Find x from following data if the Value Index Number is 200. Commodity Base Year Current Year Prive Quantity Price Quantity A 10 10 20 10 B 8 20 22 15 C 2 x 8 10 D 9 10 16 10 E 5 6 3 10 - Mathematics and Statistics

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Find x from following data if the Value Index Number is 200.

Commodity Base Year Current Year
Prive Quantity Price Quantity
A 10 10 20 10
B 8 20 22 15
C 2 x 8 10
D 9 10 16 10
E 5 6 3 10
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Solution

Commodity Bae yer Current Year    
Price
p0
Quantity
q0
Price
p1
Quantity
q1
p0q0 p1q1
A 10 10 20 10 100 200
B 8 20 22 15 160 330
C 2 x 8 10 2x 80
D 9 10 16 10 90 160
E 5 6 3 10 30 30
Total         380 + 2x 800

Form the table, `sum"p"_0"q"_0` = 380 + 2x, `sum"p"_1"q"_1` = 800

Value Index Number (V01) = `(sum"p"_1"q"_1)/(sum"p"_0"q"_0) xx 100`

∴ 200 = `800/(380 + 2x) xx 100`

∴ 380 + 2x = `800/200 xx 100`

∴ 380 + 2x = 400

∴ 2x = 20 

∴ x = 10

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Chapter 2.5: Index Numbers - Q.4

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