Q.If the cost of living index number of the current year has increased to 180 from the base year index number 100 and if the average income of workers has increased from $\text{\text{₹}}\,6{,}000$ to $\text{\text{₹}}\,9{,}000$, is there an increase or decrease in the purchasing power of the workers? How much is it?

$\text{Real wage}=\dfrac{\text{Money (nominal) wage}}{\text{Cost of living index number}}\times100.$

The real wage expresses the money wage in terms of the base-year purchasing power. Dividing the money wage by the current cost-of-living index number and multiplying by $100$ gives the real wage - the true value of the wage after allowing for price changes. This is a standard GSEB / Gujarat HSC Class-12 Statistics formula for the deflating (real-wage) …

Purchasing power of money is the reciprocal of the price index number. With purchasing power $= 0.75$, the price index $= \dfrac{100}{0.75} = 133.33$ — option (c).

This is a deflating / purchasing-power question from the GSEB Class-12 Statistics Index Number chapter.

The relationship is:

$\text{Purchasing power of money} = \frac{1}{\text{Price index (as a ratio)}} = \frac{100}{\text{Price Index Number}}$ …

Purchasing power $= \dfrac{100}{\text{price index}}$, so a purchasing power of $0.75$ gives a price index of $\dfrac{100}{0.75} = \mathbf{133.33}$.

Given: purchasing power of money in 2021 (base 2020) $= 0.75$.

Step 1 — relation. Purchasing power of money is the reciprocal of the price index:

$\text{Purchasing power} = \frac{100}{\text{Price Index}}.$

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Purchasing power $= \dfrac{100}{P_{01}}$, so $P_{01} = \dfrac{100}{0.75} = 133.33$ — option (c).

The purchasing power of money for a year (with respect to a base) is the reciprocal of that year's price index number, taken as a proportion:

$\text{Purchasing power} = \frac{100}{\text{Price Index Number}}$

Here the purchasing power in 2019 (base 2018) is $0.75$. Substituting:

$0.75 = \frac{100}{P_{01}} \implies P_{01} = \frac{100}{0.75} = 133.33$

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