Costo Volumen Utilidad 2,016 - I Unt

 

@JMRJSYGMKAEYJ IA LJP @JPYJP

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@jej`ar `jmj sa `jmpjrtge ljs `jstjs rasultg ÿtkl g lg gimkekstrg`kðe pgrg mÿltkplas prjpðsktjs? astgcla`ar vjlÿmaeas ia vaetg, prjya`tgr ljs `jstjs y lgs utklkigias. Pa iaca kiaetkfk`gr ljs fg`tjras ia `jstjs j naeargijras ia `jstjs y lg as`glg ia g`tkvkigi j rgenj ralavgeta.

 

@LGPKFK@G@KJE IA LJP @JPYJP RJS PQ @JMRJSYGMKAEYJ

 

@JPYJP VGSKGCLAP •

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Ljs `jstjs vgrkgclas sje gqualljs qua `gmckge ae prjpjr`kðe `je ljs `gmckjs ae al ekval ia g`tkvkigi. @ugeij al ekval ia g`tkvkigi sa mkia ae uekigias prjiu`kigs, ljs `jstjs ia ljs mgtarkglas ikra`tjs y ia mgej ia jcrg ikra`tg pjr lj naeargl sa `lgskfk`ge `jmj `jstjs vgrkgclas.

 

@JPYJP VGSKGCLAP •

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Ljs `jstjs vgrkgclas tjtglas sje ikra`tgmaeta prjpjr`kjeglas g ue fg`tjr ia `jstjs ? Qekigias prjiu`kigs, hjrgs mçqukeg, hjrgs ia mgej ia jcrg ikra`tg, eÿmarj ia paikijs, dm. Sa`jrrkijs, eÿmarj ia pg`kaetas, at`. Ljs `jstjs vgrkgclas pjr uekigi ae `gmckj sa mgetkaeae `jestgetas iaetrj ial rgenj ralavgeta ia g`tkvkigi.

 

@JPYJ IA MGYASKGLAP IKSA@YJP Qekigias

@jstj stj uektgrkj

@jstj stj tjtgl

1222

72

12222

72222

72

722222

71222

72

712222

32222

72

322222

31222

72

312222

02222

72

022222

 

@JPYJ FKOJ •

Ljs `jstjs fkojs sje gqualljs qua parmgea`ae `jestgetas g maikig qua `gmckg al ekval ia g`tkvkigi.

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@ugeij ekval ia prjiu`kigs g`tkvkigi sa mkia aeal uekigias lg iapra`kg`kðe, ljs glquklaras, sanurjs, kmpuastj praikgl, sualijs ial parsjegl gimkekstrgtkvj, sa `lgskfk`ge `jmj `jstjs fkojs.

 

@JPYJ FKOJ •

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Ljs `jstjs fkojs tjtglas ej tkaeae ralg`kðe ia `gusg afa`tj `je al fg`tjr ia `jstjs y sa raprasaetge pjr ueg líeag pgrglalg gl aoa hjrkzjetgl. Ljs `jstjs fkojs pjr uekigi `gmckge g maikig qua gumaetg j iksmkeuya al fg`tjr ia `jstjs, sa raprasaetg pjr ueg líeag ia`ra`kaeta ae ralg`kðe gl vjlumae.

 

@JMRJSYGMKAEYJ IAL @JPYJ YKRJ IA @JPYJ

YJYGL

QEKYGSKJ

@jstj vgrkgcla

Gumaetg j iksmkeuya ikra`tgmaeta

Pa mgetkaea fkoj j `jestgeta iaetrj ial

prjpjr`kjegl gl fg`tjr ia `jstjs.

rgenj ralavgeta ia g`tkvkigi.

Pa mgetkaea `jestgeta iaetrj ial rgenj ralavgeta ia g`tkvkigi.

As vgrkgcla, ae ralg`kðe kevarsg gl fg`tjr ia `jstjs.

