Question 13 Marks
The wholesale price index numbers for commodities with the base year $2007- 08$ are as follows. Compute the chain base index numbers.
AnswerThe base year $2007-08$ is mentioned here. Hence, we will take the given fixed base index number for the year $2008-09$ as chain base index number. Thus, the chain base index number for the first year is $126.$ Chain base index number $=\frac{\text { Fixed base index number of the current year }}{\text { Fixed base index number of the preceding year }} \times 100$
View full question & answer→Question 23 Marks
The following data are available about the crimes in a city. Find the general index number by fixed base method considering the year $2010$ as base year.
AnswerFixed base index number $I=\frac{\text { Value of variable in current year (period) }}{\text { Value of variable in base year (period) }} \times 100$
View full question & answer→Question 33 Marks
The prices of three items $A, B$ and $C$ among five items have increased in the year $2015$ by $90 \%, 120 \%$ and $70 \%$ respectively with respect to the year $2010,$ whereas the prices of two items $D$ and $E$ have decreased by $2 “/0$ and $5 "a$ respectively. Item $A$ is four times important than item $B$ and item $C$ is six times important than item $A.$ The importance of items $D$ and $E$ is two and half times the importance of item $B.$ Compute the general price index number of the year $2015$ for all the five items.
AnswerThe percentage increase and decrease in the prices of items is given here. Similarly,the weight $W$ of the items are the numbers showing their relative importance. Suppose the relative importance of item $B$ is $1.$ Then the importance of item $A$ will be $4,$ importance of $C$ will be $24$ and that of $D$ and $E$ will be $2.5$ each.The general price index number will be calculated as follows :
$ \text { General price index number } =\frac{\Sigma I W}{\Sigma W}$
$ =\frac{5542.5}{34}$
$ =163.0147$
$ \simeq 163.01 $
Thus, it can be said that there is a rise of$(163.01 — 100) = 63.01 \%$ in the prices in the current year $2015$ as compared to the base year $2014.$ View full question & answer→Question 43 Marks
The prices per unit $R$ of six food items in the year $2014$ and $2015$ are given in the following table. Taking $2014$ as the base year, compute the general index number for the price of food items and state the overall rise in prices of these food items.
AnswerA general index number for the price of these items for the current year $2015$ is to be obtained with the base year $2014.$ We will find price relatives $\frac{p_{1}}{p_{0}}$ by taking base year price as $p_{0}$ and current year price as $p_{1}$. The calculation is shown in the following table :
General index number of six food items $I=\frac{\Sigma\left[\frac{p_{1}}{p_{0}}\right]}{n} \times 100$$ =\frac{6.6795}{6} \times 100$
$ =111.33$
$\therefore$ General price index number of six food items is $I = 111.33.$
It can be seen from the value of the index number I that there is an overall rise in pricesof food items by $(111.33 - 100) = 11.33 \%$ in the year $2015$ as compared to the year $2014.$
View full question & answer→Question 53 Marks
Find the cost of living index number by the family budget method from the following information about index numbers of different groups ofitems for living and their weights.
AnswerThe index numbers of different groups and their weights are given here. Hence, we will use family budget method which is a method of weighted average.
$ \text { Index number } I =\frac{\Sigma I W}{\Sigma W}$
$ =\frac{24512}{100}$
$ =245.12 $
Thus, it can be said that there is a rise of $(245.12 - 100) = 145.12 \%$ in the total expenditure in the current year as compared to the base year. View full question & answer→Question 63 Marks
The health department has implemented a certain policy for the industrial units in the year $2003$ to control the possibility of cancer due to the chemical process which is hazardous to the health of workers employed in the industrial units of a certain industrial area who are residing in the same area. To evaluate this policy, a survey was conducted about deaths due to cancer of persons in the different age groups. The following data are obtained for the years $2003$ and $2008.$ Find the index number of deaths due to cancer using weighted average method by taking the population of this industrial area in the year $2003$ as weight and interpret it.
AnswerWe shall obtain the general index number by finding the relative percentages of cancer deaths for the year $2008$ and taking the population in different age-groups in $2003$ as weights.
