The index number calculated for the data below by simple weighted aggregate method is 110.| Item | Price (Current) | Price (Base) | Weights || :--- | - Mathematics MCQ Mathematics Mock Test - 4 2026 | ExamTest.live

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The index number calculated for the data below by simple weighted aggregate method is 110.| Item | Price (Current) | Price (Base) | Weights || :--- | :--- | :--- | :--- || A | p | 4 | 60 || B | 3 | 2 | q || C | 2 | 3 | 40 |Given 60 p + 3 q = 360, then the value of p will be:

Solution & Step-by-step Explanation

Index Number = \frac{\sum P _{1} Q _{i}}{\sum P _{0} Q _{i}} \times 100 Current Year Sum: \sum P_{1} Q_{i} = (p \times 60) + (3 \times q) + (2 \times 40) = 60 p + 3 q + 80 Base Year Sum: \sum P_{0} Q_{i} = (4 \times 60) + (2 \times q) + (3 \times 40) = 240 + 2 q + 120 = 360 + 2 q Given: Index Number = 110 $ 110 = \frac{60 p + 3 q + 80}{360 + 2 q} \times 100 $ 1.1 = \frac{60 p + 3 q + 80}{360 + 2 q} Substitute 60 p + 3 q = 360 : 1.1 = \frac{360 + 80}{360 + 2 q} \Rightarrow 1.1 = \frac{440}{360 + 2 q} 360 + 2 q = \frac{440}{1.1} = 400 2 q = 40 \Rightarrow q = 20 Substitute q = 20 in 60 p + 3 q = 360 : 60 p + 3 (20) = 360 \Rightarrow 60 p = 300 \Rightarrow p = 5

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The index number calculated for the data below by simple weighted aggregate method is 110.| Item | Price (Current) | Price (Base) | Weights || :--- | :--- | :--- | :--- || A | p | 4 | 60 || B | 3 | 2 | q || C | 2 | 3 | 40 |Given 60 p + 3 q = 360, then the value of p will be:

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