The correct answer is option 'D' - Laspeyres Method.

Explanation:
The consumer price index (CPI) is a statistical tool that measures changes in the prices of goods and services purchased by households over time. It is an important economic indicator that helps in measuring inflation and determining the cost of living.

To construct the CPI, various methods are used. One of the most commonly used methods is the Laspeyres Method, which is explained below:

Laspeyres Method:
The Laspeyres method is a fixed-base method of constructing the CPI. It is named after the German economist, Etienne Laspeyres, who first proposed this method. This method is widely used because it is relatively easy to compute and gives accurate results.

In this method, a fixed basket of goods and services is chosen, which represents the consumption pattern of a typical household. The prices of the items in the basket are then collected at a specific point in time, called the base period. The total cost of the basket is calculated by multiplying the prices of each item by its quantity.

The same basket is then priced at different points in time, called the current period. The total cost of the basket in the current period is calculated in the same way as in the base period. The ratio of the two costs gives the price index for the current period relative to the base period.

The Laspeyres method has the following advantages:

- It is easy to compute and gives accurate results.
- It is based on a fixed basket of goods and services, which makes it easy to compare prices over time.
- It is less affected by changes in consumer behavior, as the basket is fixed.

However, it also has some limitations, such as:

- It does not take into account changes in the quality of goods and services over time.
- It may overstate the inflation rate, as it does not account for substitution effects - i.e. consumers may switch to cheaper substitutes when prices rise.

Conclusion:
In conclusion, the Laspeyres method is a widely used method for constructing the CPI. It is a fixed-base method that uses a fixed basket of goods and services to measure changes in prices over time. While it has some limitations, it is still considered an accurate and reliable method for measuring inflation and determining the cost of living.