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Index Numbers — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsIndex Numbers4 Marks
Question
From the following data, construct a weighted index number for $2010$ with $2000$ as base year:
Items Weight Prices
2000 2010
Wheat 15 10 15
Rice 10 8 16
Pulses 5 5 10
Milk 4 2 4
Oil 6 4 6
Sugar 7 3 6
Salt 3 1 2
✓

Answer

Items Weight % Weight Price Price relative $\Big(\frac{\text{p}_1}{\text{p} _0}\times100\Big)$
2000 $(p_0)$ 2011 $(p_1)$
Wheat 15 30 10 15 150
Rice 10 20 8 16 200
Pulses 5 10 5 10 200
Milk 4 8 2 4 200
Oil 6 12 4 6 150
Sugar 7 14 3 6 200
Salt 3 6 1 2 200
Weighted Price Index is:
$\text{p}_{01}=\frac{\Sigma\text{wi}\Big(\frac{\text{P}_{11}}{\text{P}_{01}}\times100\Big)}{\Sigma\text{wi}}$
$=\frac{30\times150+20\times200+10\times200+8\times200+12\times150+14\times200+6\times200}{100}$
$=\frac{4500+4000+2000+1600+1800+2800+1200}{100}$
$\text{p}_{01}=\frac{17900}{100}=179$
$\therefore$ The Price Index has risen by $79\%$.

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