ul0ft
sIff (
k/LIf0fsf nflu
g]kfn ;/sf/
lzIff, lj1fg tyf kl| jlw dGqfno
kf7o\ jm| d ljsf; s]Gb|
;fgfl] 7dL, eStk'/
ul0ft
sIff (
k/LIf0fsf nflu
g]kfn ;/sf/
lzIff, lj1fg tyf k|ljlw dGqfno
kf7\oj|md ljsf; s]Gb|
;fgf]l7dL, eStk/'
ks| fzs M
g]kfn ;/sf/
lzIff, lj1fg tyf kl| jlw dGqfno
kf7o\ jm| d ljsf; s]Gb|
;fgfl] 7dL, eStk/'
© ;jfl{ wsf/ kf7\ojm| d ljsf; sG] b|
o; kf7\ok':ts;DaGwL ;Dk"0f{ clwsf/ kf7o\ j|md ljsf; s]Gb| ;fgf]l7dL, eStk'/df lglxt
/x]sf] 5 . kf7\ojm| d ljsf; sG] bs| f] lnlvt :jLs[ltlagf Jofkfl/s k|of]hgsf nflu o;sf]
k'/} jf cf+lzs efu x'ax' k|sfzg ug{, kl/jt{g u//] ks| fzg ug{, sg' } ljBt' Lo ;fwg jf
cGo k|ljlwaf6 /]s8{ ug{ / k|ltlnlk lgsfNg kfOg] 5}g .
k/LIf0f ;:+ s/0f M lj=;+ @)&*
d"No ?=
kf7\ok':ts;DaGwL kf7sx¿sf s'g} klg k|sf/sf ;´' fjx¿ ePdf kf7\ojm| d ljsf; s]Gb|,
;dGjo tyf ks| fzg zfvfdf k7fOlbg'x'g cg'/f]w 5 . kf7sx¿af6 cfpg] ;'´fjx¿nfO{
sG] b| xflbs{ :jfut ub5{ .
xfd|f] egfO
lzIffnfO{ p2]Zodn" s, Jofjxfl/s, ;d;fdlos / /fh] uf/d"ns agfpg ljleGg ;dodf kf7\oj|md,
kf7o\ k:' ts ljsf; tyf kl/dfh{g sfon{ fO{ lg/Gt/tf lbObF } cfPsf] 5 . ljBfyL{df 1fgsf] vf]hL u/L
l;sfO / jf:tljs hLjglar ;DaGw :yflkt ug],{ l;4fGt / Jojxf/sf] ;dGjo ug{,] :jk/fjltt{
xF'b} 1fg, l;k / IfdtfnfO{ cBfjlws ug{] ;Ifdtfsf] ljsf; xg' ' cfjZos 5 . ljBfyL{df clwsf/,
:jtGqtf / ;dfgtfsf] k|jw{g ug,{] :j:y hLjgsf] cEof; ug],{ tfls{s ljZn]if0f u/L lg0fo{ ug],{
j}1flgs ljZni] f0fsf cfwf/df JolSt, ;dfh / /fi6«sf] lbuf] ljsf;df ;l/s xg' ] ;Ifdtfsf] ljsf;
klg lzIffn] ugk{' 5{ . ljBfyL{df gl} ts cfr/0f kb| z{g ug,{] ;fdflhs ;b\efjkl| t ;j+ ]bgzLn x'g,]
kofj{ /0fLo ;Gt'ngkl| t ;+jb] gzLn xg' ], åGå Joj:yfkg ub}{ lbuf] zflGtsf nflu kl| ta4 /xg] ;Ifdtfsf]
ljsf; klg dfWolds txsf] lzIffaf6 ck]lIft 5g\ . o; txsf] lzIffaf6 cfw'lgs 1fg, l;k, ;"rgf
tyf ;~rf/ k|ljlwsf] ko| fu] ug{], :jfjnDaL / Joj;fod'vL l;ksf] cEof; ug,{] /fi6«, /fli6o« tf /
