A price index two items of A and B is being estimated. If two items are assigned weights of 64 and 36 respectively, the price index becomes 279. Similarly, if they are assigned weights of 50 each, the price index turns out to be 265. Determine the individual price index numbers of items A and B.

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Solution

There are two situations in the given condition. Let $I_{1}$ be the index for the first item and $I_{2}$ be the index for the second item.

$\begin{matrix} First Situation : 279 & = \frac{64 I_{1} + 36 I_{2}}{64 + 36} Second Situation : 265 & = \frac{50 I_{1} + 50 I_{2}}{50 + 50} \end{matrix} ⎫ ⎪ ⎬ ⎪ ⎭$ $[∵ P_{01} = \frac{I_{1} W_{1} + I - 2 W_{2}}{W_{1} + W_{2}}]$ ...(i)

From (i), $64 I_{1} + 36 I_{2} = 27900 \Rightarrow 16 I_{1} + 9 I_{2} = 6975$

From (ii), $I_{1} + I_{2}$ = 530

Solving (iii) and (iv), we get $I_{1}$ = 315, $I_{2}$ = 215

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