$ \text { Index number for year } 2008 ~I =\frac{\Sigma I W}{\Sigma W}$
$ =\frac{8280.6}{118}$
$ =70.1745$
$ \simeq 70.17 $
Thus, it can be said that there is a decrease of $(100 -70.17) = 29.83 \%$ in the deaths due to cancer in the year $2008$ as compared to the year $2003.$ View full question & answer→Question 73 Marks
Find the ideal index number for the year $2015$ from the following data.
AnswerFisher's index number is considered as an ideal index number. So, we will find Fisher's index number here. We will take price $p_{0}$ and quantity $q_{0}$ for base year, price $p_{1}$ and quantity $q_{1}$ for the current year.
${\text{Fisher's index number}} ~I_{F} =\sqrt{\frac{\Sigma p_{1} q_{0}}{\Sigma p_{0} q_{0}} \times \frac{\Sigma p_{1} q_{1}}{\Sigma p_{0} q_{1}}} \times 100$
$ =\sqrt{\frac{1056}{852} \times \frac{1116}{900}} \times 100$
$ =\sqrt{1.5369} \times 100$
$ =1.2397 \times 100$
$I_{F} =123.97 $
Thus, it can be said that there is $(123.97 - 100) = 23.97 \%$ rise in the prices in the year $2015$ as compared to the year $2014.$ View full question & answer→Question 83 Marks
Find the index number for the year $2016$ with base year $2011$ by weighted average method from the following data of price and weights of five different items.
AnswerThe weights of different items are given here. We shall compute the general index number from the price relatives of the year $2016$ based on the prices of the year $2011.$
$ \text { Index number of year } 2016 I =\frac{\Sigma I W}{\Sigma W}$
$ =\frac{14550}{100}$
$ =145.50 $
Thus, we say that there is an increase of $(145.50 - 100) : 45.5 \%$ in prices in the year $2016$ as compared to the year $2011.$ View full question & answer→Question 93 Marks
The chain base index numbers obtained for food items from the year $2008- 09$ to $2015-16$ are as follows. Compute the fixed base index numbers. $($Take $2007-08$ as base year$)$
AnswerThe year $2007-08$ is to be taken as the base year here.
Hence, the fixed base index number for the year $2008-09$ will not change.
Current year fixed base index number $=\frac{\left(\begin{array}{c}\text { Current year chain base } \\ \text { index number }\end{array}\right) \times\left(\begin{array}{c}\text { Fixed base index number of } \\ \text { preceding year to current year }\end{array}\right)}{100}$
View full question & answer→Question 103 Marks
The index numbers of average closing prices of shares of a certain company in different months with the base January $2014$ are as follows. Find the chain base index numbers.
| Month |
Jan.’$14$ |
Feb.’$14$ |
March $14$ |
April $14$ |
May $14$ |
June $14$ |
| Fixed base index number |
$100$ |
$104$ |
$105$ |
$108$ |
$109$ |
$127$ |
View full question & answer→Question 113 Marks
Find the fixed base index numbers from the following data about average annual income of workers in a company from the year $2008$ to the year $2014.$ $($Take base year as $2008)$
| Year |
$2008$ |
$2009$ |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
| Average annual income $(Rs. 10,000)$ |
$36$ |
$40$ |
$48$ |
$52$ |
$60$ |
$80$ |
$95$ |
View full question & answer→Question 123 Marks
The price of three items among five fuel items increased by $50\%, 90\%$ and $110\%$ in the year $2015$ as compared to the base year $2014.$ The prices of other two items decreased by $5\%$ and $2\%$ respectively. If the ratio of importance of these five items is $5:4:3:2:1,$ find the index number of fuel prices for the year $2015.$
View full question & answer→Question 133 Marks
State the limitations of cost of living index number.
Answer
Limitations of Cost of Living Index Number : Following are the limitations of Cost of Living Index Number.
- A common cost of living index number for all the classes of people can not be constructed.
- It represents the average percentage change occurring in the cost of living for a particular class.
- Thus, it can not measure the changes occurring in the cost of living for an individual person.
- Different index numbers are to be constructed for different classes of people and also for different regions.
- The cost of living index number obtained for a particular class of people in a region can not be used for the same class at people in some other region.