/fli6o« cfbzs{ f] ;Ddfg ug],{ ;dfh :jLsfo{ cfr/0f / sfo{ ;:+ sl[ tsf] cjnDag ug{,] ;lxi0f'efj /fVg]
;Ifdtf ePsf] gful/s tof/ ug]{ ckI] ff /x]sf] 5 . To:t}, l;h{gzLn, sNkgfzLn, pBdzLn Pjd\
pRr ;f]r / cfbz{df cfwfl/t Jojxf/ ug]{, ;d;fdlos rg' ft} Lx¿sf] ;kmn Joj:yfkg ugn{] ufotsf
ljzi] ftfn] o'St :jfjnDaL, bz] eSt, kl/jt{gd'vL, lrGtgzLn Pjd\ ;dfjz] L ;dfh lgdf0{ fdf ofu] bfg
ug{ ;Sg] ;Ifdtf;lxtsf] gful/s tof/ ug{' dfWolds lzIffsf] nIo /x]sf] 5 . oxL nIo k"lt{sf
nflu dfWolds lzIffsf] /fli6«o kf7o\ j|md k|f¿k, @)&^ sf] ddc{ g¿' k ljsf; ePsf] dfWolds lzIff
-sIff (–!)_ kf7o\ j|md, @)&& cg';f/ k/LIf0fsf nflu of] gdg' f kf7o\ k:' ts tof/ kfl/Psf] xf] .
o; kf7\ok:' tssf] nv] g >L u0f]zk;| fb ;fksf6] f, >L g/xl/ cfrfo,{ >L zlStk|;fb cfrfo{ /
>L huGgfy clwsf/Laf6 ePsf] xf] . kf7o\ k:' tsnfO{ o; ¿kdf Nofpg] sfo{df o; sG] bs| f
dxflgb{]zs >L c0fk|;fb Gof}kfg,] 8f= /fdhLk;| fb kl08t, >L kl| dnf avtL, >L s]zj/fh km' nf/f,
>L /fd xf8f, >L lgdn{ f uft} d / >L /fdrGb| 9sfnsf] ofu] bfg /xs] f] 5 . o; kf7\ok:' tssf]
efiff ;Dkfbg >L u0f]zk|;fb e66\ /fO{ / lrgfsd' f/L lg/fn} faf6 ePsf] xf] . o;sf] n]cfp6 l8hfOg
>L gj/fh k/' Laf6 ePsf] xf] . pxfxF ¿nufot o;sf] ljsf;df ;+nUg ;Dk"0fk{ |lt sG] b| xflbs{ s[t1tf
ks| 6 ub{5 .
kf7o\ k:' tsnfO{ lzIf0fl;sfOsf] dxŒjk0" f{ ;fwgsf ¿kdf lnOG5 . o;af6 ljBfyLn{ ] kf7\oj|mdåf/f
nlIft ;Ifdtf xfl;n ug{ dbt k'Ug] ck]Iff ul/Psf] 5 . o; kf7o\ k':tsnfO{ ;s];Dd lj|mofsnfkdv' L
/ ?lrs/ agfpg] ko| Tg ul/Psf] 5 . kf7o\ k':tsnfO{ cem} kl/is[t kfgs{ f nflu lzIfs, ljBfyL,{
cleefjs, al' 4hLjL Pjd\ ;Dk0" f{ kf7sx¿sf] ;dt] dxŒjk0" f{ e"ldsf /xg] xFb' f ;Da4 ;a}sf] /rgfTds
;e' mfjsf nflu kf7o\ jm| d ljsf; s]Gb| xflb{s cg/' f]w u5{ .
lj= ;+= @)&* g]kfn ;/sf/
lzIff, lj1fg tyf k|ljlw dGqfno
kf7o\ j|md ljsf; s]Gb|
ljifo;r" L
kf7 zLif{s k[i7;ªV\ of
! ;d"x ! – !@
@ s/ !# – #!
