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Solve the following.
In a market survey, three commodities A, B and C were studied. Each commodity had three varieties…
In a market survey, three commodities A, B and C were studied. Each commodity had three varieties. To find out the index number of A, B and C fixed weights were assigned to the three varieties of each of the commodities.
The table given below shows the result of the survey.
Find the value of P, Q and R if the weights assigned to A, B and C are 2 kg, 3 kg and 1 kg respectively.
| Commodity / Variety | I | II | III | Total weight |
|---|---|---|---|---|
| A | 1 | 2 | 3 | P |
| B | 2 | 4 | 5 | Q |
| C | 3 | 5 | 6 | R |
Answer
Answer
AI$\begin{pmatrix} P \\ Q \\ R \end{pmatrix} = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix}\begin{pmatrix} 2 \\ 3 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 + 6 + 3 \\ 4 + 12 + 5 \\ 6 + 15 + 6 \end{pmatrix} = \begin{pmatrix} 11 \\ 21 \\ 27 \end{pmatrix}$
Final answer: $P = 11,\ Q = 21,\ R = 27$ kg
From ISC 2025 Improvement Mathematics Paper 1, question 6(ii).