- It depends upon the size of the family way of living style, habits, attitudes etc.
- Therefore, the pattern of expenditure of families belonging to the same class may not be the same.
- Thus, an average family may not be the ideal family.
- In computation of this index, an assumption that there is no change in the expenditure for the base year is not quite valid.
- There is always change in the fashion, habits, choice etc. of the people with passage of times.
- Hence, it is therefore essential to carry out the family budget inquiry at regular intervals of time and also to make changes in the commodity as well as their weights wherever and whenever such changes are warranted.
View full question & answer→Question 143 Marks
State the uses of cost of living index number.
AnswerUse of Cost of Living Index Number is as follows :
- The cost of living index number obtained for a class provides a realistic picture of the economic condition of the people of that class.
- Hence, it is useful to recommend for the changes occurring in wages; dearness allowance, bonus etc. to be paid to that class of people.
- Index number provides a guideline to the government to exercise control on the price of some commodity or to subsidies a given commodity.
- Also we come to know about the effect of tax levied on a commodity to the different classes of people on the basis of the cost of living index number.
- Accordingly planning for taxation policy can be implemented by government.
- (Rs.) With the help of this index number, the changes occurring in the purchasing power of money, can be measured.
- The index number is very useful to government and other public institutions to determine the type of facilities and incentives that could be provided to different classes of people in order to raise their standard of living.
View full question & answer→Question 153 Marks
Give the meaning of cost of living index number and state the points to be considered for its construction.
AnswerMeaning of cost of living index number: The number showing the percentage of relative changes in the cost of living of the people of a certain section of the society in the current year as composed to the base year is called the cost of living index number.The following points should be taken into account while constructing the cost of living index number :
$1.$ Purpose of construction : While constructing the cost of living index number, first of all its purpose should be defined. It should be made clear about the class of people for whom this index number is to be constructed. The decision regarding selection of commodities, their numbers, their quantities, etc. can be taken after knowing the requirements of different classes of people. This means that it is absolutely necessary to clarify the purpose for which the cost of living index number is to be constructed.
$2.$ Family budget inquiry : For family budget inquiry, a random sample for specified class of people is selected for whom the cost of living Index number is to be constructed.
$3.$ Classification of commodities : Generally, the list of commodities obtained by family budget inquiry can be classified into five heads :
$1.$ Food items,
$2.$ Clothing,
$3.$ House rent,
$4.$ Fuel and Light,
$5.$ Miscellaneous expenditure
$4.$ Availability of prices of items : The retail prices of items of consumption by families are collected from the government recognised or approved shops located in the area where the families of that class of people reside. Sometimes the simple average of retail prices obtained from different shops at different times are taken into consideration. To obtain retail prices of commodities unit of quantity is taken as base unit.
For example, price is obtained as $₹ 10$ per kg and not as $₹ 1$ per $100\ gm.$ This type of retail prices are obtained according to the requirements of index numbers as weekly, fortnightly, monthly or yearly basis.
$5.$ Selection of base year : The year with normal events should be selected as the base year and price relatives of all the selected items are obtained as follows :
$\text { Price relative }(\mathrm{l})==\frac{\text { Retail price of the current year }}{\text { Retail price of the base year }} \times 100$
$6.$ Selection of average : For obtaining common price relative from different price relatives of different commodities, appropriate average should be used. Theoretically, the Geometric mean is an ideal average for construction of Index number, but it’s computation is difficult. Hence, weighted average is used in the practice.
$7.$ Selection of weighted method : In the context of total expenditure, importance $($weight$)$ of each group and each item is determined and by the following two methods cost of living index number is constructed :
$1.$ Total expenditure method and
$2.$ Family budget method.
View full question & answer→Question 163 Marks
Give difference between fixed base and chain base methods.
