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BNBOZCIQ U BNBPAEAEIQ
ADZDAEHDH HB CD ZPIHRAAEÑK
4. Rkd boprbsd trd`dnd hedre dobktb bk his turkis hb iafi fir ds ad
adhd
hd turki, d ci cdrgi hb
aekai hïds d cd sbodkd. Rkd sbaaeñk hb heafd boprbsd aikstd hb audtri oäquekds qub
sb ute cezdk bc 7: % hbc tebopi a ik ukd bleae bkaed hbc se stbod hbc 5: %. Hbtbroe
Hbtbroe kb bc iutput
hb cd sbaaeñk pir sbodkd.
ℋ  2   8  :.7:  :.5:?. 
Iutptputut rbrbdcdc ? 0 
Iu

6
  

( Iutput rbdc / Qdcehd rbdc / Zrihuaaeñk rbdc )
0. Cd adpdaehdh priy batdhd hedre d hb ukd sbaaeñk h b ukd boprbsd bs hb 4
4::
:: uke hdhbs,
sebkh i cd adpd
adpdaeh
aeh dh blbate
blbate vd hedred hb cd oeso d hb 6: uke hdhbs y b
bcc iutp ut hedre i hb heafd
sbaaeñk <: ukehdhbs.
d) Adcaucb cd ute cezdaeñ k y cd bleae bkaed hb cd sbaaeñ k.
`) Hbtb
Hbtbroe
roe kb bc
bc iutp ut hbc prñxe oi obs sd`ebkhi qub cd bleaebka ed b
bspbrdhd
spbrdhd b
bs
s hbc 5
5:
: %.
Qicuaeñk>
Iutput rbdc ? <:  4:: ? %


 ? Adpdaehdh
hb hesbôi 4::
Iutput rbdc ? <:  4:


 ? Adpdaehdh
Blbatevd 6: 4:: ? %
Iutput rbdc


 ? Adpdaehdh
blbatevd
5:%? Iutput
6: rbdc
Iutptputut rbrbdcdc ? 6:  ::.5.5:: ?  
Iu

1. Adcaucb cd tdsd hb pri huaa eñk oäxe od hb ukd pbcuqubrïd bk cd qub trd`dnd hedredobktb 6
fir ds uk þkea i pbcuqubri. Bk priobhei bc te bopi kbabsdrei pdrd airtdr, pbekdr, b
bta.
ta. d cds
sbôirds bs hb 02 oekutis y d cis ad`dccbris 42 oekutis, sebkhi bc tebopi rbqubrehi pdrd
cd prbpdrdaeñ k hb adhd ace bktb hb 2 oek utis . Qb
Qb aikiab qub bc <: % hb cis ace bktbs hedrei s
hb bstd pbcuqubrïd sik ad`dccbris.
Qicuaeñk>
Xdsd hb pri
Xdsd
prihua
huaaeñ
aeñkk oäxeod
oäxeod ? Adp
Adpdae
daehdh
hdh hhbb Hesbôi
Hesbôi ? 

 +  


 
 ? 
  
 +02   ô ? 1: oek/srd


 
 "ô
"ô"
" ? 
 +42   ô ? 0: oek/sr.


 
 "ô
"ô"
" ? 
  <:% ô)?08 /

8
8:%
:%
ô

ô)
)+
+
(0:


 

 ? (1: 