@jstj Fkoj

@JPYJ VJLQMAE QYKLKIGI

 

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Al mjialj `jstj vjlumae utklkigi (@VQ) utklkigi (@VQ) as `jeskiargij ueg vglkjsg harrgmkaetg pgrg lg plgekfk`g`kðe y lg tjmg ia ia`kskjeas, rasgltg lgs ketarralg`kjeas ia ljs `jstjs, al vjlumae ia vaetgs y al kmpg`tj sjcra lgs utklkigias ia ueg amprasg. Rgrg su gplk`g`kðe, sa raqukara geglkzgr al `jmpjrtgmkaetj `jmpjrtgmkaetj ia ljs `jstjs hg`kaeij ue geçlksks ia g`tkvkigias, kiaetkfk`geij quë pgrtkigs ia ljs `jstjs sa vae gfa`tgijs pjr ljs `gmckjs ae ljs ekvalas ia g`tkvkigi iaetrj ia ue rgenj ralavgeta ia jparg`kðe.

GRLK@G@KJEAP @JPYJ VJLQMAE QYKLKIGI

 

 

Al mjialj `jstj vjlumae utklkigi usuglmaeta as gplk`gij ae ikfaraetas tkpjs ia amprasgs? @gl`ulgr al puetj ia aquklkcrkj jpargtkvj y ia `karra. Rrjya`tgr lgs utklkigias ia lg amprasg g ikfaraetas ekvalas ia vaetgs Astgcla`ar lg maz`lg ia prjiu`tjs

 

Geglkzgr ljs `gmckjs ae `uglqukarg ia lgs vgrkgclas partkeaetas ial mjialj @VQ.

 

 

RQEYJ IA AWQKLKCSKJ •

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Al puetj ia aquklkcrkj as al ekval ia jparg`kjeas ae al `ugl ljs kenrasjs y ljs `jstjs aspargijs ia ueg amprasg sje axg`tgmaeta knuglas. Ae aquklkcrkj ueg amprasg ej taeirç ek përikigs ek utklkigias. Al puetj ia aquklkcrkj as ÿtkl ae lg plgeag`kðe ia amprasgs,saaeaxpgeiae aspa`kgl `ugeij lgs jparg`kjeas j ia`ra`ae.

 

RQEYJ IA AWQKLKCSKJ

 

 

 

 

 

 

Kenrasj tjtgl = @jstj tjtgl R.W = F + v.W  R.W - v.W = F W(R-V)=F

W* =

F R-V

Ruetj ia aquklkcrkj ae uekigias

 

 

RQEYJ IA AWQKLKCSKJ

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Ae fjrmulg R =lgRra`kj ia getarkjr? vaetg prjmaikj pjr uekigi ( Pke KNV) v = @jstj vgrkgcla uektgrkj F = @jstj fkoj tjtgl W = vjlumae físk`j ae uekigias vaeikigs.

 

 

RQEYJ IA AWQKLKCSKJ •

R - V = Mgrnae ia `jetrkcu`kðe uektgrkj

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Mgrnae ia `jetrkcu`kðe ej as lj mksmj qua mgrnae crutj j utklkigi crutg.

P* = F   7 ‐ v/p

Ruetj ia aquklkcrkj ae uekigias mjeatgrkgs

 

RQEYJ IA AWQKLKCSKJ •

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7 - v/p = Sgzðe ial mgrnae ia `jetrkcu`kðe

Mgrnae ia Panurkigi? Ikfarae`kg aetra

lgs vaetgs raglas y lgs vaetgs ae al puetj ia aquklkcrkj. Keik`g lg pjskcla iksmkeu`kðe ae vaetgs qua puaia j`urrkr getas qua rasulta ueg parikig ia jparg`kðe, ejs keik`g al ekval ia rkasnj ia jparg`kðe ia ueg amprasg.

 

AOAMRLJ IA GRLK@G@KJE •

@lguikg Sgmíraz as prjpkatgrkg ia lg Cjutkqua Al Vkrray, sa iaik`g g lg `jmar`kglkzg`kðe ia `gmksgs pgrg `gcgllarjs. Iurgeta al mas ia Aearj ial g÷j 3,276 vaeikð 92 `gmksgs ae su

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prkmar mas ia jparg`kjeas. Al `jetgijr ia @lguikg prapgrð al sknukaeta astgij ia rasultgijs gl 07 ia Aearj ial g÷j 3,276?

