Using $2005$ as base year , the price of a commodity in $2006$ are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

84.75

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82.18

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81.18

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78.07

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Solution

The correct option is C 84.75
$N = 1$ (Since only one commodity)
Take price $= R s .100$ as base price for $2005$
$⟹ p_{1} = 100$
$p_{0} = 118$ (given)
$⟹$ index no. $= \frac{1}{N} (\sum \frac{p_{1}}{p_{0}} \times 100)$
$⟹ \frac{1}{1} (\sum \frac{100}{118} \times 100) = 84.775 \approx 84.75$

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Using 2005 as base year , the price of a commodity in 2006 are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

The correct option is C 84.75N=1 (Since only one commodity)Take price =Rs.100 as base price for 2005⟹p1=100p0=118 (given)⟹ index no. =1N(∑p1p0×100)⟹11(∑100118×100)=84.775≈84.75

Using $2005$ as base year , the price of a commodity in $2006$ are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

The correct option is C 84.75
$N = 1$ (Since only one commodity)
Take price $= R s .100$ as base price for $2005$
$⟹ p_{1} = 100$
$p_{0} = 118$ (given)
$⟹$ index no. $= \frac{1}{N} (\sum \frac{p_{1}}{p_{0}} \times 100)$
$⟹ \frac{1}{1} (\sum \frac{100}{118} \times 100) = 84.775 \approx 84.75$