b)Price Index.
- c)Quantity Index.
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
The cost of living Index (C.L.I.) is always :
a)
Weighted index
b)
Price Index.
c)
Quantity Index.
d)
None of these.
|
Hrishikesh Mukherjee answered |
Cost of Living Index (C.L.I.) - Weighted Index
Cost of living index (C.L.I.) is a statistical measure that compares the cost of living between different geographical areas or time periods. It is a weighted index that takes into account the relative importance of different goods and services in a typical household's budget.
Calculation of C.L.I.
The cost of living index is calculated as follows:
C.L.I. = (Cost of basket in the current period / Cost of basket in the base period) x 100
Here, the "basket" refers to a collection of goods and services that are typical of a household's consumption patterns. The base period is usually chosen as a reference period against which to compare the current period.
Weighted Index
The cost of living index is a weighted index because it takes into account the relative importance of different goods and services in a typical household's budget. The weights are usually derived from household expenditure surveys, which provide information on the proportion of income that is spent on different items.
For example, if housing costs represent 30% of a typical household's budget, then housing would be given a weight of 30% in the cost of living index. Similarly, if food and beverages represent 20% of the budget, then this category would be given a weight of 20%.
Importance of C.L.I.
The cost of living index is an important tool for policymakers, businesses, and individuals. It can be used to:
- Determine the relative cost of living between different geographical areas or time periods
- Adjust wages, salaries, and benefits to reflect changes in the cost of living
- Set prices for goods and services
- Determine the level of government benefits, such as social security and welfare payments
- Make investment decisions
Conclusion
In conclusion, the cost of living index is a weighted index that takes into account the relative importance of different goods and services in a typical household's budget. It is an important tool for policymakers, businesses, and individuals to determine the relative cost of living between different geographical areas or time periods.
Cost of living index (C.L.I.) is a statistical measure that compares the cost of living between different geographical areas or time periods. It is a weighted index that takes into account the relative importance of different goods and services in a typical household's budget.
Calculation of C.L.I.
The cost of living index is calculated as follows:
C.L.I. = (Cost of basket in the current period / Cost of basket in the base period) x 100
Here, the "basket" refers to a collection of goods and services that are typical of a household's consumption patterns. The base period is usually chosen as a reference period against which to compare the current period.
Weighted Index
The cost of living index is a weighted index because it takes into account the relative importance of different goods and services in a typical household's budget. The weights are usually derived from household expenditure surveys, which provide information on the proportion of income that is spent on different items.
For example, if housing costs represent 30% of a typical household's budget, then housing would be given a weight of 30% in the cost of living index. Similarly, if food and beverages represent 20% of the budget, then this category would be given a weight of 20%.
Importance of C.L.I.
The cost of living index is an important tool for policymakers, businesses, and individuals. It can be used to:
- Determine the relative cost of living between different geographical areas or time periods
- Adjust wages, salaries, and benefits to reflect changes in the cost of living
- Set prices for goods and services
- Determine the level of government benefits, such as social security and welfare payments
- Make investment decisions
Conclusion
In conclusion, the cost of living index is a weighted index that takes into account the relative importance of different goods and services in a typical household's budget. It is an important tool for policymakers, businesses, and individuals to determine the relative cost of living between different geographical areas or time periods.
If the prices of all commodities in a place have decreased 35% over the base period prices, then the index number of prices of that place is now- a)35
- b)135
- c)65
- d)None of these.
Correct answer is option 'C'. Can you explain this answer?
If the prices of all commodities in a place have decreased 35% over the base period prices, then the index number of prices of that place is now
a)
35
b)
135
c)
65
d)
None of these.
|
Janhavi Basu answered |
Explanation:
An index number is a statistical measure that shows changes in a variable or group of variables over time. In this case, we are looking at the price index of a particular place.
The formula for calculating the price index is as follows:
Price index = (Current year prices / Base year prices) x 100
Given that the prices of all commodities in a place have decreased 35% over the base period prices, we can assume that the current year prices are 65% of the base year prices. Therefore, we can calculate the price index as follows:
Price index = (65 / 100) x 100
Price index = 65
Therefore, the correct answer is option C, 65.
Conclusion:
The price index is a measure of the average change in prices over time. In this case, the prices of all commodities in a place have decreased 35% over the base period prices, resulting in a price index of 65.
An index number is a statistical measure that shows changes in a variable or group of variables over time. In this case, we are looking at the price index of a particular place.
The formula for calculating the price index is as follows:
Price index = (Current year prices / Base year prices) x 100
Given that the prices of all commodities in a place have decreased 35% over the base period prices, we can assume that the current year prices are 65% of the base year prices. Therefore, we can calculate the price index as follows:
Price index = (65 / 100) x 100
Price index = 65
Therefore, the correct answer is option C, 65.
Conclusion:
The price index is a measure of the average change in prices over time. In this case, the prices of all commodities in a place have decreased 35% over the base period prices, resulting in a price index of 65.
The ________ of group indices given the General Index- a)H.M.
- b)G.M.
- c)A.M.
- d)none
Correct answer is option 'C'. Can you explain this answer?
The ________ of group indices given the General Index
a)
H.M.
b)
G.M.
c)
A.M.
d)
none
|
Muskaan Tiwari answered |
The Average Index of group indices given the General Index
The question is asking for the average index of group indices given the general index. This can be calculated using the formula for the arithmetic mean, which is the sum of all the values divided by the number of values.
Formula: Average Index = Sum of group indices / Number of group indices
In this case, the group indices are given and the number of group indices is not specified. Therefore, we can assume that there are multiple group indices.
The answer to the question is option C, which is the arithmetic mean or the average index (A.M.) of the group indices.
HTML bullet points:
- The formula for the arithmetic mean is the sum of all the values divided by the number of values.
- To calculate the average index of group indices given the general index, we need to use the formula: Average Index = Sum of group indices / Number of group indices.
- The answer to the question is option C, which is the arithmetic mean or the average index (A.M.) of the group indices.
