Construction of index numbers - class-XI

Question 1 Multiple Choice (Single Answer)

Laspeyre's index $= 110$, Paasche's index $= 108$, then Fisher's Ideal index is equal to:

$110$
$108$
$100$
$109$

Question 2 Multiple Choice (Single Answer)

If all the values are not of equal importance the index number is called:

Simple
Unweighted
Weighted
None

Question 3 Multiple Choice (Single Answer)

The aggregative expenditure method and family budget method always give:

Different results
Approximate results
Same results
None of them

Question 4 Multiple Choice (Single Answer)

A factory uses three raw materials A ,B and C in the manufacturing process.The price of material were as shown below: Calculate a simple aggregate index for $2005$.

Commodity	Price in Rs in 1995	Price in Rs in 2005
A	4	5
B	60	57
C	36	42

119
106
104
108

Commodity	Price in Rs in $1995$ $({p} _{0})$	Price in Rs in $2005$ $({p} _{1})$
		Commodity
A	$4$	$5$
B	$60$	$57$
C	$36$	$42$

Question 5 Multiple Choice (Single Answer)

The most appropriate average in averaging the price relatives is:

Median
Harmonic mean
Arithmetic mean
Geometric mean

Question 6 Multiple Choice (Single Answer)

Using simple aggregate method, calculate price index number from the following data:

Commodity	A	B	C	D	E
1993 prices (in Rs)	50	40	10	5	2
1995 prices(in Rs)	80	60	20	10	6

164.69
154.75
162.69
152.75

$Commodity$	$Price, in, 1993$ $( In, Rs.)$ $P _0$	$Price, in, 1995$$(In, Rs.)$ $P _1$
$A$	$50$	$80$
$B$	$40$	$60$
$C$	$10$	$20$
$D$	$5$	$10$
$E$	$2$	$6$
$Total$	$\sum,P _0=107$	$\sum,P _1=176$

Question 7 Multiple Choice (Single Answer)

Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.

Commodity	A	B	C	D	E
Weight	40	25	5	20	10
Price(Rs) per unit 1996	32	80	1	10.24	4
Price(Rs) per unit 2006	40	120	1	15.36	3

130
133.34
138.34
139.45

$Commodity$	$Weight$ $w$	$Price,in,1996$$(Rs.),,P _0$	$Price,in,2006$$(Rs.),,P _1$	$Price,relative$$I=\dfrac{P _1}{P _0}\times 100$	$I.w$
$A$	$40$	$32$	$40$	$125$	$5000$
$B$	$25$	$80$	$120$	$150$	$3750$
$C$	$5$	$1$	$1$	$100$	$500$
$D$	$20$	$10.24$	$15.36$	$150$	$3000$
$E$	$10$	$4$	$3$	$75$	$750$
$Total$	$100$				$13000$

Question 8 Multiple Choice (Single Answer)

Calculate price index for the following by using price relative method.

Material	Cement	Timber	Steel	Bricks
Price in 1969 (in Rs)	5	9.5	35	12
Price in 1970 (in Rs)	8	14.3	42	24

152.34
135.5
157.5
154.25

$Material$	$Price, in, 1969$$(in,Rs.),[P _0]$	$Price,in,1970$$(in,Rs.),[P _1]$	$Price, Relative$$\dfrac{P _1}{P _0}\times 100$
$Cement$	$5$	$8$	$160.00$
$Timber$	$9.5$	$14.3$	$150.52$
$Steel$	$35$	$42$	$120.00$
$Bricks$	$12$	$24$	$200.00$
$Total$			$630.52$

Question 9 Multiple Choice (Single Answer)

Construct a composite index number as a weighted mean from the following data:

Index Number	122	145	101	98	137	116
Weight	7	2	4	1	6	5

120
122
130
132

$Index,number$ $I$	$Weight$$w$	$I.w$
$122$	$7$	$854$
$145$	$2$	$290$
$101$	$4$	$404$
$98$	$1$	$98$
$137$	$6$	$822$
$116$	$5$	$580$
$Total$	$\sum w=25$	$\sum Iw=3048$

Question 10 Multiple Choice (Single Answer)

A firm uses three raw materials E ,F ,G in processing . The price per kg of these materials are as shown:

Item	1957	1967
E	4	3
F	60	57
G	36	42

Calculate simple aggregate price index for 1967 using 1957 as the base year.

104
98
100
102

$Item$	$Price,in,1957$ $P _0$	$Price,in,1967$ $P _1$
$E$	$4$	$3$
$F$	$60$	$57$
$G$	$36$	$42$
$Total$	$\sum P _0=100$	$\sum P _1=102$

Question 11 Multiple Choice (Single Answer)

Compute a price index for the following by simple aggregate method.

Commodity	A	B	C	D	E	F
Price in 1986 (Rs)	20	30	10	25	40	50
Price in 1991 (Rs)	25	30	15	35	45	55

117.14
118.13
119.13
107.13

commodity	price in $1986$ $({p} _{0})$	price in $1991$ $({p} _{1})$
A	$20$	$25$
B	$30$	$30$
C	$10$	$15$
D	$25$	$35$
E	$40$	$45$
F	$50$	$50$

Question 12 Multiple Choice (Single Answer)

Compute the consumer price index for 1990 taking 1989 as the base year.