# sldzg / nfef+z #@ – $!
$ 3/fo;L cªs\ ul0ft $@ – ^@
% Ifq] kmn ^# – *!
^ lk|Hd *@ – ($
& jn] gf / ufn] f (% – !@#
* v08Ls/0f !@$ – !#&
( dxQd ;dfkjts{ / n3Q' d ;dfkjTo{ !#* – !%%
!) /]vLo ;dLs/0f !%^ – !&%
!! 3ftfª\s !&^ – !()
!@ lqe'h !(! – @!^
!# rte' 'h{ @!& – @@&
!$ /rgf @@* – @#$
!% j[Q @#% – @$^
!^ tYofª\ssf] juL{s/0f / k|:tt' Ls/0f @$& – @^^
!& s]Gb|Lo kj| l[ Qsf] dfkg @^& – @*&
!* ;DefJotf @** – #)!
!( lqsf]0fldlt #)@ – #!*
kf7 1 ;d"x (Sets)
1.0 k'g/jnf]sg (Review)
sIff ( sf rf/ hgf ljBfyL{x¿;uF pgLx¿sf] v]taf/Ldf nufOPsf afnLgfnLx¿sf] af/d] f
5nkmn ubf{ o;k|sf/ hfgsf/L k|fKt eof] M
-s_ PGhnsf] v]taf/Ldf nufPsf afnLx¿ M wfg, ux,'F sf]bf], tf/] L, sfpnL, s]/fp, /fof]
-v_ ladnfsf] vt] af/Ldf nufPsf afnLx¿ M ux',F kmfk/, tf/] L, ufn] e]8f, eG6f, v;' f{gL, hf,}
cfn', l;dL
-u_ kD] afsf] vt] af/Ldf nufPsf afnLx¿ M kmfk/, hf,} cfn', l;dL, ds}
-3_ /fdljnf;sf] vt] af/Ldf nufPsf afnLx¿ M ux,F' tf]/L, wfg ds}, s]/f, pv', aGbf
dflysf tYox¿sf] cfwf/df tnsf k|Zgx¿sf] pQ/ vf]Hgx' f];\ M
dflysf k|Tos] tYox¿nfO{ ;r" Ls/0f lalwaf6 n]Vgx' f;] \ .
PGhnsf] vt] af/Ldf / kD] afsf] vt] af/Ldf nufOPsf afnLsf ;d"xx¿ s:Tff ;dx"
xf]nfg\ <
ladnfsf] v]taf/Ldf nufOPsf afnL / /fdljnf;sf] vt] af/Ldf nufPsf afnLsf ;d"xx¿
s:tf ;dx" x¿ xfn] fg\ <
ladnfsf] v]taf/Ldf / PGhnsf] v]taf/Ldf nufOPsf afnLsf ;dx" x¿ s:tf ;d"xx¿
xfn] fg\ <
kD] afsf] vt] af/Lsf afNfLaf6 lgDgfg;' f/ pk;dx" x¿ lgdf{0f ug'{xf];\ / s:tf ;d"x eP
nV] gx' f;] \ .
— cGgafnLsf] ;d"x
— kmnkm"nsf] ;dx"
— t/sf/Lsf] ;d"x
;d"xdf dflysf k|Zgx¿df 5nkmn u/L lgisif{nfO{ sIffdf k|:t't ug'x{ f];\ .
