Question

Taking 1975 as the base year with an index number 100 , calculate an index number for 1985 based on weighted average of price relatives.

Commodity	A	B	C	D
weight	20	30	10	40
Price per unit in 1975	10	20	5	40
Price per unit in 1985	30	35	10	80

• A. 212.5
• B. 217.5
• C. 219.5
• D. 345.65

Answer 1

Answer: (A)

212.5

$Commodity$	$Weight$ $w$	$Pricein1975$ $P_0$	$Pricein1985$ $P_1$	$Pricerelative$ $I=\frac{P_1}{P_0}\times 100$	$I.w$
$A$	$20$	$10$	$30$	$300$	$6000$
$B$	$30$	$20$	$35$	$175$	$5250$
$C$	$10$	$5$	$10$	$200$	$2000$
$D$	$40$	$40$	$80$	$200$	$8000$
$Total$	$\sum w=100$				$\sum I.w=21250$

$\Rightarrow$ By using weighted average of price relative method,

$\Rightarrow$ $P_{01}=\frac{\sum I.w}{\sum w}=\frac{21250}{100}=212.5$