Answer
| Fixed base method |
Chain base method |
| $1.$ The year with normal events is taken as the base year. |
$1.$ The year preceding the current year for which the index is to be obtained, is taken as the base year. |
| $2.$ The base year remains constant for computing index number for the given time period. |
$2.$ The base year keeps on changing for the given time period. |
| $3.$ Since the base year is fixed, uniformity is maintained in comparing changes in the values of a variable quantity. |
$3.$ Since the base year is changing, uniformity is not maintained in comparing changes in the values of variable quantity. |
| $4.$ In this method, new items in demand cannot be included and old items out of use or having no preferences cannot be removed. |
$4.$ This method permits inclusion of items in demand and exclusion of items out of use or having no preferences. |
| $5.$ The work of selection of a base year is difficult. |
$5.$ The question of selecting a base year does not arise as it is automatically selected. |
| $6.$ The base year is to be changed with lapse of time. |
$6.$ No such problem arises in this method. |
| $7.$ This method is quite useful for comparing long-term changes in the value of a variable quantity. |
$7.$ This method is useful only for comparing short-term changes in the value of a variable quantity. |
| $8.$ It is easy to understand and easy in computation. |
$8.$ In this method if there is any mistake in the calculations of Index number of one year then that mistake is carried on in all the subsequent years. |
View full question & answer→Question 173 Marks
If the ratio of Laspeyre’s and Paasche’s index number is $4 : 5$ and Fisher’s index number is $150,$ find Paashe’s index number.
AnswerHere, $I_L: I_P=4: 5$;
$\mathrm{I}_{\mathrm{F}}=150,$
$ \mathrm{I}_{\mathrm{P}}=?$
$ \therefore \frac{I_L}{I_p}=\frac{4}{5}$
$ \therefore \mathrm{I}_{\mathrm{L}}=\frac{4}{5} \mathrm{l}_{\mathrm{p}}$
$ \text { Now, } \mathrm{I}_{\mathrm{F}}=\sqrt{I_L \times I_P}$
$ \therefore 150=\sqrt{\frac{4}{5} \mathrm{I}_{\mathrm{P}} \times \mathrm{I}_{\mathrm{P}}}$
$ \therefore(150)^2=\frac{4}{5} \mathrm{I_P}^2$
$ \therefore \frac{22500 \times 5}{4}=\mathrm{I}_{\mathrm{p}}{ }^2$
$ \therefore \mathrm{I}^2=28125$
$ \therefore \mathrm{Ip}^2=167.71$
View full question & answer→Question 183 Marks
If $\Sigma p_1 q_0: \Sigma p_0 q_0=5: 3$ and $\Sigma p_1 q_1: \Sigma p_0 q_1=3: 2$, compute the Laspeyre's, Paasche's and Fisher's index numbers.
Answer$\Sigma p_1 q_0: \Sigma p_0 q_0=5: 3$
$\therefore \frac{\Sigma p_1 q_0}{\Sigma p_0 q_0}=\frac{5}{3}$
$\Sigma p_1 q_1: \Sigma p_0 q_1=3: 2$
$\therefore \frac{\Sigma p_1 q_1}{\Sigma p_0 q_1}=\frac{3}{2}$
Now,
Laspeyre's index number :
$\mathrm{I}_{\mathrm{L}} =\frac{\Sigma p_1 q_0}{\Sigma p_0 q_0} \times 100 \quad$
$ =\frac{5}{3} \times 100$
$ =166.67$
Paasche's index number:
$\mathrm{I}_{\mathrm{P}} =\frac{\Sigma p_1 q_1}{\Sigma p_0 q_1} \times 100$
$ =\frac{3}{2} \times 100$
$ =150$
Fisher's index number:
$\mathrm{I}_{\mathrm{F}} =\sqrt{\mathrm{I}_{\mathrm{L}} \times \mathrm{I}_P}$
$ =\sqrt{166.67 \times 150}$
$ =\sqrt{25000.5} \quad$
$ =158.12$
View full question & answer→Question 193 Marks
Find the cost of living index number from the given information for the month of April, $2015$ regarding group index numbers and weights of items of living of industrial workers.
| Group |
$A$ |
$B$ |
$C$ |
$D$ |
$E$ |
$F$ |
| Index Number |
$247$ |
$167$ |
$259$ |
$196$ |
$212$ |
$253$ |
| Weight |
$44$ |
$20$ |
$16$ |
$6$ |
$10$ |
$4$ |
View full question & answer→Question 203 Marks
Find the chain base index number from the following data regarding the price of an item.
| Month |
$2009$ |
$2010$ |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
| Index number |
$40$ |
$45$ |
$48$ |
$55$ |
$60$ |
$70$ |
View full question & answer→Question 213 Marks
Find the fixed base index number from the chain base index numbers given below :
| Year |
$2011$ |
$2012$ |
$2013$ |
$2014$ |
| Index number |
$120$ |
$90$ |
$140$ |
$125$ |
View full question & answer→Question 223 Marks
State the merits and limitations of fixed base method.
