Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is 125 . Given:Prices in 1985: 75, 85 - Mathematics MCQ Mathematics Mock Test - 2 2026 | ExamTest.live

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Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is 125 . Given:Prices in 1985: 75, 85, α, 100 Prices in 1986: 90, 115, 75, β Find the value of (4 β - 5 α) .

Solution & Step-by-step Explanation

Simple Aggregate Index Number formula: I = \frac{\sum P _{1}}{\sum P _{0}} \times 100 Where \sum P_{0} = 75 + 85 + α + 100 = 260 + α And \sum P_{1} = 90 + 115 + 75 + β = 280 + β Given I = 125 : 125 = \frac{280 + β}{260 + α} \times 100 \frac{125}{100} = \frac{280 + β}{260 + α} \frac{5}{4} = \frac{280 + β}{260 + α} 5 (260 + α) = 4 (280 + β) 1300 + 5 α = 1120 + 4 β 1300 - 1120 = 4 β - 5 α 180 = 4 β - 5 α

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Using the base year 1985, the index number calculated by the simple aggregate method for four items (A, B, C, D) is 125 . Given:Prices in 1985: 75, 85, α, 100 Prices in 1986: 90, 115, 75, β Find the value of (4 β - 5 α) .

185

240

180

Cannot be calculated

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