Ans.\t\tDifficulties in the Selection of the Base Period: The first difficulty relates to the selection of the base year. The base year should be normal. But it is difficult to determine a truly normal year.\t\t\tDifficulties in the Selection of Commodities:The selection of representative commodities for the index number is another difficulty. The choice of representative commodities is not an easy matter. They have to be selected from a wide range of commodities which the majority of people consume.\t\t\tDifficulties in the Collection of Prices:Another difficulty is that of collecting adequate and accurate prices. It is often not possible to get them from the same source or place.\t\t\tArbitrary Assigning of Weights:In calculating weighted price index, a number of difficulties arise.The problem is to give different weights to commodities.The selection of higher weight for one commodity and a lower weight for another is simply arbitrary. There is no set rule and it entirely depends on the investigator.\t\t\tDifficulty of Selecting the Method of Averaging:Another difficulty is to select an appropriate method of calculating averages. There are a number of methods which can be used for this purpose.\t\t\tDifficulties Arising from Changes Overtime:In the present times, changes in the nature of commodities are taking place continuously overtime due to technological changes. As a result, new commodities are introduced and people start consuming them in place of the old ones.\t\t\tNot All Purpose:An index number constructed for a particular purpose cannot be used for some other purpose.\t\t\tInternational Comparisons not Possible:International price comparisons are not possible with index numbers. The commodities consumed and included in the construction of an index number differ from country to country.\t\t\tComparisons of Different Places not Possible:Even if different places within a country are taken, it is not possible to apply the same index number to them. This is because of differences in the consumption habits of people.\t\t\tNot Applicable to an Individual:An index number is not applicable to an individual belonging to a group for which it is constructed. If an index number shows a rise in the price level, an individual may not be affected by it. This is because an index number reflects averages.\tConclusion:It may be concluded from the difficulties and limitations of index numbers that index numbers are at best approximations to measure changes in the value of money. However, these difficulties become less significant if index numbers are constructed for short intervals. This is because habits, tastes, techniques of production and the qualities of commodities entering into a price index number do not change during the short period.