 

“ Cjutkqua Al Vkrray ” Astgij ia Sasultgijs gl 07 ia Aearj ial 3,276 Vaetgs eatgs ? 92 @gmksgs x P/.82 @jstj ia vaetgs? 92 `gmksgs x P/.92 Qtklkigi crutg Ngstjs ia vaetgs ;22 Ngstjs ia gimkekstrg`kðe 7,022 Rërikig jpargtkvg

P/. 0,322 7,622 7,622 3,322 ( 622) =====

 

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Lg prjpkatgrkg sa ae`jetrgcg sgtksfa`hg `je ljs rasultgijs pjr `ugetj ej aspargcg qua lg tkaeig fuarg g sar raetgcla ae su prkmar mas. Rgrg al mas sknukaeta astkmð qua raquaríg ke`ramaetgr lgs vaetgs ae sjlj 71 `gmksgs pgrg `ucrkr sus @gig `jstjs. Pussa `çl`uljs arge ljs sknukaetas? `gmksg vaeia g P/. 82.22 y su `jstj ia giquksk`kðe as P/. 92.22, lj qua naeargcg ueg utklkigi crutg ia 92.22 pjr `/u. Pk vaeiíg 11 `gmksgs jctaeiríg ueg utklkigi crutg ia 3,322, `kfrg qua `ucra axg`tgmaeta ljs ngstjs ia jparg`kðe. Gl fkeglkzgr al mas ia Facrarj ial 3,276, al `jetgijr la prasaetð al sknukaeta astgij ia rasultgijs?

 

“ Cjutkqua Al Vkrray ” Astgij ia Sasultgijs gl 38 ia Facrarj ial 3,276 Vaetgs eatgs? 11 `gmksgs x P/.82 P/. 9,922 @jstj ia vaetgs ? 11 `gmksgs x P/.92 3,322 Qtklkigi crutg 3,322 Ngstjs ia vaetgs 7,212 Ngstjs ia gimkekstrg`kje 7,022 3,012 Rërikig jpargtkvg ( 712) =====

 

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Lg prjpkatgrkg sa sketkð ia`ap`kjegig y ej aetaeiíg pjrqua su eanj`kj hgcíg taekij përikigs. @je lg gyuig ia su `jetgijr geglkzð al `jmpjrtgmkaetj ia ljs `jstjs? - @jstj ia mar`ge`ígs ? tjijs vgrkgclas - Ngstjs ia vaetgs? P/.922 vgrkgclas y al rastj as fkoj. -@je Ngstjs P/. 7,022 sje fkojs. astg gimkekstrgtkvjs? kefjrmg`kðe, vjlvkð g fjrmulgr al astgij ia rasultgijs gl 07 ia Aearj ial 3,276?

 

“ Cjutkqua Al Vkrray ” Astgij ia Sasultgijs gl 07 ia Aearj ial 3,276 3 ,276  

Vaetgs eatgs( 92 @gmksgs x P/.82 ) @jstj vgrkgcla @jstj mar`ge`kgs ( 92 x 92) 7,622 Ngstjs vaetgs (92 x 72 ) 922 Mgrnae ia `jetrkcu`kðe @jstjs fkojs Ngstjs vaetgs Ngstjs Gimkekst. Rërikig jpargtkvg

122 7,022

P/. 0,322

3,222 7,322

7,822 ( 622 ) =====

   

@GL@QLJ IAL RQEYJ IA AWQKLKCSKJ  

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Gplk`geij lg fjrmulg? fjrmulg? W* = 7,822 82 ‐ 12 W* = 62 `gmksgs gl mas

 

 

 

P* = 7,822 7 ‐ 12/82 P* = P/. 9,822 / maesugl.

 

“ Cjutkqua Al Vkrray ” Astgij ia Sasultgijs gl 38 ia Facrarj ial 3,276 Vaetg aetgs s eat atgs gs ( 62 `gm `gmksg ksgs x P/ P/.8 .82 2) P/ P/.. 9,822 ,822 @jstj @jstj vgrkgc vgrkgcla la ( 62 `gm `gmksg ksgs s x P/.12 P/.12 ) 0,2 0,222 22   Mgrnae ia `jetrkcu`kðe 7,822 @jstjs fkojs

   

   

 

Ngstjs vaetgs Ngstjs Gimkekst. Qtklkigi Jpargtkvg =====

122 7,022

7,822 =.=

   

NSGFK@G IAL RQEYJ IA AWQKLKCSKJ P/.