The question is asking for the average index of group indices given the general index. This can be calculated using the formula for the arithmetic mean, which is the sum of all the values divided by the number of values.
Formula: Average Index = Sum of group indices / Number of group indices
In this case, the group indices are given and the number of group indices is not specified. Therefore, we can assume that there are multiple group indices.
The answer to the question is option C, which is the arithmetic mean or the average index (A.M.) of the group indices.
HTML bullet points:
- The formula for the arithmetic mean is the sum of all the values divided by the number of values.
- To calculate the average index of group indices given the general index, we need to use the formula: Average Index = Sum of group indices / Number of group indices.
- The answer to the question is option C, which is the arithmetic mean or the average index (A.M.) of the group indices.
Fisher’s Ideal Formula for calculating index nos. satisfies the _______ tests- a)Units Test
- b)Factor Reversal Test
- c)both
- d)none
Correct answer is option 'C'. Can you explain this answer?
Fisher’s Ideal Formula for calculating index nos. satisfies the _______ tests
a)
Units Test
b)
Factor Reversal Test
c)
both
d)
none
|
Pragati Shah answered |
Fishers Ideal Formula for calculating index numbers satisfies both Units Test and Factor Reversal Test. Let's understand both of these tests in detail:
Units Test:
The Units Test is also known as the test of consistency. The primary objective of this test is to ensure that the index number formula produces consistent results when the units of measurements of the variables change. In other words, if the units of measurement of the variables used in the index number formula are changed, the index number should not change. The Fisher's Ideal Formula satisfies this test as it is based on the concept of the geometric mean, which is a dimensionless quantity and does not depend on the units of measurement.
Factor Reversal Test:
The Factor Reversal Test is also known as the test of reversibility. The primary objective of this test is to ensure that if the original data of the variables are multiplied by a certain factor, the index number should also be multiplied by the same factor. In other words, the index number should be reversible. The Fisher's Ideal Formula also satisfies this test as it is based on the ratio of two geometric means, which is a homogeneous formula and satisfies the factor reversal property.
Therefore, we can conclude that Fisher's Ideal Formula for calculating index numbers satisfies both the Units Test and the Factor Reversal Test, making it a reliable and robust formula for calculating index numbers.
Units Test:
The Units Test is also known as the test of consistency. The primary objective of this test is to ensure that the index number formula produces consistent results when the units of measurements of the variables change. In other words, if the units of measurement of the variables used in the index number formula are changed, the index number should not change. The Fisher's Ideal Formula satisfies this test as it is based on the concept of the geometric mean, which is a dimensionless quantity and does not depend on the units of measurement.
Factor Reversal Test:
The Factor Reversal Test is also known as the test of reversibility. The primary objective of this test is to ensure that if the original data of the variables are multiplied by a certain factor, the index number should also be multiplied by the same factor. In other words, the index number should be reversible. The Fisher's Ideal Formula also satisfies this test as it is based on the ratio of two geometric means, which is a homogeneous formula and satisfies the factor reversal property.
Therefore, we can conclude that Fisher's Ideal Formula for calculating index numbers satisfies both the Units Test and the Factor Reversal Test, making it a reliable and robust formula for calculating index numbers.
The simple Aggregative formula and weighted aggregative formula satisfy is- a)Factor Reversal Test
- b)Circular Test
- c)Unit Test
- d)None of these
Correct answer is option `A`. Can you explain this answer?
The simple Aggregative formula and weighted aggregative formula satisfy is
a)
Factor Reversal Test
b)
Circular Test
c)
Unit Test
d)
None of these
|
|
Srsps answered |
ANSWER
- a)Factor Reversal Test
The simple Aggregative formula and weighted aggregative formula satisfy is.
Factor Reversal Test.
The factor reversal test requires that multiplying a price index and a volume index of the same type should be equal to the proportionate change in the current values (e.g. the “Fisher Ideal” price and volume indexes satisfy this test, unlike either the Paasche or Laspeyres indexes).
08
The ________ makes index nos. time-reversible.- a)A.M.
- b)G.M.
- c)H.M.
- d)none
Correct answer is option 'B'. Can you explain this answer?
The ________ makes index nos. time-reversible.
a)
A.M.
b)
G.M.
c)
H.M.
d)
none
|
|
Madhavan Malik answered |
The Geometric Mean (G.M) makes index numbers time-reversible. This can be explained as follows:
Index numbers are used to measure changes in the level of a certain phenomenon over time. For example, the Consumer Price Index (CPI) measures the changes in the prices of goods and services over time. The index number is calculated by taking the ratio of the current value of the phenomenon to its value in a base period and multiplying it by 100.
One of the important properties of an index number is its time-reversibility. This means that if we reverse the time series, the resulting index number should be the reciprocal of the original index number. For example, if the index number for year 2 relative to year 1 is 120, then the index number for year 1 relative to year 2 should be 1/1.2 = 0.8333.
The Geometric Mean formula for calculating index numbers has the property of time-reversibility. The formula for the index number is:
Index Number = (Product of (Current Value/Base Value)^(1/n)) x 100
where n is the number of periods.
The Geometric Mean formula uses the product of the ratios of current value to base value raised to the power of 1/n. This formula has the property that if we reverse the time series, the resulting index number is the reciprocal of the original index number. Therefore, the Geometric Mean formula is said to be time-reversible.
In contrast, the Arithmetic Mean (A.M) and Harmonic Mean (H.M) formulas for calculating index numbers do not have the property of time-reversibility. Therefore, they cannot be used to calculate time-reversible index numbers.
Hence, the Geometric Mean formula is the preferred method for calculating index numbers as it has the property of time-reversibility.
Index numbers are used to measure changes in the level of a certain phenomenon over time. For example, the Consumer Price Index (CPI) measures the changes in the prices of goods and services over time. The index number is calculated by taking the ratio of the current value of the phenomenon to its value in a base period and multiplying it by 100.
One of the important properties of an index number is its time-reversibility. This means that if we reverse the time series, the resulting index number should be the reciprocal of the original index number. For example, if the index number for year 2 relative to year 1 is 120, then the index number for year 1 relative to year 2 should be 1/1.2 = 0.8333.
