Question

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

Answer 1

There are two situations in the given conditions. Let $I_1$ be the index for the first item and $I_2$ be the index for the second item.

First Situation: $279=\frac{64I_1+36I_2}{64+36}$ $[\because P_{01}=\frac{I_1{W}_1+I_2{W}_2}{W_1+W_2}]$ ..... (i)

Second Situation: $265=\frac{50I_1+50I_2}{50+50}$ ..... (ii)

From equation (i), $64I_1+36I_2=27900$

$\Rightarrow 16I_1+9I_2=6975$ ....... (iii)

From equation (ii), $I_1+I_2=530$ ...... (iv)

On solving equation (iii) and equation (iv), we get $I_1=315,I_2=215$