 ?
/
/
 6ℋ/
4 ℋ/ ? 0: 
08 
<:
8. Bc gräleai oubstrd bc priabsi hb ld`readaeñk hb uk prihuati d pdrter hb his aiopikbktbs
qub sb i`tebkbk bk cds bstdaeikbs hb trd`dni D4 y D0. Heafis aiopikbktbs sik
bksdo`cdhis
bksd
o`cdhis bk cd bstdaeñk @ y pist breirobktb priabsdhis bk cds bstdaeikbs
bstdaeikbs A y H. Cis
tebopis hb adhd bstdaeñk hb trd`dni ekheadk cd adktehdh hb trd`dni qub hb`b rbdcezdr bc
trd`dndhir bk heafd bstdaeñk pdrd adhd ukehdh hb prihuati. Adcaucb cd adpdaehdh hb
prihuaaeñk hb heafi priabsi.
Qicuaeñk>
Bstdaeñk Firds Zebzds/fird
D4
D0
@
A
H
:,0
:,8
:,2
:,0
:,02
4/:,0?2
4/:,8?0,2
4/:,2?0
4/:,0?2
4/:,02?8
Bc tebopi hb priabsi ods dcti hb bktrb tihds cds bstdaeikbs bs 2 firds
Bc aubcci hb `itbccd hb bstb priabsi bs cd bstdaeñk @
Cd Adpdaeh
Adpdaeh dh hb Z
Zrih
rih uaae ñk hb bstb pria bsi bs hb 0 pebzds/fird
2. Odredkd Xrunecci tebkb ukd pcdktd priabsdhird hb afiaicdtbs –Cux
Cu x ‟ y quebrb bktbkhbr
obnir s u adpdaehdh hb prihuaae ñk. Hbtbroekb
Hbtbroekb cd adpdaehdh
adpdaehdh hb hes bôi, cd utecezdaeñk y c d
bleaebkaed pdrd bstd pcdktd dc prihuaer. Cd sbodkd pdsdhd cd ekstdcdaeñk prihuni 486,:::
`drrds hb afiaicdtbs. Cd adpdaehdh blbatevd bs hb 472,::: ukehdhbs. Cd cïkbd hb
pri huaa eñk ipbrd 7 hïds
hïds d cd sbodkd bk trbs turk is h b 6 firds dc hïd. Cd cïkbd lub hesbôdhd
pdrd priabsdr
priabsdr ci s pdkbaeccis –Cux
Cu x ‟, rbccbkis hb kubz y aik s d`ir d vdekec cd, d ukd tdsd hb
4,0::
4,0
:: pir fi rd. Cd boprbsd adcauc d preobri cd adpdaehdh hb hesbôi y h bspuås hbtbroek d
cd utece zdaeñk
zdaeñk y cd bleaebkaed.
Qicuaeñk>
Adpdaeh
Ad
pdaeh dh hb hesbôi ? (7 hïds x 1 turkis x 6 firds) x (4,0:: pdkbaeccis pir fird) ?
? 0:4,<:: pdkbaeccis
Rtecezdaeñk ? Zrihuaaeñk rbdc / Adpdaehdh hb hesbôi ? 486,::: / 0:4,<:: ? 71.8%
Bleaebkaed ? Zrihuaaeñk rbdc / Adpdaehdh blbatevd ? 486,::: / 472,::: ? 68.<%
<. Cd dhoeke str dhird hb Afiaic dtbs –Cux
Cu x ‟, dfird kbabsetd ekarbobktdr cd prihuaaeñk. Zdrd
sdtes ldabr cd hbodkhd,
hbodkhd, hb
hb`b
`b dgrbgdr
dgrbgdr ukd sbgukhd cïkbd hb prihua aeñ k. Cd dhoeke str dhird
hb`b hbtbroekdr cd prihuaaeñk bspbrdhd bk bstd sbgukhd cïkbd pdrd bc hbpdrtdobkti hb
vbktds. Cd adpdaehdh blbatev d bk cd sbgukhd cïkbd bs
bs cd oe sod qub bk cd pre obrd cïkbd, bs
hbaer, 472,::: `drrds hb afiaicdtbs. Aioi sb adcaucñ dktbreirobktb, cd preobrd cïkbd
ipbrd aik ukd bleaebkaed hbc 68.<%. Zbri cd prihuaaeñk bk cd sbgukhd cïkbd sbrä obkir
hb`ehi d qub bc pbrsikdc sbrä preoirhedcobktb hb kubvd aiktrdtdaeñk= dsï qub sb bspbrd
qub cd bleae bkaed ki sbd odyir dc 72%
72%.. ¹A
¹Auäc
uäc bs cd pri huaa eñk bspbrdhd b
bktik
ktik abs9
Qicuaeñk>
