Add Maths Index Number

The prices of a pair of shoes in 2003 and 2004 are RM80 and RM96 respectively. Calculate the index in 2004 given that 2003 is the base year.

The price of a graph book was 90 sen in 1999. Its price became RM1.35 in 2003. Calculate the price index of the graph book in 2003 based on the year 1999.

P1999 =90

P2003 =135

135 I= × 100 90 = 150

The table shows the number of PMR candidates of SMK Bukit Kepayang from 2000 to 2004. year

2000

2001

2002

2003

2004

Number of candicates

120

144

150

168

200

Calculate the index number of 2002 by using (ii) 2000 as base year (iii) 2004 as base year

(i)

150 I= × 100 120 = 125

(ii)

150 I= × 100 200 = 75

The index numbers of a computer in 1995 and 2001 based on the year 1992 are 120 and 150 respectively. If the price of the computer in 2001 was RM4200, find (b)the price index of the computer in 2001 based on the year 1995, (c)The prices of the computer in 1992 and 1995.

The index numbers of a computer in 1995 and 2001 based on the year 1992 are 120 and 150 respectively. If the price of the computer in 2001 was RM4200, find (b) the price index of the computer in 2001 based on the year 1995.

I1995 /1992 = 120

I 2001/1992 = 150

P2001 = RM 4200

I 2001/1995 = ? I1995 /1992 =

P1995 × 100 = 120 p1992 P1995

I 2001/1995

I 2001/1992 =

P2001 × 100 = 150 p1992

120 = × P1992 100

P2001 = × 100 P1995

=

P2001 150 × P1992 100 120 × P1992 100

150 = × 100 120

× 100

= 125

150 = × P1992 100

The index numbers of a computer in 1995 and 2001 based on the year 1992 are 120 and 150 respectively. If the price of the computer in 2001 was RM4200, find I =? 2001 / 1995

(b)the price index of the computer in 2001 based on the year 1995.

I1995 /1992 = 120 I 2001/1992 = 150 (a)

P2001 : 150% → 4200 P1992 : 100% → 100 × 4200 = RM 2800 150 P1995 : 120% → ? P1992 : 100% → RM 2800 P1992 : 100% → RM 2800 P1995 : 120% → 120 × 2800 = RM 3360 100

P2001 = 4200 I 2001/1995

=

4200 × 100 3360

= 125

The index numbers of a computer in 1995 and 2001 based on the year 1992 are 120 and 150 respectively. If the price of the computer in 2001 was RM4200, find (b)the price index of the computer in 2001 based on the year 1995. I 2001/1995 = ?

I1995 /1992 = 120 (a)

I 2001/1992 = 150 P2001 = 4200

I 2001/1992 = 150

I1995 /1992 = 120

P2001 ×100 =150 P1992

P1995 ×100 =120 P1992

4200 ×100 = 150 P1992

P1995 ×100 = 120 2800

P1992

4200 = ×100 150 = RM2800

P1995 = 120 × 28 = RM 3360

I 2001/1995

=

4200 × 100 3360

= 125

The index numbers of a computer in 1995 and 2001 based on the year 1992 are 120 and 150 respectively. If the price of the computer in 2001 was RM4200, find (b) The prices of the computer in 1992 and 1995.

I1995 /1992 = 120 Form (a)

I 2001/1992 = 150 P2001 = 4200 I 2001/1995 = 125

I 2001/ 1995 = 125 I 2001/1995 =

I 2001/1992 =

P2001 × 100 = 150 p1992

4200 × 100 = 125 P1995

4200 × 100 = 150 P1992

4200 × 100 = P1995 125

4200 × 100 = P1992 150

P1995 = RM 3360

P1995 = RM 2800

The table shows the price per kg of 3 types of fish: P, Q and R in the years 1995 and 1999. Types of fish

Price 1995

1999

Price index in 1999 (base year = 1995)

P

RM1.20

RM1.60

Z

Q

X

RM2.30

110

R

RM0.60

Y

102

Find the values of x, y and z.

