�

11 Index Number

1. Indexnumberofaveragetemperaturefortheyear2005basedontheyear2000

=Temperatureintheyear2005

————————————–Temperatureintheyear2000

�00

= 35—–30

�00

=��6.7

2. Indexnumberofbooks sold in theyear2006basedontheyear2005

=Volumeofbooksintheyear2006

——————————————–Volumeofbooksintheyear2005

�00

= �0.6—––�0.7

�00

=99.�

3. Price index for the year 2000 based on the year�900

=Incomefortheyear2000

———————————Incomefortheyear�900

�00

= �0000—––—6000

�00

=�66.7

4. (a) IndexnumberinFebruarybasedonJanuary

=VolumeofrainfallinFebruary—————————————VolumeofrainfallinJanuary

�00

= �5—–�0

�00

=�50

(b) IndexnumberinMarchbasedonJanuary

=VolumeofrainfallinMarch

—————————————VolumeofrainfallinJanuary

�00

= 5—–�0

�00

=50

5. (a) Priceindexfortheyear2007basedontheyear2000

=Priceintheyear2007

—————————–Priceintheyear2000

�00

= 2.00—––�.20

�00

=�66.7

(b) Priceindexfortheyear2005basedontheyear2007

=Priceintheyear2005

—————————–Priceintheyear2007

�00

= �.50—––2.00

�00

=75

6. Indexnumberfortheyear2006basedontheyear2005=�20.5

Numberofcarssoldintheyear2006

—————————–Numberofcarssold

intheyear2005

�00=�20.5

x———–�0000

�00=�20.5

x=�20.5�00 =�2050

7. Priceindexfortheyear2006basedontheyear200�=85

Priceintheyear2006—————————–Priceintheyear200�

�00=85

4—y ×�00=85

y=4×�00————

85 =4.7�

8. Indexnumberforhousessoldintheyear2005basedontheyear2000=�20

Numberofhousessoldintheyear2005—————————————————Numberofhousessoldintheyear2000

�00

=�20

2

Numberofhousessoldintheyear2005

= �20—––�00

�0200

=�2240

9. Priceindexintheyear2003basedontheyear2000=�30

Priceintheyear2003

—————————–Priceintheyear2000

�00=�30

Priceintheyear2003

—————————–�2

�00=�30

Priceintheyear2003= �30×�2————�00

=RM�5.60

10. Priceindexintheyear2006basedontheyear2005=��0

Priceintheyear2006—————————–Priceintheyear2005

�00=��0

�25

—————————–Priceintheyear2005

�00=��0

Priceintheyear2005= �25×�00———–—��0

=RM��3.64

11. Compositeindex=∑wiIi——–∑wi

=

(2�20)+(3��5)+(��30)+(3��0)+(��26)

————————————––2+3+�+3+�

=��7.�

12. (a) PriceindexforA= �00—––80

�00

=�25

PriceindexforB= �20—––94

�00

=�27.7

PriceindexforC= �50—––�30

�00

=��5.4

(b) Composite index in theyear2006basedon theyear2005

=∑wiIi——–∑wi

=(2×�25)+(3×�27.7)+(�× ��5.4)——————————————–—

2+3+� =�24.8

13. Compositeindex=�03(4×��0)+90x+(6×�20)——————————––––

4+x+6=�03

440+90x+720=�03(�0+x) ��60+90x=�030+�03x �03x–90x=��60–�030 �3x=�30 x=�0

14. (a) Compositepriceindexintheyear2002basedontheyear2005=�22

(2×�00)+4x+(3×�30)+(�×�50)—————————————–———

2+4+3+�=�22

4x+740=�22(�0) =�220 4x =480 x=�20

(b) PriceindexofitemCfortheyear2002basedontheyear2005=�30

Priceintheyear2002

—————————–Priceintheyear2005

�00=�30

2000

—————————–Priceintheyear2005

�00=�30

Priceintheyear2005= 2000×�00—————�30

=RM�538.46

15. (a) Compositeindexfortheyear2002basedontheyear2000

=(4×�20)+(2×��0)+(3×�30)+(�×�50)———————————————————

4+2+3+� =�24

(b) Price index for food in theyear2002basedontheyear2000=�20

Priceintheyear2002

——————————Priceintheyear2000

�00=�20

Priceintheyear2002

——————————600

�00=�20

Priceintheyear2002=RM720

(c) Compositeindexfortheyear2002basedontheyear2000=�24

Averagemonthlyexpenditurefortheyear2002

—————————————Averagemonthlyexpenditure

fortheyear2000

�00=�24

Averagemonthlyexpenditurefortheyear2002

—————————————600+�00+400+500

�00=�24

3

Averagemonthlyexpenditurefortheyear2002

= �24—––�00

�600

=RM�984

16. (a) Compositeindexnumberfortheyear200�basedontheyear2000=��5

7+m+2+4——————3+4+5+8

�00=��5

�3+m= ��5—––�00

×20

=23 m=�0

(b) Compositeindexfortheyear2002basedontheyear2000

= �2+5+6+4——————–3+4+5+8

�00

= 27—–20

�00

=�35

17. (a) PriceindexofAfortheyear�995basedontheyear�990

=�25��0% =�37.5

PriceindexofBfortheyear�995basedontheyear�990

=�30�05% =�36.5

PriceindexofCfortheyear�995basedontheyear�990

=�60

(b) Thecompositeindexfortheyear�995basedontheyear�990

=∑wiIi——–∑wi

=(2�37.5)+(��36.5)+(3�60)

