Find the consumer price index number for 1991 on the base of 1990 from the following data using the method of weighted relatives.
Item Quantity(units) Price in 1990 Price in 1991
A 20 200 320
B 14 400 420
C 15 100 120
D 18 40 60
E 10 20 28

123.45

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113.47

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198.26

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137.27

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Solution

The correct option is D 137.27
$I t e m$ $Q u a n t i t y$
$(U n i t s)$ $w$ $P r i c e i n 1990$
$P_{0}$ $P r i c e i n 1991$
$P_{1}$ $P r i c e r e l a t i v e$
$I = \frac{P_{1}}{P_{0}} \times 100$ $I w$
$A$ $20$ $200$ $320$ $160$ $3200$
$B$ $14$ $400$ $420$ $105$ $1470$
$C$ $15$ $100$ $120$ $120$ $1800$
$D$ $18$ $40$ $60$ $150$ $2700$
$E$ $10$ $20$ $28$ $140$ $1400$
$T o t a l$ $(\sum)$ $77$ $10570$
$\Rightarrow$ $P_{01} = \frac{\sum I w}{\sum w} = \frac{10570}{77} = 137.27$

Suggest Corrections

$I t e m$	$Q u a n t i t y$ $(U n i t s)$ $w$	$P r i c e i n 1990$ $P_{0}$	$P r i c e i n 1991$ $P_{1}$	$P r i c e r e l a t i v e$ $I = \frac{P_{1}}{P_{0}} \times 100$	$I w$
$A$	$20$	$200$	$320$	$160$	$3200$
$B$	$14$	$400$	$420$	$105$	$1470$
$C$	$15$	$100$	$120$	$120$	$1800$
$D$	$18$	$40$	$60$	$150$	$2700$
$E$	$10$	$20$	$28$	$140$	$1400$
$T o t a l$ $(\sum)$	$77$				$10570$