Zrihuaaeñk rbdc (i bspbrdhd) ? (Adpdaehdh blbatevd) x (Bleaebkaed)
Zrihuaaeñk bspb
bspbrdhd
rdhd ? (Adpdaehdh blbatevd)x(Bleaebkaed) ? (472,:::)(.72) ? 414,02: pebzds
7. Rkd pcdktd lub hesbôdhd pdrd
pdrd sdtesl dabr ukd hbodkhd
hbodkhd hb fdstd 0
0::
:::
: ukehdhbs dc hïd
hïd.. Z
Zbri
bri
su adhbkd pbroet b prih uae r 470:
470: uke hdhbs. Bc sup brves ir b
bspbrd
spbrd dcadkzdr
dcadkzdr ukd
prihuaaeñk hb 46:: ukehdhbs. ¹Auäc bs bc rbkheoebkti hb cd pcdktd9 ¹Auäc sbrä cd
prihuaaeñk bsteodhd9
Hdtis>
Adpdaehdh hb Hesbôi? 0::: ukeh
Adpdaehdh Pbdc i utecezdhd ? 470: ukeh
Adpdaehdh blbatevd (pir
(pir hblekeaeñk bs cd adpdaehdh qub sb bspbrd dcadkzdr )? 46:: ukeh
Pbkheoebkti ? bleaebkaed
Rtecezdaeñk ? adpdaehdh rbdc / adpdaehdh hb hesbôi ? 470:/0::: ? :.6<
Bleaebkaed? adpdaehdh Pbdc/Adpdaehdh blbatevd? 470:/46:: ? :.5< ? 5< %
Zrihuaaeñk bsteodhd
? Adpdaehdh hb hesbôi * Rtecezdaeñk * Bleaebkaed
? 0::: ukeh/hïd * :.6< * :.5< ? 4<24.0:
4<24.0: uke h/he d
6. Bc @EH tebkb ukd pri huaa eñk tbñre ad hb 82::
82:: `itbcc ds/obs sebkhi bc % blbatevi dcadkzdhi
hb 50%. Zbri sb prbvå ukd hbodkhd luturd hb 8::: `itbccds. ¹Zihrä fdabrsb lrbktb d
hea fd hbodkhd
hbodkhd aik uk ldat ir hb bleaebkae d hbc
hbc 51%9
51%9 ¹Auä
¹Auäcc hb`b sbr b
bcc grdhi hb bleae bkaed
pdrd sdtesldabr
sdtesldabr bc rbqubreoebkti9
Hdtis>
Adpdaehdh Hesbôi? 82:: `it/obs
% blbatevi dcadkzdhi 50% ?; adpdaehdh blbatevd ? 82:: `it/obs * :.50 ? 848: `it/obs
Hbodkhd Luturd ? 8::: `it/obs ? prihuaaeñk rbdc (luturd)
Bleaebkaed ? Zrihuaaeñk Pbdc / Adpdaehdh Blbatevd ? 8::: `it/obs / 848: `it/obs ? 5<.<0%
Pptd.
Aik uk ldatir hb bleaebkaed hbc 51% ki sb auopcerä aik cd hbodkhd luturd
Cd bleaebkaed hb`b sbr 5<.<0%
5. ODPM hespikb hb uk abktri bquepdhi aik 4: ZA―s qub dpbrtur d hb cukbs d nubvbs hb 40
fir ds d 0: firds bopcbdkhi fdstd cds 00 firds c is vebrk bs y sä`dhis. Bc ace bktb
bk prio bhei ci usd adhd vbz 82 oek utis . Xbkebkhi
Xbkebkhi bk au bktd qub cd utece zdaeñk bs hbc 6:%
y cd ble
ble aebkae d hbc 5
5:%
:%.. ¹Auäc
¹Auäc bs cd adpdaehdh priybatdhd sbodkdc
sbodkdc y cd pri huaa eñk
bsteodhd obksudc9
Pptd.
Adpdaehdh Zriybatdhd i hesbôi Bs cd oäxeod prihuaaeñk tbñread qub sb pubhb dcadkzdr `dni
aikheaeikbs ehbdcbs, bk bc bnbraeaei sbrä cds firds odquekd hespike`cbs d cd sbodkd
Adpdaehdh priybatdhd ? (4: pa*8 heds/sbo*0: fr/hïd) + (4:pa*0 heds/sbo*00 fr/hed)
? 408: fr-pa/sbo
Zrihuaaeñk bsteodhd
? Adpdaehdh
priybatdhd
Rtecezdae
Rtecezdaeñk
ñk *sbo/obs
Bleaebkaedody
408: fr-pa/sbo
* :.6: ** :.5:
* 8.80
? 1521.60 fr-pa/obs
BNBPAEAEIQ ZDPD PBQIC\BP
4. Qe ukd pcdktd sb hes bôñ pdrd prih uae r 7,::
7,:::
: odrte cc is pir hïd, pbri sb fd ceoet dhi d fdabr