———————————————––2+�+3

=�48.6

18. Given–I

2006,2005=�20

P

2006——–P

2005

�00=�20

P

2006——–P

2005

= �20—––�00

–I

2006,2002=�30

P2006——–

P2002

�00=�30

P

2006——–P

2002

= �30—––�00

Thecompositeindexfortheyear2005basedontheyear2002

=P

2005——–P

2002

�00

=P

2005——–P

2006

×P

2006——–P

2002

�00

= �00—––�20

× �30—––�00

�00

=�08.3

1. (a) IndexnumberofPintheyear2006basedontheyear2003=��0

t—–�2

�00=��0

t=��0× �2—––�00

=�3.20

(b) IndexnumberofQintheyear2006basedontheyear2003

= IndexnumberofRintheyear2006basedon theyear2003–�0

y—x ×�00= �5—–

�0×�00–�0

=�40

y—x = �40—––

�00

y=7—5

x......................1

SumofQfortheyears2003and2006=�2

x+y=�2..............................2

Substitute1into2,

x+7—5

x=�2

�2x—––5

=�2

x=�2× 5—–�2

=5

Substitutex=5into2, 5+y=�2 y=7

(c) (i) Giventhecompositeindexintheyear2006basedontheyear2003=�30

Costpriceintheyear2006———————————–Costpriceintheyear2003

�00=�30

Costpriceintheyear2006———————————–

�000�00=�30

Costpriceintheyear2006=RM�300

4

(ii) Compositeindexfortheyear2006basedontheyear2003=�30

(2×��0)+(n×y—x ×�00)

+(�× �5—–�0

×�00)———————————–

2+n+� =�30

220+1n×7—5

�002+�50 =�30(3+n)

�40n+370 =390+�30n �0n=390–370 n=2

2. (a) x—––�.80

�00=��2

x=��2× �.80—––�00

=2.02

y= 3.00—––2.40

�00

=�25

�.50—––z

�00=�25

z= �.50×�00————––�25

=�.20

(b) Compositeindexfortheyear2002basedontheyear2000

=∑wiIi——–∑wi

=

(5��2)+(�0�25)+(�5�25)+(20�20)

———————————————–5+�0+�5+20

=�2�.7

(c)

Totalmonthlycostintheyear2002

———————–––Totalmonthlycostintheyear2000

�00=�2�.7

Totalmonthlycostintheyear2002

=�2�.7×250000———————

�00 =304250

(d) Compositeindexfortheyear2004basedontheyear2000

=�25%�2�.7 =�52.�

3. (a) x——�.50

�00=�80

x=�80× �.50——�00

=2.70

y= 2.50——2.00

�00

=�25

�.50——z ×�00=�50

z= �.50×�00————–�50

=�.00

(b) (i) ∠A=360°–�00°–80°–�40° =40°

A:B:C:D=40:�40:80:�00 =2:7:4:5

Compositeindexintheyear2003basedontheyear2000

=∑wiIi——–∑wi

=

(2�60)+(7�80)+(4�25)+(5�50)

——————————————2+7+4+5

=�57.2

(ii)Costintheyear2003

—————————–Costintheyear2000

�00=�57.2

\Costintheyear2003

=�57.2×3020

——————�00

=RM4747.44

(c) Thecompositeindexfortheyear2005basedontheyear2000

=95%�57.2 =�49.3

4. (a) (i)PriceofAintheyear2005———————————–PriceofAintheyear2000

�00=�50

500

———————————–PriceofAintheyear2000

�00=�50

PriceofAintheyear2000 = 500×�00————–�50

=RM333.33

(ii) PriceindexofBintheyear2005basedontheyear2003

=P

2005——–P

2003

�00

=P

2005——–P

2000

×P

2000——–P

2003

�00

=1 �30—––�00 2×1 �00—––

�20 2�00

=�08.3

5

(b) (i) Compositeindexfortheyear2005basedontheyear2000

=∑wiIi——–∑wi

=�30

(2×�50)+(2×�30)+(�×m)+(5×�25)

—————————————–2+2+�+5

=�30

��85+m=�300 m=�300–��85 =��5

(ii)

Priceofbreadintheyear2005

—————————Priceofbreadinthe

year2000

�00=�30

Priceofbreadintheyear2005

= �30×5———–�00

=RM6.50

1. (a) x—–20

�00=�20

x= 20——�00

�20

=24

�3—–y ×�00 =�30

y=�3×�00———–�30

=�0

z= �8—–�2

�00

=�50

(b)PriceforDintheyear2005

————————————PriceforDintheyear2000

�00=200

3000

————————————PriceforDintheyear2000

�00=200

PriceforDintheyear2000 = 3000×�00——–——–200

=RM�500

(c) (i) Compositeindexfortheyear2005basedontheyear2000

=∑wiIi——–∑wi

=

(2×�20)+(4×�30)+(�×�50)+(3×200)