Types of fish

1995

1999

Price index in 1999 (base year = 1995)

P Q R

RM1.20 X RM0.60

RM1.60 RM2.30 Y

Z 110 102

Price

Q,

I1999 / 1995 =

R,

2.30 × 100 = 110 x 2.30 ×100 = x 110 x = RM 2.09

y × 100 = 102 0.60 102 y= × 0.60 100 y = RM 0.61 y = RM 0.612 wrong

P,

1.60 z= × 100 1.20 = 133 13

∑ I i wi I= ∑ wi

I1 w1 +I 2 w2 +I 3 w3 = w1 +w2 +w3

I = Index number w = weightage

∑ I i wi I= ∑ wi

=

I1 w1 +I 2 w2 +I 3 w3 w1 +w2 +w3

Calculate the composite index for the table below. a

things

index weightage

A

100

4

B

120

2

C

145

4

I =

100(4) +120(2) +145(4) 4 +2 +4

= 122

∑ I i wi I= ∑ wi

=

I1 w1 +I 2 w2 +I 3 w3 w1 +w2 +w3

Calculate the composite index for the table below. b

things

index weightage

P

105

3

Q

150

4

R

210

5

163.75

∑ I i wi I= ∑ wi

=

I1 w1 +I 2 w2 +I 3 w3 w1 +w2 +w3

Calculate the composite index for the table below. c

things

index weightage

X

110

4

Y

130

8

Z

142

6

129.56

vegetables

Price in 1995

Price in 1998

weightage

A

RM 4.00

RM 8.00

4

B

RM 6.00

RM 9.00

3

C

RM 7.50

RM 8.50

7

D

RM 8.00 RM 10.50

6

IA =

8.00 ×100 = 200 4.00

IB = IC

9.00 ×100 = 150 6.00

8.50 = ×100 = 113 13 7.50

ID =

10.50 ×100 = 131.25 8.00

I= =

The table shows the price per kg of four types of vegetables in 1995 and 1998 and the corresponding weightages. By using 1995 as the base year, find (b) The price index of vegetables A, B, C and D in 1998, (c) the composite index of 1998.

200( 4) +150(3) +113 13 (7) +131.25(6) 4 +3 +7 +6 2830 56 20

= 141 13 24

Things

Price index

weightage

Shirt

120

m

Trousers

105

8

The table shows the price indeices and the weightages of four things in 1997 based on the year 1992. Given that the composite index of 1997 is 127. Calculate

Bag

140

4

(b) The value of m,

shoes Shoes

150 150

6

(c) the price of a pair of shoes in 1997 if its price in 1992 is RM 60. P = RM 60 1992

I=

120(m) + 105(8) + 140(4) + 150(6) m+8+ 4+ 6

= 127

120m + 2300 = 127 m +18 120m + 2300 = 127 m + 2286 2300 − 2286 = 127 m −120m 7 m = 14 m=2

P1997 × 100 = 150 60 P1997

150 × 60 = 100 = 90

component s

Price in

Price in

1998

2002

Price index in 2002 (1998 is the base year)

wP = 90

wQ = 60

∑ w = 360

(a) x= RM0.60

y=140

z = RM3.30

(b) 143.54

(d) 186.6

(c)RM358.85

Test Table 4 showe the prices and the price indices of five components P, Q, R, S and T, used to produce a kind of toy. Diagram 6 shows a pie chart which represents the relative quantity of components used. components

Price(RM) in 2004

Price (RM) in 2006

Price index for the year 2006 based on the year 2004

P

1.20

1.50

125

Q

X

2.20

110

R

4.00

6.00

150

S

3.00

2.70

Y

T

2.00

2.80

140

components

Price(RM) in 2004

Price (RM) in 2006

Price index for the year 2006 based on the year 2004

P

1.20

1.50

125

Q

X

2.20

110

R

4.00

6.00

150

S

3.00

2.70

Y

T

2.00

2.80

140

(a) Find the value of x and of y.

[3 marks]

(a) Calculate the composite index for the production cost of the toys in the year 2006 based on the year 2004. [3 marks] (a)The price of each component increases by 20% from the year 2006 to the year 2008. Given that the production cost of one toy in the year 2004 is RM55, calculate the corresponding cost in the year 2008.