AnswerThe merits and limitations of fixed base method are as follows :
Merits :
- The base year is constant throughout the period of comparison.
- As the base year remains constant, uniformity is maintained in the comparison of the relative changes in the values of variable.
- This method is useful to compare the long term changes in the values of the variable.
- It is easy to understand and simple to compute.
Limitations :
- With change in time the taste, habits and fashion of consumers also changed and the items used by consumers will be changed. In this method the items which are not of much usage cannot be removed and the new items of usage cannot be considered.
- It is not always possible to have a standard year with normal conditions as the base year. So the selection of base year is difficult.
- If the base year is not selected appropriately, the reliability of the index number reduces.
- It is not suitable to compare short term changes in the value of the variable.
- It is not possible to make necessary change in determining weights of the items due to change in the quality of the items.
- If the base year is a year of very remote past, the comparison of relative changes in the value of the variable cannot be considered appropriate.
View full question & answer→Question 233 Marks
The information about six different items used in the production of an electronics item is follows. Find the index number and interpret it.
| Items |
$A$ |
$B$ |
$C$ |
$D$ |
$E$ |
$F$ |
| Weight |
$5$ |
$10$ |
$10$ |
$30$ |
$20$ |
$25$ |
| Percentage price relative |
$290$ |
$315$ |
$280$ |
$300$ |
$315$ |
$320$ |
AnswerTable of calculation is as under
| Items |
Percentage Price Relative$(I)$ |
Weight$(W)$ |
$(IW)$ |
| $A$ |
$290$ |
$5$ |
$1,450$ |
| $B$ |
$315$ |
$10$ |
$3,150$ |
| $C$ |
$280$ |
$10$ |
$2,800$ |
| $D$ |
$300$ |
$30$ |
$9,000$ |
| $E$ |
$315$ |
$20$ |
$6,300$ |
| $F$ |
$320$ |
$25$ |
$8,000$ |
| Total |
$-$ |
$\Sigma w = 100$ |
$\Sigma lw = 30,700$ |
Index Number = $\frac{\Sigma lw}{\Sigma w}$
$=\frac{30,700}{100}$
$= 307$
$\therefore$ Index Number $= 307$
Thus, $207\%$ Increased in expenditure View full question & answer→Question 243 Marks
If for an item $ 3∑p_1q_0 =4∑p_1q_1 = 1800 $ and $ 2∑p_0q_0=2.5∑p_0q_1=1000 $, find Laspeyre’s and Paasche’s index number.
Answer$ I_L= 120; I_P = 112.5$
View full question & answer→Question 253 Marks
From the following data construct the cost of living index number for workers:
It is given that index number of clothing is $224.1,$ index number for food is $3/2$ times the base year, the prices of fuel have increase by $220\%,$ the expenditure on rent for $2005$ has increased to $2200$ from ? $1000$ and the index number for miscellaneous items ha increased by $1.75$ times that of the base ye index number and the expenditure Incurred on these groups are $18\%, 40\%, 12\%, 20\%$ and $10\%$ respectively.