Vaetgs

>3 @jstj Yjtgl

62   s    l   a   j 9,8   s   a    i   s 0,6   a    l    k    M3,9

Qtklkigi

Rarikig

7,3 2

@jstj Fkoj 71

02

91

62

>1

Vjlumae ia vaetgs

@gmksgs

 

Pupuastjs ial geçlksks `jstj

 

 

   

 

 

vjlumae utklkigi Lgs va vaetgs y ljs `j `jstjs tk tkaeae

7.`jmpjrtgmkaetj lkeagl.

ue ue

3.- Ljs `jstjs puaiae sar `lgskfk`gijs ae `jstjs vgrkgclas y `jstjs fkojs. 0.- Iaetrj ial rgenj ralavgeta, lg afk`kae`kg as `jestgeta. 9.- Lg maz`lg ia vaetgs as `jestgeta. 1.- Ej hgy `gmckjs ae ljs ekvalas ia kevaetgrkj.

 

RSJ[A@@KJE IA QYKLKIGIAP •

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Al geçlksks @VQ parmkta prjya`tgr lgs utklkigias ia lg amprasg. R.W = F + v.W + Q W=

F + Q R-v

 

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Rgrg al `gsj ia euastrj aoamplj? sk al jcoatkvj ial eanj`kj as jctaear ueg utklkigi ia P/. 0,222.- iurgeta al mas ia Mgrzj ial 3,276 @uçetgs `gmksgs sa

 

tkaeae qua vaeiar :  W = 7,822 + 0,222 82 - 12

 

W = 762 `gmksgs gl mas.

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  “ Cjutkqua Al Vkrray ”   Astgij ia Sasultgijs gl 07 ia Mgrzj ial 3,276  Vaetgs ea  Va eatgs? 76 762 ` `g gmksgs x P/.82 P/.73,822.22 Maejs? Maej s? @jstj vgrkg vgrkgcla? cla? 762 `gmksgs `gmksgs x P/.12 8,222.22 8,222.22 Mgrnae ia `jetrkcu`kðe 9,822.22 Maejs? @jstjs fkojs 7,822.22 Qtklkigi jpargtkvg 0,222.22

 

RQEYJ IA AWQKLKCSKJ [ MA_@LG

 

 

IA VAEYGP Ae lg mgyjr pgrta ia lgs amprasgs sa vaeia mgs ia ue prjiu`tj g pra`kjs ia vaetg ikfaraetas. Giamçs ljs prjiu`tjs sualae taear `jstjs vgrkgclas uektgrkjs ikfaraetas y `gig prjiu`tj jfra`a ueg `jetrkcu`kðe ikstketg g lgs utklkigias. Rarj al puetj

 

ia aquklkcrkj iapaeia ia lg maz`lg ia vaetgs. Lg Maz`lg ia vaetgs as lg `jmckeg`kðe ralgtkvg ia lgs vaetgs aetra ljs ikvarsjs prjiu`tjs qua vaeia ueg amprasg.

 

GRLK@G@KÐE IAL RQEYJ IA AWQKLKCSKJ Vkiaj Ouanjs Dkis, as ueg amprasg qua prjiu`a y vaeia Eketaeijs y Pupar Eketaeijs pgrg ek÷js. Iurgeta al g÷j 3,270 vaeikð 8,222 uekigias ia Eketaeijs y 3,222 uekigias ia Pÿpar Eketaeijs. Lg maz`lg ia vaetgs sa puaia sa axprasgr `jmj pjr`aetgoas? 82% y 32% j `jmj `jm j ueg prjpjr`kðe? 9 g 7. I Rrgat`jksj ia vaEektegtae;i2j.s- Pupar Ek7e9t2a.e-ijs @jstj vgrkgcla > 2 .; 1 .Ljs `jstjs fkojs sje `jmueas pgrg gmcjs prjiu`tjs y gs`kaeiae g P/. 322,222 geugl.

