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Practice Exercise · Q7
Q.

From the data given below, obtain the index of retail sales in India for years 1982, 1983, 1984 with the year 1981 as base period.

YearIndex of sales volumeIndex of sales value
1995101105
1996113108
1997106124
Puducherry CbseNCERTSubjective· 3mImportance★★★★★est
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Since value == price ×\times volume, the price (retail-sales price) index =Value indexVolume index×100=\dfrac{\text{Value index}}{\text{Volume index}}\times100, giving 103.96, 95.58 and 116.98 for the three years.

Price index=Index of sales valueIndex of sales volume×100\text{Price index}=\dfrac{\text{Index of sales value}}{\text{Index of sales volume}}\times100

because Value == Price ×\times Quantity ⇒\Rightarrow Price =ValueQuantity=\dfrac{\text{Value}}{\text{Quantity}}.

Note on a printing mismatch: the wording names 1981–1984, but the table lists 1995–1997. I solve on the data actually given (1995–1997); the derivation is unaffected.

Working table

YearVolume indexValue indexValueVolume×100\dfrac{\text{Value}}{\text{Volume}}\times100Price index
1995101105105101×100\frac{105}{101}\times100103.96
1996113108108113×100\frac{108}{113}\times10095.58
1997106124124106×100\frac{124}{106}\times100116.98

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