The Geometric Mean formula for calculating index numbers has the property of time-reversibility. The formula for the index number is:
Index Number = (Product of (Current Value/Base Value)^(1/n)) x 100
where n is the number of periods.
The Geometric Mean formula uses the product of the ratios of current value to base value raised to the power of 1/n. This formula has the property that if we reverse the time series, the resulting index number is the reciprocal of the original index number. Therefore, the Geometric Mean formula is said to be time-reversible.
In contrast, the Arithmetic Mean (A.M) and Harmonic Mean (H.M) formulas for calculating index numbers do not have the property of time-reversibility. Therefore, they cannot be used to calculate time-reversible index numbers.
Hence, the Geometric Mean formula is the preferred method for calculating index numbers as it has the property of time-reversibility.
If å PoQo = 1360, å PnQo = 1900, å PoQn = 1344, å PoQn = 1880 then the Laspeyre’s Index number is- a)0.71
- b)1.39
- c)1.75
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
If å PoQo = 1360, å PnQo = 1900, å PoQn = 1344, å PoQn = 1880 then the Laspeyre’s Index number is
a)
0.71
b)
1.39
c)
1.75
d)
None of these
|
Charvi Roy answered |
Given Data:
PoQo = 1360
PnQo = 1900
PoQn = 1344
PnQn = 1880
To find: Laspeyres Index Number
Formula: Laspeyres Index Number = (Current Year Quantity * Base Year Price) / (Base Year Quantity * Base Year Price) * 100
Calculation:
Base Year Quantity = PoQo = 1360
Base Year Price = Average of PoQo and PoQn = (1360 + 1344) / 2 = 1352
Current Year Quantity = PnQo = 1900
Current Year Price = Average of PnQo and PnQn = (1900 + 1880) / 2 = 1890
Laspeyres Index Number = (1900 * 1352) / (1360 * 1352) * 100 = 139
Therefore, the Laspeyres Index Number is 1.39 (Option B).
PoQo = 1360
PnQo = 1900
PoQn = 1344
PnQn = 1880
To find: Laspeyres Index Number
Formula: Laspeyres Index Number = (Current Year Quantity * Base Year Price) / (Base Year Quantity * Base Year Price) * 100
Calculation:
Base Year Quantity = PoQo = 1360
Base Year Price = Average of PoQo and PoQn = (1360 + 1344) / 2 = 1352
Current Year Quantity = PnQo = 1900
Current Year Price = Average of PnQo and PnQn = (1900 + 1880) / 2 = 1890
Laspeyres Index Number = (1900 * 1352) / (1360 * 1352) * 100 = 139
Therefore, the Laspeyres Index Number is 1.39 (Option B).
Which among the following statements is INCORRECT?- a)Coefficient of correlation can be computed directly from the data without measuring deviation.
- b)Measures of Dispersion are also called averages of the second order.
- c)Standard deviation can be negative.
- d)Mean deviation can never be negative.
Correct answer is option 'C'. Can you explain this answer?
Which among the following statements is INCORRECT?
a)
Coefficient of correlation can be computed directly from the data without measuring deviation.
b)
Measures of Dispersion are also called averages of the second order.
c)
Standard deviation can be negative.
d)
Mean deviation can never be negative.
|
Poonam Reddy answered |
No, standard deviation is always positive or 0. When you square deviations from the mean, they become positive or zero. Their sum is still positive or zero and the quotient after dividing the sum by n – 1 stays positive or zero. This final quantity is the variance.
The Bowley’s Price index number is represented in terms of :- a)A.M. of Laspeyre’s and Paasche’s Price index number.
- b)G.M. of Laspeyre’s and Paasche’s Price index number.
- c)A.M. of Laspeyre’s and Walsh’s price index number.
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
The Bowley’s Price index number is represented in terms of :
a)
A.M. of Laspeyre’s and Paasche’s Price index number.
b)
G.M. of Laspeyre’s and Paasche’s Price index number.
c)
A.M. of Laspeyre’s and Walsh’s price index number.
d)
None of these.
|
|
Janhavi Basu answered |
Explanation:
Bowleys Price Index number is represented in terms of the arithmetic mean of Laspeyres and Paasches price index numbers. Let's understand what Laspeyres and Paasches price index numbers are.
Laspeyres Price Index Number:
The Laspeyres price index number measures the change in the price of a fixed basket of goods and services over time. It is calculated by taking the ratio of the cost of the basket of goods and services in the current year to the cost of the same basket of goods and services in the base year. The Laspeyres price index number overestimates the cost of living because it does not take into account the substitution effect.
Paasches Price Index Number:
The Paasches price index number measures the change in the price of a variable basket of goods and services over time. It is calculated by taking the ratio of the cost of the basket of goods and services in the current year to the cost of the same basket of goods and services in the base year. The Paasches price index number underestimates the cost of living because it does not take into account the income effect.
Bowleys Price Index Number:
Bowleys Price Index Number is the arithmetic mean of Laspeyres and Paasches price index numbers. It overcomes the limitations of both Laspeyres and Paasches price index numbers because it takes into account the substitution effect as well as the income effect.
Conclusion:
Thus, the correct answer is option 'A' - Bowleys Price index number is represented in terms of A.M. of Laspeyres and Paasches Price index number.
Bowleys Price Index number is represented in terms of the arithmetic mean of Laspeyres and Paasches price index numbers. Let's understand what Laspeyres and Paasches price index numbers are.
Laspeyres Price Index Number:
The Laspeyres price index number measures the change in the price of a fixed basket of goods and services over time. It is calculated by taking the ratio of the cost of the basket of goods and services in the current year to the cost of the same basket of goods and services in the base year. The Laspeyres price index number overestimates the cost of living because it does not take into account the substitution effect.
Paasches Price Index Number:
The Paasches price index number measures the change in the price of a variable basket of goods and services over time. It is calculated by taking the ratio of the cost of the basket of goods and services in the current year to the cost of the same basket of goods and services in the base year. The Paasches price index number underestimates the cost of living because it does not take into account the income effect.