Pa pkia? @gl`ulgr al puetj ia aquklkcrkj `jeskiargeij lg maz`lg ia vaetgs pgrg gmcjs prjiu`tjs

 

  Gplk`geij  Gplk`geij lg fðrmulg fðrmulg ia puetj puetj ia aquklkcrkj aquklkcrkj RW = F + VW  ;2 (9W) + 792W = 322,222 + >2 (9W) + ;1 W  062W + 792 W = 322,222 + 382W + ;1 W 122W ‐ 0>1W   731W

= 322,222 = 322,222

  W* 9W*  

= 7,622 Pÿpar Eketaeijs = 6,922 Eketaeijs

 

APYGIJ IA SAPQLYGIJP IAYGLLA EKEYAEIJ Vaetgs ? 6,922 x ;2 1>6,222 7,622 x 792 Yjtgl Vaetgs @jstjs Vgrkgclas? 6,922 x >2 998,222 7,622 x ;1 Yjtgl @jstj vgrkgc Mgrnae ia @jetrkcu`kðe @jstjs Fkojs Qtklkigi ia jparg`kðe

PQRAS

YJYGL

339,222

1>6,222 339,222 822,222

713,222

998,222 713,222 622,222 322,222 322,222 =.= ======

 

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Pupjengmjs ghjrg qua al jcoatkvj ia lg amprasg as gl`gezgr ueg utklkigi jcoatkvj ia P/. 122,222, ejs pranuetgmjs? º@uçetjs eketaeijs y supar eketaeijs sa taeiríge qua vaeiar :

 

 Gplk`geij lg fðrmulg  Gplk`geij fðrmulg ia puetj puetj ia aquklkcrkj aquklkcrkj RW = F + VW + Q  ;2 (9W) + 792W = 322,222 + >2 (9W) + ;1 W+ 122,222  062W + 792 W = 322,222 + 382W + ;1 W +122,222  122W ‐ 0>1W = >22,222  

731W

= >22,222

  W* 9W*

= 1,622 Pÿpar Eketaeijs = 33,922 Eketaeijs

 

APYGIJ IA SAPQLYGIJP IAYGLLA Vaetgs ? 33,922 x ;2 1,622 x 792 Yjtgl Vaetgs

EKEYAEIJ

PQRAS

3‛276,222

@jstjs Vgrkgclas? 33,922 x >2 7‛168,222 1,622 x ;1 Yjtgl @jstj vgrkgc Mgrnae ia @jetrkcu`kðe @jstjs Fkojs Qtklkigi ia jparg`kðe

>89,222

103,222

YJYGL 3‛276,222 >89,222 3‛822,222 7‛168,222 103,222 3‛722,222 >22,222 322,222 122,222 ======

   

GRGLGE@GMKAEYJ IA JRASG@KÐE Lg maz`lg ralgtkvg ia `jstjs vgrkgclas y `jstjs fkojs ia ueg amprasg sa mkiae pjr al gpglge`gmkaetj gpglge`gmkaetj ia jparg`kðe. jparg`kðe. Asta sa `gl`ulg `jmj sknua? Gpglge`gmkaetj Gpglge`gm kaetj ia jparg`kðe = Mgrnae ia @jetrkcu`kðe @jetrkcu`kðe Qtklkigi ia jparg`kðe @jmj lg ikfarae`kg aetra mgrnae ia `jetrkcu`kðe y lg utklkigi jpargtkvg sje ljs `jstjs fkojs, lgs `jmpg÷ígs `je `jstjs fkojs gltjs tkaeae ue gpglge`gmkaetj ia jparg`kðe gltj. Rjr tgetj lgs amprasgs `je `gpktgl ketaeskvj `jmj lgs garjlíeags y lg gutjmjtrkz, sualae taear ue gpglge`gmkaetj ia jparg`kðe gltj. Qe gpglge`gmkaetj ia jparg`kðe cgoj as ejrmgl pgrg lgs keiustrkgs keiustrkgs `je mgej ia jcrg ketaeskvg. Ljs gimkekstrgijras mkiae al kmpg`tj ia ljs `gmckjs ae lgs vaetgs sjcra al kenrasj ia jparg`kðe maikgeta al nrgij ia gpglge`gmkaetj jpargtkvj. Qe gpglge`gmkaetj gltj keik`g qua ue paqua÷j ke`ramaetj ae vaetgs  prjpjr`  prj pjr`kjegrç kjegrç ue nrge ke`ramae ke`r amaetj tj ae lg utklkigi utklki gi ia jparg`kðe. jpa rg`kðe. Ae `jetrgsta `jetr gsta,, ue gpglge`gmkaetj cgoj keik`g qua as ea`asgrkj ue nrge ke`ramaetj ae lgs vaetgs pgrg gumaetgr ia mgearg sknekfk`gtkvg lg utklkigi jpargtkvg.

