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Using simple average of relatives method, the price index for 2011, taking 2001 as base year, was found to be 127. If Σp0=263\Sigma p_0 = 263, then x and y from the following data are :

CommoditiesABCDEF
Prices (in Rs.) in 20018070x201825
Prices (in Rs.) in 201110087.506122y32.50

Solution

✅ Correct Option: 1

From Σp0=263\Sigma p_0 = 263: 80+70+x+20+18+25=26380 + 70 + x + 20 + 18 + 25 = 263, so x=50x = 50.

Index =16∑p1p0×100=127= \frac{1}{6}\sum \frac{p_1}{p_0} \times 100 = 127, so ∑p1p0=7.62\sum \frac{p_1}{p_0} = 7.62.

1.25+1.25+1.22+1.1+y18+1.3=7.621.25 + 1.25 + 1.22 + 1.1 + \frac{y}{18} + 1.3 = 7.62, giving y18=1.5\frac{y}{18} = 1.5, so y=27y = 27.

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