Q.Cost of living index number is used in calculating purchasing power of money.

The weighted relatives (family budget) method computes the cost of living index as the weighted average of the price relatives, $\text{CLI} = \dfrac{\sum IW}{\sum W}$, so the given formula is correct.

In the weighted relative method (also called the family budget method) for the cost of living index number:

• For each item or group, the price relative is $I = \dfrac{p_1}{p_0}\times 100$, comparing the current price $p_1$ with the base price $p_0$.
• Each relative is assigned a weight $W$, usually the expenditure (value) of that item, $W = p_0 q_0$.

The cost of living index is then the weighted mean of these relatives:

…

Purchasing power of money $=\dfrac{1}{\text{Cost of living index number}}\times 100$, so the cost-of-living index is indeed used to calculate the purchasing power of money; the statement is True.

The cost-of-living index number (consumer price index) measures the average change in the prices of a fixed basket of goods and services consumed by a particular group of people. When prices rise, the same amount of money buys less, so the purchasing power of money falls. This inverse relationship is expressed as …

By the weighted relative (family budget) method, the cost-of-living index number is $\text{CLI}=\dfrac{\sum I\,W}{\sum W}$, where $I=\dfrac{p_1}{p_0}\times 100$ is each commodity's price relative and $W$ is its weight.

The weighted relative method builds the cost-of-living index from the price relatives of the individual commodities:

• For each commodity, compute the price relative $I=\dfrac{p_1}{p_0}\times 100$, comparing the current price $p_1$ with the base price $p_0$.
• Assign each commodity a weight $W$ (usually its base-year value $W=p_0 q_0$, reflecting its share in the family budget).
• Take the weighted arithmetic mean of the price relatives: …