View full question & answer→Question 263 Marks
As compared to the year $2015,$ the prices of three items $A, B$ and $C$ have increased by $90\%, 120\%$ and $75\%$ respectively in the year $2017,$ while the prices of remaining two items $D$ and $E$ have decreased by $10\%$ and $15\%$ respectively. Relative importance of $A$ is twice that of $B$ and relative importance of $C$ is thrice that of $A.$ Relative importance of $D$ and $E$ are one and half times that of $C.$ Construct general index number of price for $2017.$
View full question & answer→Question 273 Marks
As compared to $2015,$ the price of wheat increases by $60\%,$ the price of rice increases by $30\%,$ the price of millet decreases by $15\%,$ the price of oil increases by $40\%$ and the price of ghee decreases by $5\%$ in $2017.$ The relative importance of oil is three times that of ghee, the relative importance of rice is twice that of ghee, the relative importance of wheat and millet each is twice that of rice. Find the index number of price for the group of these five items for the year $2017.$
View full question & answer→Question 283 Marks
As compared to $2016,$ the price of three items have increased by $240\%, 350\%$ and $160\%$ respectively while the price of two items have decreased by $5\%$ and $10\%$ respectively in $2017.$ If the percentage of expense on these items are $16, 12, 28, 36$ and $8$ respectively, find the index number of price for $2017.$
View full question & answer→Question 293 Marks
The prices of three items among five fuel items were increased by 50 %, 90 % and 110 % in the year 2024 as compared to the base year 2023. The prices of other two items were decreased by 5 % and 2 % respectively. If the ratio of importance of these five items is 5 : 4 : 3 : 2 : 1, find the index number of fuel prices for the year 2024.
AnswerItems (I) : (100+50)=150, (100+90)=190, (100+110)=210, (100-5)=95, (100-2)=98.
Weights (W) : 5, 4, 3, 2, 1. $\Sigma W = 15$.
IW : 750, 760, 630, 190, 98. $\Sigma IW = 2428$.
Index Number = $\frac{\Sigma IW}{\Sigma W} = \frac{2428}{15} = 161.87$.
View full question & answer→Question 303 Marks
The chain base index numbers of sales of a certain type of scooter from the year 2020 to 2024 are as follows. Find fixed base index numbers :
| Year | 2020 | 2021 | 2022 | 2023 | 2024 |
| Index Number of Sale | 110 | 112 | 109 | 108 | 105 |
Answer$FBI _{\text {current year }}=\frac{\left( CBI _{\text {current year }} \times FBI _{\text {previous year }}\right)}{100}$| Year | Chain Base Index | Calculation for Fixed Base Index | Fixed Base Index |
| 2018 - 19 | 110 | $\frac{110 \times 100}{100}$ | 110 |
| 2019 - 20 | 112 | $\frac{112 \times 110}{100}$ | 123.2 |
| 2020 - 21 | 109 | $\frac{109 \times 123.2}{100}$ | 134.29 |
| 2021 - 22 | 108 | $\frac{108 \times 134.29}{100}$ | 145.03 |
| 2022 - 23 | 105 | $\frac{105 \times 145.03}{100}$ | 152.28 |
| 2023 - 24 | 111 | $\frac{111 \times 152.28}{100}$ | 169.03 |
View full question & answer→Question 313 Marks
If the increase in the price relatives of three items are 250%, 265% and 300% respectively and if the ratio of the importance of these items are 8 : 7 : 5, find the general price index number.
AnswerLet items be A, B, C.
Index I :
$I_{A} = 100 + 250 = 350$
$I_{B} = 100 + 265 = 365$
$I_{C} = 100 + 300 = 400$
Weight W: 8, 7, 5.
$\sum W = 20$
IW :
$A: 350 \times 8 = 2800$
$B: 365 \times 7 = 2555$
$C: 400 \times 5 = 2000$
$\sum IW = 7355$
General Index = $\frac{\sum IW}{\sum W} = \frac{7355}{20} = 367.75$.