Commodity	Price in 1989	Price in 1990
Butter	20	21
Cheese	16	12
Milk	3	3
Eggs	2.80	2.80

93
94
95
96

$Commodity$	$Price,in,1989$$P _0$	$Price,in,1990$$P _1$
$Butter$	$20$	$21$
$Cheese$	$16$	$12$
$Milk$	$3$	$3$
$Eggs$	$2.80$	$2.80$
$Total$	$\sum P _0=41.8$	$\sum P _1=38.8$

Question 13 Multiple Choice (Single Answer)

Calculate cost of living index from the following table of prices and weights.

Commodity	Weight	Price index
Food	35	108.5
Rent	9	102.6
Clothes	10	97
Fuel	7	100.9
MIscellaneous	39	103.7

104.4
106.5
126.5
128.5

$Commodity$	$Weight$$w$	$Price,index$$I$	$I.w$
$Food$	$35$	$108.5$	$3797.5$
$Rent$	$9$	$102.6$	$923.4$
$Clothes$	$10$	$97$	$970$
$Fuel$	$7$	$100.9$	$706.3$
$Miscellaneous$	$39$	$103.7$	$4044.3$
$Total$	$\sum w=100$		$\sum I.w=10441.5$

Question 14 Multiple Choice (Single Answer)

Calculate weighted index number for 2001 from the following data:

Item	A	B	C
Quantity	20	15	10
Price in 2000	200	100	20
Price in 2001	320	120	28

134.56
142.22
148.77
150.78

$Item$	$Quantity$$w$	$Price,in,2000$$P _0$	$Price,in,2001$$P _1$	$I=\dfrac{P _1}{P _0}\times100$	$Iw$
$A$	$20$	$ 200$	$320$	$160$	$3200 $
$B$	$15$	$100$	$120$	$120$	$1800$
$C$	$10$	$20$	$28$	$140$	$1400$
$Total$	$\sum w=45$				$\sum Iw=6400$

Question 15 Multiple Choice (Single Answer)

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

212.5
217.5
219.5
345.65

$Commodity$	$Weight$$w$	$Price,in,1975$$P _0$	$Price,in,1985$ $P _1$	$Price,relative $$I=\dfrac{P _1}{P _0}\times 100$	$I.w$
$A$	$20$	$10$	$30$	$300$	$6000$
$B$	$30$	$20$	$35$	$175$	$5250$
$C$	$10$	$5$	$10$	$200$	$2000$
$D$	$40$	$40$	$80$	$200$	$8000$
$Total$	$\sum w=100$				$\sum I.w=21250$

Question 16 Multiple Choice (Single Answer)

The quotations for four different commodities for the years 2000 and 2005 are given below. Calculate the index number for 2005 , with 2000 as base year by using weighted average of price relatives method.

$164.05$
$161.05$
$154.05$
$151.05$

Question 17 Multiple Choice (Single Answer)

Calculate the cost of living index(approximately) from the following data:

Group	Weights	Group Index No.
Food	47	247
Fuel and Lightning	7	293
Clothing	8	289
House Rent	13	100
Miscellaneous	14	236

$231.2$
$265.4$
$245.7$
$123.78$

Question 18 Multiple Choice (Single Answer)

Using simple aggregate method, calculate price index number from the following data:

Commodity	A	B	C	D
Price in 1997	90	40	90	30
Price in 1998	95	60	110	35

110
120
130
140

$Commodity$	$Price, in, 1997$ $P _0$	$Price, in, 1998$ $P _1$
$A$	$90$	$95$
$B$	$40$	$60$
$C$	$90$	$110$
$D$	$30$	$35$
$Total$	$\sum P _0=250$	$\sum P _1=300$

Question 19 Multiple Choice (Single Answer)

Construct a composite index number from the following index numbers and weights:

Index Numbers	127	142	186	172	115
Weight	5	4	3	6	8

$134$
$145$
$143$
$149$

Question 20 Multiple Choice (Single Answer)

The following commodities have the given price indices relative to a base of $100$. The weights are also given:

Commodity	Relative Index	Weight
Butter	181	4
Bread	116	12
Tea	110	3
Bacon	152	7

Calculate the new index for this set of commodities

$132$
$133$
$134$
$135$

Question 21 Multiple Choice (Single Answer)

If all the values are of equal importance, the index numbers are called:

Weighted
Unweighted
Composite
Value index

Question 22 Multiple Choice (Single Answer)

Using $2005$ as base year , the price of a commodity in $2007$ is 125. Calculate the index number for 2007 if 2006 is taken as the base year.

105.93
104.23
103.93
112.3

Question 23 Multiple Choice (Single Answer)

Using $2005$ as base year , the price of a commodity in $2006$ are 118. Calculate the index number for 2005 if 2006 is taken as the base year.

84.75
82.18
81.18
78.07

Construction of index numbers - class-XI

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