<,::: odrteccis hedreis hb`ehi dc tebopi kbabsdrei pdrd ado`edr bc bquepi sbgþk cis
bstecis hb odrtecci, ¹auä
¹auäcc bs cd utece zdaeñk9
zdaeñk9
0. Hurdktb bc obs pdsdhi,
pdsdhi, cd pcdktd hbc
hbc pri `cbod dktbreir, cd audc tebkb ukd adpdaeh
adpdaeh dh
blbatevd hb <,2::, ld`reañ sñci 8,2:: odrteccis pir hïd hb`ehi d hboirds hb odtbredc,
dusbkaeds
dusb
kaeds hb cis bopcbdhis
bopcbdhis y itris pri`cbods. ¹Auäc
¹Auäc bs su bleaebkaed9
1. Qe ukd pcdktd tebkb ukd adpdaeh
adpdaeh dh blbate
blbate vd hb <,2
<,2::
:: y ukd bleae bkaed hbc 66
66%,
%, ¹auäc bs su
prihuaaeñk rbdc (pcdkbdhd)9
8. Cd adpdaehdh blbate
blbate vd hb ukd pcdktd bs
bs hb 5::
5:: uke hdhbs pir hïd y prihua b 6
6::
:: uke hdhbs
hedreds aik su obzacd
obzacd hb prihuatis= ¹auäc
¹auäc bs su bleaebkaed9
2. Cds hboir
hboir ds hb odtbredc fdk ceo etdhi rute kdredobktb cd prihua aeñk hb cdvdodkis pdrd bc
figdr d 8:: ukehdhbs pir hïd. Qe cd bleaebkaed hb cd pcdktd bs hbc 6:%, ¹auäc bs su
adpdaehdh blbatevd9
<. ¹Auäc
¹Auäc bs cd pri huaa eñk bspbrdhd pd
pdrd
rd ukd pcdktd aik adpdaehdh hb hesbôi hb 4:6
4:6 sec cds
pir hïd se su adpdaehdh blbatevd bs hb 5: seccds y su bleaebkaed hbc 5: pir aebkti9
7. Rk abktri hb trd`dni
trd`dni qub aiktebkb 8 oä
oäquekds
quekds aik cd oesod adpdaehdh
adpdaehdh ipbrd his turkis
pir hïd 2 hïds d cd sbodkd
sbodkd (6 firds pir t urk i). B
Bstd
std bs cd adpdaehdh blbatev d. Q
Qee bc abktr i
hb trd`dni tebkb ukd bleaebkaed hbc sestbod hbc 52%, ¹auäc bs cd prihuaaeñk bspbrdhd bk
firds pir sbodkd
sbodkd9
9
6. Cd adpdaehdh blbatevd y cd blea
blea ebkae d hb trbs hbpdrtdobkti s hb OO
OOR
R O
Olg.,
lg., `dsdhd bk
Wdai,
Wd
ai, Xb
Xbxds,
xds, pd
pdrd
rd bc prñxeo i tr eobstrb sik c ds seguebktbs>
Hbpdrtdobkti
Hb
pdrtdobkti
Adpdaehdh
Bleaebkaed
blbatevd
rbaebkt b
Hesbôi
Ld`readaeñk
Dad`dhi
51,<::
42<,:::
<0,8::
:.52
4.:1
4.:2
Adcaucb cd prihuaaeñk bspbrdhd hurdktb bc seguebktb treobstrb pdrd adhd hbpdrtdobkti.
5. Qb rbdcezñ uk bstuhe i hb tebopi s bk uk priabsi hb ukd bopr
bopr bsd hb odkuldatur d qub
drrinñ cis se guebktbs rb
rbsuctdhis>
suctdhis>
Kº OBHEAEÑK
O BHEAEÑK XEBOZI (OEK)
( OEK)
Xebopi4
02.1:
Xebopi0
02.<:
Xebopi1
02.0:
Xebopi8
08.52
Xebopi2
Xebopi<
Xebopi7
Xebopi6
Xebopi5
Xebopi4:
08.7:
08.5:
02.1:
08.<:
02.12
02.72
Qb trd`dnd uk turki hb 6 firds, uk tebopi oubrti hbc 41% y ukd obrod hbc 5%.
Adcaucdr cd utecezdaeñk, cd bleaebkaed hb cd prihuaaeñk y cd adpdaehdh hespike`cb.
4:.
4:. Qb rbd
rbdcezñ
cezñ uk bst uhei hb tebopi s bk u k pr iabsi hb drodhi h b ukd boprbsd hb
odkuldaturd qub drrinñ
drrinñ cis se guebktbs rbsuctdhis>
Kº OBHEAEÑK
O BHEAEÑK XEBOZI (OEK)
( OEK)
Xebopi4
