Q.5 (B)(i) If for the following data, Walsh's Price Index Number is 150, find ‘x’: CommodityBase year price p₀ Base year quantity q₀ Current year price p₁ Current year quantity q₁ A53103 B x 4169 C155235 D102268

Answer: x = 50/3 ≈ 16.67 Walsh's index: P₀₁ = (Σ p₁√(q₀q₁))/(Σ p₀√(q₀q₁))× 100. Commodity q₀q₁ √(q₀q₁) p₀√(q₀q₁) p₁√(q₀q₁) A931530 B366 6x 96 C25575115 D16440104 Total 130 + 6x 345 150 = 345/(130 + 6x)× 100 ⇒ 130 + 6x = 34500/150 = 230 ⇒ 6x = 100 ⇒ x = 50/3 = 16.67 (approx.).

Chapter: Index Numbers· Mathematics & Statistics (Commerce) Part 2

If for the following data, Walsh's Price Index Number is 150, find ‘x’ :CommodityBase year price \(p_0\)Base year quantity \(q_0\)Current year price \(p_1\)Current year quantity \(q_1\)A53103B\(x\)4169C155235D102268

Q.5 (B)(i) If for the following data, Walsh's Price Index Number is 150, find ‘x’ :

Commodity	Base year price \(p_0\)	Base year quantity \(q_0\)	Current year price \(p_1\)	Current year quantity \(q_1\)
A	5	3	10	3
B	\(x\)	4	16	9
C	15	5	23	5
D	10	2	26	8

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Answer: \(x = \dfrac{50}{3} \approx 16.67\)

Walsh's index: \(P_{01} = \dfrac{\sum p_1\sqrt{q_0q_1}}{\sum p_0\sqrt{q_0q_1}}\times 100\).

Commodity	\(q_0q_1\)	\(\sqrt{q_0q_1}\)	\(p_0\sqrt{q_0q_1}\)	\(p_1\sqrt{q_0q_1}\)
A	9	3	15	30
B	36	6	\(6x\)	96
C	25	5	75	115
D	16	4	40	104
Total			\(130 + 6x\)	345

\(150 = \dfrac{345}{130 + 6x}\times 100 \Rightarrow 130 + 6x = \dfrac{34500}{150} = 230 \Rightarrow 6x = 100 \Rightarrow x = \dfrac{50}{3} = 16.67\) (approx.).

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If for the following data, Walsh's Price Index Number is 150, find ‘x’ :CommodityBase year price \(p_0\)Base year quantity \(q_0\)Current year price \(p_1\)Current year quantity \(q_1\)A53103B\(x\)4169C155235D102268

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