View full question & answer→Question 323 Marks
The chain base index numbers obtained for food items from the year 2008-09 to 2015-16 are as follows. Compute the fixed base index numbers (Take 2007-08 as base year) :
| Years | 2008-09 | 2009-10 | 2010-11 | 2011-12 |
| Index number of food items | 134.8 | 115.28 | 115.57 | 107.29 |
| Years | 2012-13 | 2013-14 | 2014-15 | 2015-16 |
| Index number of food items | 109.91 | 112.80 | 106.24 | 102.48 |
AnswerFixed Base Index (Current Year) $=\frac{\text { Chain Base Index (Current Year) × Fixed Base Indes }}{100}$| Year | Chain Base Index | Fixed Base Index Calculation | Fixed Base Index |
| 2008-09 | 134.8 | $\frac{134.8 \times 100}{100}$ | 134.80 |
| 2009-10 | 115.28 | $\frac{115.28 \times 134.80}{100}$ | 155.40 |
| 2010-11 | 115.57 | $\frac{115.57 \times 155.40}{100}$ | 179.60 |
| 2011-12 | 107.29 | $\frac{107.29 \times 179.60}{100}$ | 192.69 |
| 2012-13 | 109.91 | $\frac{109.91 \times 192.69}{100}$ | 211.79 |
| 2013-14 | 112.80 | $\frac{112.80 \times 211.79}{100}$ | 238.90 |
| 2014-15 | 106.24 | $\frac{106.24 \times 238.90}{100}$ | 253.81 |
| 2015-16 | 102.48 | $\frac{102.48 \times 253.81}{100}$ | 260.10 |
View full question & answer→Question 333 Marks
Differentiate between Fixed base and Chain base methods. (Any 3 points)
AnswerDifferentiation: Fixed Base vs. Chain Base Method
| Feature | Fixed Base Method | Chain Base Method |
| Base Period | Remains constant (fixed) for all years. | Changes every year; the preceding year is the base. |
| Comparison | Easy to compare current data with a specific past period | Ideal for comparing data with the immediate past. |
| Flexibility | Rigid; difficult to include new items or delete old ones. | Flexible; new items can be added or deleted easily. |
View full question & answer→Question 343 Marks
The information about six different items used in the production of an electronic item is as follows. Find the Index Number and Interpret it :
| Items | A | B | C | D | E | F |
| Weight | 5 | 10 | 10 | 30 | 20 | 25 |
| Percentage Price Relative | 290 | 315 | 280 | 300 | 315 | 320 |
AnswerIndex Number $=\frac{\sum I W}{\sum W}$| Items | Weight ( $W$ ) | Price Relative ( $I$ ) | $I W(I \times W)$ |
| A | 5 | 290 | 1450 |
| B | 10 | 315 | 3150 |
| C | 10 | 280 | 2800 |
| D | 30 | 300 | 9000 |
| E | 20 | 315 | 6300 |
| F | 25 | 320 | 8000 |
| $\sum W=100$ | | $\sum I W=30,700$ |
Index Number $=\frac{30,700}{100}=307$
Calculation: $307-100=207$ View full question & answer→Question 353 Marks
The chain base index numbers obtained for food items from the year 2018-19 to 2023-24 are as follows. Compute the fixed base index numbers. [Take 2017-18 as base year]
| Year | 2018 - 19 | 2019 - 20 | 2020 - 21 | 2021 - 22 | 2022 - 23 | 2023 - 24 |
| Index number of food items | 110 | 112 | 109 | 108 | 105 | 111 |
Answer$FBI _{\text {current year }}=\frac{\left( CBI _{\text {current year }} \times FBI _{\text {previous year }}\right)}{100}$| Year | Chain Base Index | Calculation for Fixed Base Index | Fixed Base Index |
| 2018 - 19 | 110 | $\frac{110 \times 100}{100}$ | 110 |
| 2019 - 20 | 112 | $\frac{112 \times 110}{100}$ | 123.2 |
| 2020 - 21 | 109 | $\frac{109 \times 123.2}{100}$ | 134.29 |
| 2021 - 22 | 108 | $\frac{108 \times 134.29}{100}$ | 145.03 |
| 2022 - 23 | 105 | $\frac{105 \times 145.03}{100}$ | 152.28 |
| 2023 - 24 | 111 | $\frac{111 \times 152.28}{100}$ | 169.03 |
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Differentiate between fixed base and chain base method. (Any Three points)
AnswerDifferentiation : Fixed Base vs. Chain Base Method
| Feature | Fixed Base Method | Chain Base Method |
| Base Period | Remains constant (fixed) for all years. | Changes every year; the preceding year is the base. |
| Comparison | Easy to compare current data with a specific past period | Ideal for comparing data with the immediate past. |
| Flexibility | Rigid; difficult to include new items or delete old ones. | Flexible; new items can be added or deleted easily. |
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