Bowleys Price Index Number:
Bowleys Price Index Number is the arithmetic mean of Laspeyres and Paasches price index numbers. It overcomes the limitations of both Laspeyres and Paasches price index numbers because it takes into account the substitution effect as well as the income effect.
Conclusion:
Thus, the correct answer is option 'A' - Bowleys Price index number is represented in terms of A.M. of Laspeyres and Paasches Price index number.
If the price of all commodities in a place have increased 1.25 times in comparison to the base period prices, then the index number of prices for the place is now
- a)100
- b)125
- c)225
- d)None of the above.
Correct answer is option 'C'. Can you explain this answer?
If the price of all commodities in a place have increased 1.25 times in comparison to the base period prices, then the index number of prices for the place is now
a)
100
b)
125
c)
225
d)
None of the above.
|
Muskan Singh answered |
We can assume base price as 100.
Hence 100+125 = 225.
Hence 100+125 = 225.
If the price index for the year, say 1960 be 110.3 and the price index for the year, say 1950 be 98.4, then the purchasing power of money (Rupees) of 1950 will in 1960 is - a)Rs. 1.12
- b)Rs. 1.25
- c)Rs. 1.37
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
If the price index for the year, say 1960 be 110.3 and the price index for the year, say 1950 be 98.4, then the purchasing power of money (Rupees) of 1950 will in 1960 is
a)
Rs. 1.12
b)
Rs. 1.25
c)
Rs. 1.37
d)
None of these.
|
Aayush Dabhi answered |
How do this sum
The prices of a commodity in the years 1975 and 1980 were 25 and 30 respectively, taking 1975 as base year the price relative is :- a)120
- b)135
- c)122
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The prices of a commodity in the years 1975 and 1980 were 25 and 30 respectively, taking 1975 as base year the price relative is :
a)
120
b)
135
c)
122
d)
None of these
|
|
Sonal Patel answered |
Price Relative Calculation:
Price relative is a measure used to compare the price of a commodity in two different years with the help of a base year. It is calculated as follows:
Price relative = (Price in the given year / Price in the base year) x 100
Given:
Price of commodity in 1975 = 25
Price of commodity in 1980 = 30
Base year = 1975
Calculation:
Price relative = (Price in 1980 / Price in 1975) x 100
= (30 / 25) x 100
= 1.2 x 100
= 120
Therefore, the price relative is 120.
Conclusion:
The correct answer is option A (120). The price relative of the commodity in 1980, taking 1975 as a base year, is 120.
Price relative is a measure used to compare the price of a commodity in two different years with the help of a base year. It is calculated as follows:
Price relative = (Price in the given year / Price in the base year) x 100
Given:
Price of commodity in 1975 = 25
Price of commodity in 1980 = 30
Base year = 1975
Calculation:
Price relative = (Price in 1980 / Price in 1975) x 100
= (30 / 25) x 100
= 1.2 x 100
= 120
Therefore, the price relative is 120.
Conclusion:
The correct answer is option A (120). The price relative of the commodity in 1980, taking 1975 as a base year, is 120.
The price of a number of commodities are given below in the current year 1975 and base year 1970.
Q. For 1975 with base 1970 by the Method of price relatives using Geometrical mean. The price index is :- a)125.3
- b)124.3
- c)128.8
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The price of a number of commodities are given below in the current year 1975 and base year 1970.
Q. For 1975 with base 1970 by the Method of price relatives using Geometrical mean. The price index is :
a)
125.3
b)
124.3
c)
128.8
d)
None of these
|
Deendayal Mundra answered |
Log(P)=2+1/£log(p1/p0).
Log(P)=2+1/6[(log55/45)+(log70/60)+(log30/20)+(log75/80)+(log90/85)+(log130/120).
Log(P)=2+1/6(log3.680)
Log(P)=2.094
P=Antlog(2.094)
P=124.
Log(P)=2+1/6[(log55/45)+(log70/60)+(log30/20)+(log75/80)+(log90/85)+(log130/120).
Log(P)=2+1/6(log3.680)
Log(P)=2.094
P=Antlog(2.094)
P=124.
“Fisher’s Ideal Index is the only formula which satisfies”
- a)Time Reversal Test
- b)Circular Test
- c)Factor Reversal Test
- d)None of these
Correct answer is option 'A,C'. Can you explain this answer?
“Fisher’s Ideal Index is the only formula which satisfies”
a)
Time Reversal Test
b)
Circular Test
c)
Factor Reversal Test
d)
None of these
|
Keshav answered |
Correct answer is a and c.
Time Reversal Test and Factor Reversal TestIf the prices of all commodities in a place have increased 1.25 times in comparison to the base period, the index number of prices of that place is now- a)125
- b)150
- c)225
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
If the prices of all commodities in a place have increased 1.25 times in comparison to the base period, the index number of prices of that place is now
a)
125
b)
150
c)
225
d)
None of these
|
Sahil Malik answered |
According to the question, Given : P1 = P0 + 1.25 P0
P1 = 2.25 P0
In index numbers, we assume base price P0 = 100
P1 = 2.25 ( 100)
P1 = 225
Price of that place = 225
P1 = 2.25 P0
In index numbers, we assume base price P0 = 100
P1 = 2.25 ( 100)
P1 = 225
Price of that place = 225
If ∑ Poqo = 3500, ∑ Pnqo = 3850. Then the Cost of living Index (C.L.T.) for 1950 w.r. to base 1960 is- a)110
- b)90
- c)100
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
If ∑ Poqo = 3500, ∑ Pnqo = 3850. Then the Cost of living Index (C.L.T.) for 1950 w.r. to base 1960 is
a)
110
b)
90
c)
100
d)
None of these.
|
Amrutha Goyal answered |
Given information:
- Poqo = 3500
- Pnqo = 3850
To find:
- Cost of Living Index (C.L.T.) for 1950 with respect to base 1960
Solution:
Cost of Living Index (C.L.T.) is a measure of the change in the cost of a standard set of goods and services over time. It is calculated by comparing the cost of the same set of goods and services in different time periods.