—————————————–—2+4+�+3

=�5�

(ii) Compositeindexfortheyear2006basedontheyear2000

=�5���0% =�66.�

2. (a) Thecompositeindexfortheyear2006basedontheyear2000=�20

∑wiIi——–∑wi

=�20

(2��0)+(2��5)+(m+�)�20+(2�25)+m�30

————————————————2+2+(m+�)+2+m

=�20

820+250m

—————–7+2m

=�20

820+250m=�20(7+2m) =840+240m 250m–240m=840–820 �0m=20 m=2

(b)PriceforAintheyear2006

————————————PriceforAintheyear2000

�00=��0

PriceforAintheyear2006=��0× 200——�00

=RM220

(c) PriceindexforB intheyear2000basedontheyear2006

=Priceintheyear2000

——————————Priceintheyear2006

�00

= �00——��5

�00

=86.96

3. (a) PriceindexforitemAintheyear2005basedontheyear2000

= 20—–�0

�00

=200

PriceindexforitemBintheyear2005basedontheyear2000

= 30—–20

�00

=�50

6

PriceindexforitemCintheyear2005basedontheyear2000

= �0—–�0

�00

=�00

(b) (i) Compositeindexfortheyear2005basedontheyear2000

=∑wiIi——–∑wi

=(�×200)+(2×�50)+(3×�00)——————————————

�+2+3 =�33.3

(ii)Priceintheyear2005

——————————Priceintheyear2000

�00=�50

30

——————————Priceintheyear2000

�00=�50

Priceintheyear2000 = 30×�00————�50

=RM20

4. (a) (i)

Expenditurefortheyear2003

————————–Expenditureforthe

year2000

�00=�20

ExpenditureonitemAfortheyear2003

= �20×�300———–—–�00

=RM�560

(ii)

Expenditurefortheyear2003

————————–Expenditureforthe

year2000

�00=�35

�500

————————–Expenditureforthe

year2000

�00=�35

ExpenditureonitemCfortheyear2000

= �500×�00———–—–�35

=RM����.��

(b) (i) Compositeindexfortheyear2003basedontheyear2000

=∑wiIi——–∑wi

=��6

(2�20)+3x+(��35)+(4��0)

———————————–2+3+�+4

=��6

8�5+3x=��60 3x =345 x=��5

(ii)

Totalexpenditurefortheyear2003

—————————–Totalexpenditurefor

theyear2000

�00=��6

Totalexpenditurefortheyear2003

=��6× 8000——–�00

=RM9280

(c) Thecompositeindexfortheyear2005basedontheyear2000

=�20%��6 =�39.2

5. (a) x——�.�0

�00=�30

x=�30× �.�0——�00

=�.43

�.80——y ×�00=�25

y=�.80×�00———–—�25

=�.44

(b) PriceindexforitemQintheyear2004basedontheyear200�

= �.20——0.80

�00

=�50

PriceindexforitemSintheyear2004basedontheyear200�

= �.40——�.20

�00

=��6.7

(c) Composite price index for the year 2004 basedontheyear200�

=∑wiIi——–∑wi

=(�×�30)+(4×�50)+(3×�25)+(2×��6.7)———————————————————–

�+4+3+2 =�33.8

7

(d)

Totalcostofproductionintheyear2004

——————————Totalcostofproduction

intheyear200�

�00=�33.8

Totalcostofproductionintheyear2004

= �33.8×�.2———–—–�00

=RM�.606millions

(e) Thecompositeindexfortheyear2005basedontheyear200�

=�30%�33.8 =�73.9

6. (a) CompositeindexforAandB= 340——3

�00x+�20y—————–

x+y= 340——

3 300x+360y=340(x+y) =340x+340y 40x=20y y=2x x:y=�:2

CompositeindexforAandC= �65——2

�00x+80z

—————x+z

= �65——2

200x+�60z=�65x+�65z 35x=5z z=7x x:z=�:7

Therefore,x:y:z=�:2:7.

(b) Composite index in theyear2006basedon theyear200�

=(�×�00)+(2×�20)+(7×80)

——————————————�+2+7

=90

(c)PriceofBintheyear2006———————————–PriceofBintheyear200�

�00=�20

450

———————————–PriceofBintheyear200�

�00=�20

PriceofBintheyear200�= 450×�00———–—�20

=RM375

(d) Compositeindexfortheyear2007basedontheyear200�

=��0%×90 =99

Priceintheyear2006

—————————–Priceintheyear200�

�00=90

Priceintheyear2006

—————————–Priceintheyear2007

×Priceintheyear2007

—————————–Priceintheyear200�

�00=90

Priceintheyear2006

—————————–�2000

× 99——�00

�00=90

Priceintheyear2006 =90× �2000———99

=RM�0909.09