 

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Rgrg klustrgr lg utklkigi ia astjs `je`aptjs, `jeskiaramjs al `gsj ia ueg amprasg qua astç plgeageij gnrangr ueg euavg líeag ia prjiu`tjs. Lg amprasg puaia jptgr pjr utklkzgr ue skstamg ia prjiu``kðe gutjmgtkzgij j uej cgsgij ae al usj ketaeskvj ia mgej ia jcrg. Pk sa ia`kia pjr lg gutjmgtkzg`kðe ljs `jstjs fkojs sarçe mçs gltjs y ljs `jstjs vgrkgclas pjr uekigi mgs cgojs. Rgrg ue ekval ia 72,222 uekigias taeamjs lj sknukaeta?

 

 GQYJMGYK@J MGEQGL   MGEQGL    GQYJMGYK@J VAEYGP 7‛222,222 7‛222,222  @JPYJP VGSKGCLAP 122,222 822,222 MGSNAE IA @JEYSKC. 122,222 322,222 @JPYJ FKOJ 0>1,222 722,222 QYKLKIGI JRASGYKVG 731,222 722,222 ======= ====== Rra`kj ia vaetg uektgrkj 722 @jstj vgrkgcla uektgrkj 12 Mgrnae ia `jetrkcu`. Qektgrkj 12

82

722 32

 

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Nrgij ia gpglge`gmkaetj jpargtkvj? Amp. Gutjmgtkzgig = 122,222/731,222   = 9.2 Amp. Mgeugl = 322,222 / 722,222  = 3.2 º Wua pgsg `je lgs utklkigias, sk al vjlumae ia ia vaetgs gumaetg ae 92%. Rgrg geglkzgr tgl sktug`kðe, algcjrgmjs al sknukaeta astgij ia rasultgijs

 

APYGIJ IA SAPQLYGIJP •

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@je`aptj Vaetgs

Gutjmçtk`j Mgeugl 7‛922,222 7‛ 7‛922,222

@jstjs @jst js vgrk vgrkgc gcla las s >22, >22,22 222 2 7‛ 7‛73 732, 2,22 222 2 Mgrna rnae `jet jetrkc rkcu`. >22,22 ,222 382 382,222 ,222 @jstjs fkojs 0>1,222 722,222 Qtklkigi jpargtkvg

031,222 782,222

 

== ==== ==== ==== ==== == ==== ====== ==== ==== ==

 

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Lgs utklkigias ial skstamg gutjmgtkzgij, sa ke`ramaetgríge ae P/. 322,222 , as ia`kr ue gumaetj ial 762% pgrg ue ke`ramaetj ial 92% ae al vjlumae ia vaetgs. ( 92% x 9 ) Ae al skstamg mgeugl, lgs utklkigias gumaetge sjlj P/.82,222, as ia`kr ue ke`ramaetj ia 82% ( 92% x 3 ). Al skstamg gutjmgtkzgij tkaea mgyjr ke`ramaetj pjrqua tkaea ue NGJ mçs gltj.

 

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Al gpglge`gmkaetj jpargtkvj puaia sar muy caeafk`kjsj, ske amcgrnj as ueg aspgig ia ijs fkljs. Ae `gsj ia ueg iksmkeu`kðe ae lgs vaetgs, lgs përikigs sarçe mgyjras ae lg amprasg `je mgyjr NGJ. Al puetj ia aquklkcrkj pgrg al skstamg gutjmgtkzgij as ia >,122 uekigias, mkaetrgs qua pgrg al skstamg mgeugl al puetj ia aquklkcrkj as ia 1,222 uekigias. Al rkasnj jpargtkvj ial skstamg gutjmgtkzgij as mgs gltj.