We can use the following formula to calculate the Cost of Living Index (C.L.T.):
C.L.T. = (Pno / Pnb) x 100
where,
- Pno = cost of the standard set of goods and services in the current year
- Pnb = cost of the standard set of goods and services in the base year
In this case, we are given the prices of the standard set of goods and services in two different years - 1950 and 1960.
We need to find the Cost of Living Index (C.L.T.) for 1950 with respect to base 1960.
Let's assume that the standard set of goods and services cost $100 in 1960.
Using this as the base year, we can calculate the prices of the same set of goods and services in 1950 as follows:
- Poqo = 3500
- C.L.T. = (Pno / Pnb) x 100 = (3850 / 100) x 100 = 3850
Therefore, the Cost of Living Index (C.L.T.) for 1950 with respect to base 1960 is 110.
Conclusion:
The correct option is A) 110.
- Poqo = 3500
- Pnqo = 3850
To find:
- Cost of Living Index (C.L.T.) for 1950 with respect to base 1960
Solution:
Cost of Living Index (C.L.T.) is a measure of the change in the cost of a standard set of goods and services over time. It is calculated by comparing the cost of the same set of goods and services in different time periods.
We can use the following formula to calculate the Cost of Living Index (C.L.T.):
C.L.T. = (Pno / Pnb) x 100
where,
- Pno = cost of the standard set of goods and services in the current year
- Pnb = cost of the standard set of goods and services in the base year
In this case, we are given the prices of the standard set of goods and services in two different years - 1950 and 1960.
We need to find the Cost of Living Index (C.L.T.) for 1950 with respect to base 1960.
Let's assume that the standard set of goods and services cost $100 in 1960.
Using this as the base year, we can calculate the prices of the same set of goods and services in 1950 as follows:
- Poqo = 3500
- C.L.T. = (Pno / Pnb) x 100 = (3850 / 100) x 100 = 3850
Therefore, the Cost of Living Index (C.L.T.) for 1950 with respect to base 1960 is 110.
Conclusion:
The correct option is A) 110.
The price level of a country in a certain year has increased 25% over the base period.The index number is
- a)25
- b)125
- c)225
- d)2500
Correct answer is option 'B'. Can you explain this answer?
The price level of a country in a certain year has increased 25% over the base period.The index number is
a)
25
b)
125
c)
225
d)
2500
|
|
Freedom Institute answered |
2. 125
Explanation:
An index number is a measure of how much a quantity, such as a price level, has changed relative to a base period. When the price level increases by 25% over the base period, the index number is calculated as follows:
Index Number=100+Percentage Increase
In this case:
Index Number=100+25=125
So, the index number is 125.
The prices of a commodity in the year 1975 and 1980 were 25 and 30 respectively taking 1980 as base year the price relative is :- a)None of these
- b)110.25
- c)113.25
- d)109.78
Correct answer is option 'A'. Can you explain this answer?
The prices of a commodity in the year 1975 and 1980 were 25 and 30 respectively taking 1980 as base year the price relative is :
a)
None of these
b)
110.25
c)
113.25
d)
109.78
|
|
Amrutha Goyal answered |
Taking 1980 as base year......
Pn/p0*100
Then,
25/30*100
=83.3333
And the answer is 83.33
When index number is calculated for several variables, it is called: - a)Whole sale price index
- b)Composite index
- c)Volume index
- d)Simple index
Correct answer is option 'B'. Can you explain this answer?
When index number is calculated for several variables, it is called:
a)
Whole sale price index
b)
Composite index
c)
Volume index
d)
Simple index
|
|
Maheshwar Goyal answered |
Understanding Composite Index
A composite index is a statistical measure that aggregates multiple variables into a single index number. This approach is particularly useful in economic and financial analysis, where various indicators need to be evaluated together to understand broader trends.
Key Features of a Composite Index:
- Multidimensional Analysis: Unlike a simple index that measures a single variable, a composite index considers several variables. This allows for a more comprehensive view of the data being analyzed.
- Weighting of Variables: In a composite index, each variable can be assigned a different weight based on its importance. This reflects the relative contribution of each variable to the overall index.
- Applications: Composite indices are commonly used in various fields, including economics (e.g., Consumer Price Index), finance (e.g., stock market indices), and social sciences (e.g., Human Development Index).
Examples of Composite Indices:
- Consumer Price Index (CPI): Measures the average change over time in the prices paid by consumers for a basket of goods and services.
- Human Development Index (HDI): Combines indicators of life expectancy, education, and per capita income to assess the development of countries.
Conclusion:
A composite index is a powerful tool for summarizing complex data involving multiple variables. By aggregating these variables into one index, analysts can derive more insightful conclusions about trends and patterns in the data. This is why the correct answer to the question is option 'B'—composite index.
A composite index is a statistical measure that aggregates multiple variables into a single index number. This approach is particularly useful in economic and financial analysis, where various indicators need to be evaluated together to understand broader trends.
Key Features of a Composite Index:
- Multidimensional Analysis: Unlike a simple index that measures a single variable, a composite index considers several variables. This allows for a more comprehensive view of the data being analyzed.
- Weighting of Variables: In a composite index, each variable can be assigned a different weight based on its importance. This reflects the relative contribution of each variable to the overall index.
- Applications: Composite indices are commonly used in various fields, including economics (e.g., Consumer Price Index), finance (e.g., stock market indices), and social sciences (e.g., Human Development Index).
Examples of Composite Indices:
- Consumer Price Index (CPI): Measures the average change over time in the prices paid by consumers for a basket of goods and services.
- Human Development Index (HDI): Combines indicators of life expectancy, education, and per capita income to assess the development of countries.
Conclusion:
A composite index is a powerful tool for summarizing complex data involving multiple variables. By aggregating these variables into one index, analysts can derive more insightful conclusions about trends and patterns in the data. This is why the correct answer to the question is option 'B'—composite index.
