Q.Mr. Patel's monthly salary rose from Rs. 6,000 to Rs. 9,000 over a period during which the Consumer Price Index rose from 100 to 160. Has his standard of living improved, declined, or stayed the same? Support your answer with real-income figures.

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

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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