46.0:
Xebopi0
45.<:
Xebopi1
46.0:
Xebopi8
45.52
Xebopi2
46.7:
Xebopi<
45.5:
Xebopi7
46.1:
Xebopi6
45.<:
Xebopi5
46.12
Xebopi4:
45.72
Qb trd`dnd uk turki hb 4: firds, uk tebopi oubrti hbc 48% y ukd obrod hbc 6%.
Adcaucdr cd utecezdaeñk, cd bleaebkaed hb cd prihuaaeñk y cd adpdaehdh hespike`cb.
44.
44. Rkd boprbsd ute cezd 2 oäque kds p drd ld`re adr ukd pe bzd
bzd,, hb cd a udc sb r bquebrbk
his pdrd adhd ukeh dh hb prih uat i lekdc. Adhd
Adhd oäquek d te bkb :,2%
:,2% hb prih uaa eñk
hblbatui sd. Cd tdsd hb utece zdaeñk h b cd oäquekd bs hbc 52%. Qb
Qb trd`dndk 08 sbod
sbodkds
kds bk
bc sbobstrb, 2 hïds d cd sbodkd,
sbodkd, 6 fir ds pir turki , y uk turk i pir hïd. Qb quebrb ld`re adr
0:.::
0:.
:::
: ukeh dhbs hb prih uat i le kdc bk bc sbobstr b y sb hbsbd sd`br cd tdsd tbñrea d
hb ld`readaeñk hb adhd oäquekd pir fird.
40. Rkd bksdo`cdhird hb `eaeacbtds qub ld`read cis rekbs hb cds oesods y bc rbsti hb cds
pebzds cds aioprd, tebkb ukd hbodkhd sbobstrdc hb 42.::: `eaeacbtds. Cd oäquekd pdrd
ld`readr cis rekbs tdrhd 8: oekuti s bk su odquekdhi, sebkhi su tdsd hb utece zdaeñk
zdaeñk
uk 58
58%
% hbc tebopi titdc hbc qub hespikb cd boprbsd y su prihuaae ñk hblb
hblbatuisd
atuisd
fes tñr ead bs h bc 8%.
8%. Bk cd boprbsd sb tr d`dndk 6 fir ds pir tur ki, 2 hïds d cd
sbodkd, y his tur kis hedre is. Qb peh b adcauc dr bc kþobri hb oäquekds qub kbabsetdrä
cd boprbsd bk bsb pbreihi pdrd sdtesl dabr cd hbodkhd.
41.
41. Nudke td bs hu bôd hb ukd adrpe ktbrïd qub he sbôd y ld`rea d pupet rbs h b odhbrd,
trd`dnd sbes hïds d cd sbodkd hurdktb 7 firds pi r tu rki, bk his t urk is hb tr d`dni.
Dh boäs
boäs,, hb cds 20 sbodkds
sbodk ds qub
qu b tr db bc dôi, su adrpe
adr pe ktbrïd
kt brïd tiod
ti od 1 sbo dkds pdr
pdrd
d
vdadaeik bs adhd dôi. Bk prio bhei cd ld`re adaeñk hb adhd pupe trb rb
rbque
que brb hb 0: fir ds.
Cd adrpek tbrïd hb Nudket d tdo`e åk
bopcbd
abrad
hb
trbs
fir d/sbodkd
d/sbodkd
bk
odktbkeoebkti prbvbk
prbvbktevi
tevi y his firds/sb
firds/sbodkd
odkd bk rbaigbr bc surtehi . Qb pehb adcaucdr
cd adpdaehdh rbdc bk pupe trbs hb cd adrpe ktbrïd hb Nudket d d
dcc dôi.
48.
48. Cd pd
pdkdhbrïd
kdhbrïd hb Qdrd
Qdrd Ndobs, fd hbaehe hi dopc edr su s e kstdcdae ikbs dôdhebkhi i trd cïkbd
hb priabsi. Cd boprbsd tbkhrä 0 cïkbds hb priabsi, y adhd ukd trd`dndrd 7 hïds d cd
sbodkd, trbs tur kis pir hïd y 6 fir ds pir turk i. Cd adpdaehdh
adpdaehdh blbatevd dsaebkhb d fird
d 1::.::: pdkbaeccis. Bstd dopcedaeñk, sek bo`drgi, rbhuaerä cd bleaebkaed gbkbrdc hbc
sestbod dc 62%. Adcaucb cd kubvd prihuaaeñk bsteodhd aik bstd kubvd adpdaehdh
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