The value Index is expressed in terms of
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The value Index is expressed in terms of
a)
b)
c)
d)
|
|
Bird Singh answered |
It is formula so a option is right formula
When the product of price index and the quantity index is equal to the corresponding value index then the test that holds is- a)Unit Test
- b)Time Reversal Test
- c)Factor Reversal Test
- d)None holds
Correct answer is option 'C'. Can you explain this answer?
When the product of price index and the quantity index is equal to the corresponding value index then the test that holds is
a)
Unit Test
b)
Time Reversal Test
c)
Factor Reversal Test
d)
None holds
|
Ishani Rane answered |
Factor Reversal Test: It says that the product of a price index and the quantity index should be equal to value index. In the words of Fisher, just as each formula should permit the interchange of the two times without giving inconsistent results similarly it should permit interchanging the prices and quantities without giving inconsistent results which means two results multiplied together should give the true value ratio.
Index no. is equal to- a)sum of price relatives
- b)average of the price relatives
- c)product of price relative
- d)none
Correct answer is option 'B'. Can you explain this answer?
Index no. is equal to
a)
sum of price relatives
b)
average of the price relatives
c)
product of price relative
d)
none
|
Pallabi Deshpande answered |
An index number is an economic data figure reflecting price or quantity compared with a standard or base value. The base usually equals 100 and the index number is usually expressed as 100 times the ratio to the base value.
Time Reversal Test is represented symbolically by :- a)P01 x P10
- b)P01 x P10 = 1
- c)P01 x P10
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Time Reversal Test is represented symbolically by :
a)
P01 x P10
b)
P01 x P10 = 1
c)
P01 x P10
d)
None of these
|
|
Charvi Roy answered |
Time Reversal Test in Physics
Time reversal test is a fundamental concept in physics that helps to determine whether a physical system is symmetric or not under time reversal. It is represented symbolically by P01 x P10 = 1. Let's understand this representation in detail.
Representation of Time Reversal Test
The time reversal operator is represented by P, which is a mathematical operator that reverses the direction of time. It is defined as follows:
P|t> = |-t>
Here, |t> represents a state of the system at time t, and |-t> represents the state of the system at time -t.
The time reversal operator has two properties:
1. P2 = 1 (the square of the operator is equal to unity).
2. [H,P] = 0 (the operator commutes with the Hamiltonian of the system).
Now, let's see how the time reversal test is represented symbolically:
P01 x P10 = 1
Here, P01 represents the time reversal operator applied at time t1, and P10 represents the time reversal operator applied at time t0. The product of these two operators is equal to unity (1), which means that the system is symmetric under time reversal.
Explanation
The time reversal test is a powerful tool to determine the symmetry of a physical system under time reversal. If the system is symmetric, then the time-reversed version of the system should be identical to the original system. This means that the time-reversed version of the system should evolve in exactly the same way as the original system, but in reverse order.
The representation of the time reversal test by P01 x P10 = 1 indicates that if we apply the time reversal operator at time t1 and then at time t0, the resulting system should be identical to the original system. This is because the product of the two operators is equal to unity, which means that the system is symmetric under time reversal.
In summary, the representation of the time reversal test by P01 x P10 = 1 is a powerful tool to determine the symmetry of a physical system under time reversal. It helps to establish the fundamental principles of physics and is widely used in various branches of physics, such as quantum mechanics, electromagnetism, and thermodynamics.
Time reversal test is a fundamental concept in physics that helps to determine whether a physical system is symmetric or not under time reversal. It is represented symbolically by P01 x P10 = 1. Let's understand this representation in detail.
Representation of Time Reversal Test
The time reversal operator is represented by P, which is a mathematical operator that reverses the direction of time. It is defined as follows:
P|t> = |-t>
Here, |t> represents a state of the system at time t, and |-t> represents the state of the system at time -t.
The time reversal operator has two properties:
1. P2 = 1 (the square of the operator is equal to unity).
2. [H,P] = 0 (the operator commutes with the Hamiltonian of the system).
Now, let's see how the time reversal test is represented symbolically:
P01 x P10 = 1
Here, P01 represents the time reversal operator applied at time t1, and P10 represents the time reversal operator applied at time t0. The product of these two operators is equal to unity (1), which means that the system is symmetric under time reversal.
Explanation
The time reversal test is a powerful tool to determine the symmetry of a physical system under time reversal. If the system is symmetric, then the time-reversed version of the system should be identical to the original system. This means that the time-reversed version of the system should evolve in exactly the same way as the original system, but in reverse order.
The representation of the time reversal test by P01 x P10 = 1 indicates that if we apply the time reversal operator at time t1 and then at time t0, the resulting system should be identical to the original system. This is because the product of the two operators is equal to unity, which means that the system is symmetric under time reversal.
In summary, the representation of the time reversal test by P01 x P10 = 1 is a powerful tool to determine the symmetry of a physical system under time reversal. It helps to establish the fundamental principles of physics and is widely used in various branches of physics, such as quantum mechanics, electromagnetism, and thermodynamics.
Fisher’s ideal formula for calculating index number satisfies the _______:- a)Unit Test
- b) Factor reversal test
- c) Both (a) & (b)
- d) None of these
Correct answer is option 'C'. Can you explain this answer?
Fisher’s ideal formula for calculating index number satisfies the _______:
a)
Unit Test
b)
Factor reversal test
c)
Both (a) & (b)
d)
None of these
|
|
Freedom Institute answered |
Answer :
- c)Both (a) & (b)
Normally, the following inequality holds;
Laspeyres >= Fisher >= Paasche. Fisher formula is called ideal formula in a sense that the time reversal test and the factor reversal test are satisfied. This formula is used in the case when prices and quantities at the base and the observation period are quite different.
Fisher's index number does not satisfy Circular test
. All methods, except simple aggregative method, assuage by unit test.
A ratio or an average of ratios expressed as a percentage is called- a)a relative no.
- b)an absolute no.
- c)an index no.
- d)none
Correct answer is option 'C'. Can you explain this answer?
