Obviously change in prices is reflected in price index numbers. It is the most important use of price indices to measure the value of money during different time periods. We take pO as base year price and PI as current year price and it is reflected in index numbers.

We need an index number because:
Index numbers are indispensable tools of economics and business analysis.
Following are the main uses of index numbers.
1. Index numbers are used as economic barometers: Index number is a special type of averages which helps to measure the economic fluctuations on price level, money market, economic cycle like inflation, deflation etc.
2. They are useful in forecasting future economic activity: Index numbers are used not only in studying the past and present workings of our economy but also important in forecasting future economic activity. Index numbers measure the purchasing power of money. Index of Exports and Imports provides relevant information regarding foreign trade and accordingly government can formulate its export-import policy, business men who are engaged in foreign trade can take their decisions and one can predict changes in inflow or outflow of foreign exchange.
3. The cost of living index numbers determine whether the real wages are rising or falling or remain constant: The real wages can be obtained by dividing the money wages by the corresponding price index and multiplied by 100. Real wages helps us in determining the purchasing power of money. Index numbers are used in deflating. Index numbers are highly useful in deflating i.e. they are used to adjust the wages for cost of living changes and thus transform nominal wages into real wages, nominal income to real income, nominal sales to real sales etc. through appropriate index numbers.
4. Used in Deflating: Deflating means correcting or adjusting a value which has inflated. It makes allowances for the effect of price changes. When prices rise, the purchasing power of money declines. If the money incomes of people remain constant between two periods and prices of commodities are doubled the purchasing power of money is reduced to half. For example if there is an increase in the price of rice from Rs.10/ kg in the year 1980to Rs.20/kg in the year 1982. then a person can buy only half kilo of rice with no. so the purchasing power of a rupee is only 50paise in 1982 as compared to 1980.
Thus the purchasing power of money \(=\frac { 1 }{ Price\quad Index } \) In times of rising prices the money wages should be deflated by the price index to get the figure of real wages. The real wages alone tells whether a wage earner is in better position or in worst position.
For calculating real wage, the money wages or income is divided by the corresponding price index and multiplied by 100. 
Money wages i.e. Real wages = \(\\ \frac { Money\quad wages }{ Priceindex } \times 100\) 
Thus Real Wage Index \(=\frac { Realwagescurrentyear }{ Realwagesofbaseyear } \times 100\)
5. Index numbers helps in formulating suitable economic policies and planning: Many of the economic and business policies are guided by index numbers. For example while deciding the increase of DA of the employees; the employer's have to depend primarily on the cost of living index. If salaries or wages are not increased according to the cost of living it leads to strikes, lock outs etc. The index numbers provide some guide lines that one can use in making decisions.
6. They are used in studying trends and tendencies: Since index numbers are most widely used for measuring changes over a period of time, the time series so formed enable us to study the general trend of the phenomenon under study. For example for last 8 to 10 years we can say that imports are showing upward tendency. Businessmen need to know the trends in the market to take decisions about wage rates, prices of the product, prices of raw materials etc. Therefore, index numbers are very useful for them.

(i) To calculate rate of inflation for CPI of industrial workers, non-manual workers, agricultural labourers and WPI for each year, we will use the given formula: Rate of Inflation =\(\left\{ \frac { PriceIndexofCurrentYear }{ PriceIndex0f\frac { Previous }{ Base } Year } \times 100 \right\} \)
By using this formula the inflation rate for each year will be calculated.
(ii) The inflation rate has been continuously rising and it has much affected to agricultural labourers. There is much increase in wholesale price index and it has shown persistent rise in prices.
(iii) Yes, the relative values of the index numbers are comparable, but it is time consuming.

Let total weight be equal to 100 and WI and W2 be the weight of food and other items respectively. Therefore,
W_I + W₂ = 100
CPI = 125
\(\sum { } \)WR = 120W_I + 135W₂
CPI = \(\sum { } \)'WR/\(\sum { } \)W
125=\(\frac { 120{ W }_{ 1 }+135W_{ 2 } }{ 100 } \)
12500 = 120W_I + 135W₂ ... (ii)
By solving equation (i) and (ii), we get,
W_I = 66.66% and W₂ = 33.33%.
It means weight given to food is 2/3 and that of other items is one-third.

When CPI of base year is 100 and current year is 400 then his salary should be \(\frac { 4000\times 400 }{ 100 } =16,000\) Therefore, he needs an increment of 10000 rupees to maintain same standard of living.

(i) Food
(ii) Clothing
(iii) Fuel
(iv) Education
(v) Health.

General index presents the growth performance of the industrial sector over all. It also shows broad industrial categories' index numbers. It also shows that manufacturing has highest share in general index.

CPI = \(\frac{\Sigma R W}{\Sigma W}\) 
\(=\frac{18459.1}{100}\) = 184.6
Prices have risen by 84.60% in 2005 as compared to the prices in 1980.

Yes, the CPI number of urban non manual employees represents the changes in the cost of living of the president of India because it includes the government employees whether they belong to low paid jobs or high paid jobs. President of India is a part of high paid government employee. Their typical consumption basket is having different patterns but this group is least affected by changes in cost of living.

Price Index Numbers: Price index number measures the changes in the price level of one commodity or group of commodities between two points of time or two areas.
Example: Wholesale price index numbers; Retail price index numbers, Consumer price index numbers.
Quantity index number: Quantity index numbers measures the changes in the volume of production, sales, etc in different sectors of economy with respect to time period or space. For example, indices of agriculture production, industrial production, exports, imports etc.

Different categories of consumers have a different consumption pattern. CPI aims at measuring change over time in the price paid by the ultimate consumer for a specified quantity of goods and services. If goods and services which are included in estimation of price index are irrelevant then CPI also becomes irrelevant. For example, there is a wide gap in food items to be included in CPI for urban areas and CPI for rural areas. In some states rice is the main food in others, it is wheat. Therefore, keeping in mind the consumption pattern of different categories of consumers, we need to find different CPI for different consumer categories.

Desirable properties of a base year are as follows:
(a) The base period must be a normal period i.e. a period frees from all sorts of abnormalities or random fluctuations such as labor strikes, wars, floods, earthquakes etc.
(b) The base period should not be too distant from the given period. Since index numbers are essential tools in business planning and economic policies the base period should not be too far from the current period. For example for deciding increase in dearness allowance at present there is no advantage in taking 1950or 1960as the base, the comparison should be with the preceding year after which the DA has not been increased.
(c) Fixed base or chain base.While selecting the base a decision has to be made as to whether the base shall remain fixing or not i.e. whether we have fixed base or chain base. In the fixed base method the year to which the other years are compared is constant. On the other hand, in chain base method the prices of a year are linked with those of the preceding year. The chain base method gives a better picture than what is obtained by the fixed base method.