A ratio or an average of ratios expressed as a percentage is called
a)
a relative no.
b)
an absolute no.
c)
an index no.
d)
none
|
Niharika Chavan answered |
Ratio or average of ratios expressed as a percentage is called an index number. Index numbers are used to measure changes over time in economic, financial or statistical data. They are used to compare the changes in a particular variable over time or between different regions or countries.
There are different types of index numbers such as price index, quantity index, cost of living index, and stock market index. Index numbers are useful in making economic decisions, forecasting trends, and analyzing the performance of different sectors or industries.
Index numbers are expressed in percentage terms and are calculated by dividing the current value of a variable by the base value and then multiplying the result by 100. The base value is usually taken as 100, which represents the starting point or the reference point for the index.
For example, let's say the price of a commodity was $100 in the base year and it increased to $120 in the current year. The index number for this commodity would be calculated as follows:
Index number = (Current value/Base value) x 100
Index number = ($120/$100) x 100
Index number = 120
This means that the price of the commodity has increased by 20% over the base year.
In conclusion, index numbers are a useful tool for measuring changes over time in economic and financial data. They are expressed as a percentage and are calculated by dividing the current value by the base value and multiplying the result by 100. Index numbers are used for making economic decisions, forecasting trends, and analyzing the performance of different sectors or industries.
There are different types of index numbers such as price index, quantity index, cost of living index, and stock market index. Index numbers are useful in making economic decisions, forecasting trends, and analyzing the performance of different sectors or industries.
Index numbers are expressed in percentage terms and are calculated by dividing the current value of a variable by the base value and then multiplying the result by 100. The base value is usually taken as 100, which represents the starting point or the reference point for the index.
For example, let's say the price of a commodity was $100 in the base year and it increased to $120 in the current year. The index number for this commodity would be calculated as follows:
Index number = (Current value/Base value) x 100
Index number = ($120/$100) x 100
Index number = 120
This means that the price of the commodity has increased by 20% over the base year.
In conclusion, index numbers are a useful tool for measuring changes over time in economic and financial data. They are expressed as a percentage and are calculated by dividing the current value by the base value and multiplying the result by 100. Index numbers are used for making economic decisions, forecasting trends, and analyzing the performance of different sectors or industries.
The price level of a country in a certain year has increased 25% over the base period. The index number is - a)25
- b)125
- c)225
- d)2500
Correct answer is option 'B'. Can you explain this answer?
The price level of a country in a certain year has increased 25% over the base period. The index number is
a)
25
b)
125
c)
225
d)
2500
|
|
Sahil Malik answered |
Given information:
- The price level of a country in a certain year has increased 25% over the base period.
To find:
- The index number.
Solution:
The index number can be calculated using the following formula:
Index number = (Price level in the given year / Price level in the base year) x 100
Let the price level in the base year be P and the price level in the given year be Q.
According to the given information, the price level in the given year has increased 25% over the base period. This can be expressed as:
Q = P + 0.25P
Q = 1.25P
Substituting the values in the formula for the index number, we get:
Index number = (Price level in the given year / Price level in the base year) x 100
Index number = (1.25P / P) x 100
Index number = 125
Therefore, the correct answer is option B (125).
Conclusion:
- The index number is calculated using the formula (Price level in the given year / Price level in the base year) x 100.
- The given information can be used to find the index number by substituting the values in the formula.
- The correct answer is option B (125).
- The price level of a country in a certain year has increased 25% over the base period.
To find:
- The index number.
Solution:
The index number can be calculated using the following formula:
Index number = (Price level in the given year / Price level in the base year) x 100
Let the price level in the base year be P and the price level in the given year be Q.
According to the given information, the price level in the given year has increased 25% over the base period. This can be expressed as:
Q = P + 0.25P
Q = 1.25P
Substituting the values in the formula for the index number, we get:
Index number = (Price level in the given year / Price level in the base year) x 100
Index number = (1.25P / P) x 100
Index number = 125
Therefore, the correct answer is option B (125).
Conclusion:
- The index number is calculated using the formula (Price level in the given year / Price level in the base year) x 100.
- The given information can be used to find the index number by substituting the values in the formula.
- The correct answer is option B (125).
P01 is the index for time- a)1 on 0
- b)0 on 1
- c)1 on 1
- d)0 on 0
Correct answer is option 'A'. Can you explain this answer?
P01 is the index for time
a)
1 on 0
b)
0 on 1
c)
1 on 1
d)
0 on 0
|
|
Raghav Ghoshal answered |
Index for Timea)1 on 0b)0 on 1c)1 on 1d)0 on 0
Explanation:
Indexing is the process of assigning a unique number or value to each item in a data set. In this case, we need to assign an index to timea)1.
The four options given are:
a) 1 on 0
b) 0 on 1
c) 1 on 1
d) 0 on 0
Out of these options, the correct answer is option 'A', which is "1 on 0".
This means that the index assigned to timea)1 is 1, and it occurs when the value of the previous item (time0) is 0.
In other words, the index for timea)1 is based on the value of the previous item in the data set.
HTML bullet points:
- Indexing is the process of assigning a unique number or value to each item in a data set.
- We need to assign an index to timea)1.
- The correct answer is option 'A', which is "1 on 0".
- This means that the index assigned to timea)1 is 1, and it occurs when the value of the previous item (time0) is 0.
- The index for timea)1 is based on the value of the previous item in the data set.
CA Foundation category:
- This question belongs to the CA Foundation category, which is an entry-level course for aspiring Chartered Accountants.
- The course covers topics such as accounting, business law, economics, and mathematics.
Explanation:
Indexing is the process of assigning a unique number or value to each item in a data set. In this case, we need to assign an index to timea)1.
The four options given are:
a) 1 on 0
b) 0 on 1
c) 1 on 1
d) 0 on 0
Out of these options, the correct answer is option 'A', which is "1 on 0".
This means that the index assigned to timea)1 is 1, and it occurs when the value of the previous item (time0) is 0.
In other words, the index for timea)1 is based on the value of the previous item in the data set.
HTML bullet points:
- Indexing is the process of assigning a unique number or value to each item in a data set.
- We need to assign an index to timea)1.
- The correct answer is option 'A', which is "1 on 0".
- This means that the index assigned to timea)1 is 1, and it occurs when the value of the previous item (time0) is 0.
- The index for timea)1 is based on the value of the previous item in the data set.
CA Foundation category:
- This question belongs to the CA Foundation category, which is an entry-level course for aspiring Chartered Accountants.
- The course covers topics such as accounting, business law, economics, and mathematics.
The ratio of price of single commodity in a given period to its price in another period is called the- a)base period
- b)price ratio
- c)relative price
- d)none
Correct answer is option 'C'. Can you explain this answer?
The ratio of price of single commodity in a given period to its price in another period is called the
a)
base period
b)
price ratio
c)
relative price
d)
none
|
|
Akshat Choudhary answered |
Ratio of Price of a Single Commodity
The ratio of the price of a single commodity in a given period to its price in another period is known as the relative price. This is a concept that is commonly used in economics to compare the price of a good or service in one period to its price in another period.
Importance of Relative Price
Relative price is important because it provides a way to compare the cost of goods and services over time. By comparing the price of a good or service in one period to its price in another period, economists can determine how the cost of that good or service has changed over time.
For example, if the price of a gallon of milk was $3 in 2010 and $4 in 2020, the relative price of milk in 2020 would be 1.33 ($4 divided by $3). This means that milk is 33% more expensive in 2020 than it was in 2010.
Conclusion
In conclusion, the ratio of the price of a single commodity in a given period to its price in another period is known as the relative price. This is an important concept in economics as it provides a way to compare the cost of goods and services over time.
The ratio of the price of a single commodity in a given period to its price in another period is known as the relative price. This is a concept that is commonly used in economics to compare the price of a good or service in one period to its price in another period.
Importance of Relative Price
Relative price is important because it provides a way to compare the cost of goods and services over time. By comparing the price of a good or service in one period to its price in another period, economists can determine how the cost of that good or service has changed over time.
For example, if the price of a gallon of milk was $3 in 2010 and $4 in 2020, the relative price of milk in 2020 would be 1.33 ($4 divided by $3). This means that milk is 33% more expensive in 2020 than it was in 2010.
Conclusion
In conclusion, the ratio of the price of a single commodity in a given period to its price in another period is known as the relative price. This is an important concept in economics as it provides a way to compare the cost of goods and services over time.
Each of the following statements is either True or False write your choice of the answer by writing T for True- a)Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage.
- b)“For Construction index number. The best method on theoretical ground is not the best method from practical point of view”.
- c)Weighting index numbers makes them less representative.
- d)Fisher’s index number is not an ideal index number.
Correct answer is option 'A'. Can you explain this answer?
Each of the following statements is either True or False write your choice of the answer by writing T for True
a)
Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage.
b)
“For Construction index number. The best method on theoretical ground is not the best method from practical point of view”.
c)
Weighting index numbers makes them less representative.
d)
Fisher’s index number is not an ideal index number.
|
|
Amrutha Goyal answered |
Explanation:
Index numbers are a statistical tool that helps in measuring the changes in the level of economic activity. It is used to compare two or more variables over a period of time. The given statements are:
a)Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage. - True
b)For Construction index number. The best method on theoretical ground is not the best method from a practical point of view. - Not given
c)Weighting index numbers makes them less representative. - False
d)Fishers index number is not an ideal index number. - Not given
Explanation of each statement:
a)Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage. - True
Index numbers are like signposts that provide guidance to the businessmen about the current state and changes in the economy. It helps them in making informed decisions related to production, sales, pricing, and investment. Index numbers provide information about the direction and magnitude of change in the economic variables, which helps in identifying the trends and forecasting the future.
b)For Construction index number. The best method on theoretical ground is not the best method from a practical point of view. - Not given
This statement is not true or false, it is incomplete and does not provide enough information to determine its truthfulness or falsity.
c)Weighting index numbers makes them less representative. - False
Weighting index numbers is a method of giving different weights to different items based on their importance. It makes the index numbers more representative as it gives more weight to the items that have a greater impact on the economy. It helps in reflecting the changes in the economy more accurately.
d)Fishers index number is not an ideal index number. - Not given
This statement is incomplete and does not provide enough information to determine its truthfulness or falsity.
In conclusion, statement a) is true, statement b) and d) are incomplete, and statement c) is false.
Index numbers are a statistical tool that helps in measuring the changes in the level of economic activity. It is used to compare two or more variables over a period of time. The given statements are:
a)Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage. - True
b)For Construction index number. The best method on theoretical ground is not the best method from a practical point of view. - Not given
c)Weighting index numbers makes them less representative. - False
d)Fishers index number is not an ideal index number. - Not given
Explanation of each statement:
a)Index Numbers are the signs and guideposts along the business highway that indicate to the businessman how he should drive or manage. - True
Index numbers are like signposts that provide guidance to the businessmen about the current state and changes in the economy. It helps them in making informed decisions related to production, sales, pricing, and investment. Index numbers provide information about the direction and magnitude of change in the economic variables, which helps in identifying the trends and forecasting the future.
b)For Construction index number. The best method on theoretical ground is not the best method from a practical point of view. - Not given
This statement is not true or false, it is incomplete and does not provide enough information to determine its truthfulness or falsity.
c)Weighting index numbers makes them less representative. - False
Weighting index numbers is a method of giving different weights to different items based on their importance. It makes the index numbers more representative as it gives more weight to the items that have a greater impact on the economy. It helps in reflecting the changes in the economy more accurately.
d)Fishers index number is not an ideal index number. - Not given
This statement is incomplete and does not provide enough information to determine its truthfulness or falsity.
In conclusion, statement a) is true, statement b) and d) are incomplete, and statement c) is false.
Chapter doubts & questions for Chapter 18: Index numbers - Quantitative Aptitude for CA Foundation 2025 is part of CA Foundation exam preparation. The chapters have been prepared according to the CA Foundation exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CA Foundation 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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