ul0ft, sIff ( 1
1.1 ;d"xsf lj|mofx¿ (Operation of Sets)
ljm| ofsnfk 1
b'O{ bO' { hgfsf] ;d"xdf kT| os] n] km/s km/s /ªsf km"nx¿ ;ªs\ ng ug{'xf];\ / hDdf u/s] f
km"nsf /ªcg';f/ ;dx" x¿ lgdf0{ f ug{x' f;] \, h:t}, ;l' ko| fn] hDdf u/s] f kmn" sf /ªx¿sf] ;d"x
= {/ftf,] kx]nF f,] lgnf,] u'nfaL }
PlGhnfn] hDdf u/s] f km"nsf /ªx¿sf] ;dx" = {kxFn] f], ;]tf], lgnf], KofhL, ;'Gtnf, /ftf}]
dflysf ;d"xx¿sf cfwf/df tnsf ;dx" x¿ lgdf{0f ug{x' f;] \ M
-s_ ;l' ko| f cyjf PlGhnf jf bj' n} ] ;ª\sng u/]sf kmn" sf /ªx¿sf] ;d"x
-v_ ;l' k|of / PlGhnfn] b'j}n] ;ªs\ ng u/]sf km"nsf ;femf /ªx¿sf ;dx"
-u_ PlGhnfn] dfq ;ª\sng u/]sf kmn" sf /ªx¿sf] ;dx"
o;/L lgdf0{ f ul/Psf ;d"xx¿ s:tf ;dx" x¿ xf]nfg\ <
1.1.1 ;dx" x¿sf] ;+ofh] g (Union of Sets)
dflysf] ;dx" x¿df, U
;l' k|ofn] hDdf u/s] f km"nsf /ªx¿sf] ;d"x = {/ftf,]
kxFn] f,] lgnf], un' fjL}
PGhLnfn] hDdf u/]sf km"nsf /ªx¿sf] ;d"x = {kxn]F f,] /ftf] ;]tf]
;]tf], lgnf], KofhL, ;G' tnf, /ftf]} un' faL] kx]Fnf] KofhL
b'j}n] hDdf u/]sf km"nsf /ªx¿sf] ;dx" = {/ftf], kxnF] f,]
lgnf] ;'Gtnf
lgnf], un' fjL, ;t] f], KofhL, ;'Gtnf}
o;/L b'jn} ] hDdf u/]sf] /ªx¿sf] ;dx" nfO{ bj' }n] cnu
cnu ;ªsng u/]sf] kmn" sf /ªx¿sf] ;dx" sf] ;+of]hg elgG5 .
olb A / B ;j{Jofks ;dx" U sf pk;d"x ePdf U
;d"xx¿ A / B sf] ;+ofh] g nfO{ A B n] hgfOG5 . A B
A B df ;dx" A df kg]{ jf ;d"x B df kg]{ jf bj' }df
kg{] ;b:ox¿ k5g{ \ .
;dx" lgdf0{ f ljlw cg;' f/ A B = {x : x ∈ A jf
x ∈ B} n]lvG5 . lbOPsf] eg] lrqdf 5fof kfl/Psf]
efun] A B nfO{ hgfpF5 .
;d"xsf] ;o+ f]hg ubf{ b'j} ;d"xsf ;a} ;b:ox¿nfO{
gbf]xf¥] ofOs{ g lnP/ ;d"xsf] ¿kdf n]Vg'k5{ .
2 ul0ft, sIff (
pbfx/0f 1
olb P = 20 eGbf ;fgf 3 sf ckjTo{x¿sf] ;d"x / Q = 20 eGbf ;fgf 2 sf ckjTo{x¿sf] ;d"x xg' \
eg] P Q kQf nufO{ e]glrqdf k|:t't ug'x{ f];\ .
;dfwfg P U
oxfF, P = 20 eGbf ;fgf 3 sf ckjTo{x¿sf] ;dx" = {3, 6, 9, Q
12, 15, 18}, Q = 20 eGbf ;fgf 2 sf ckjTox{ ¿sf] 3 9 12 6 12 4
;dx" = {2, 4, 6, 8, 10, 12, 14, 16, 18} 15 18 16 2
P Q = {x : x ∈ P jf x ∈ Q} = {2, 3, 4, 6, 8, 9, 10, 14 8
12, 14, 15, 16, 18}
eg] lrqdf 5fof kf/]sf] efun] P Q nfO{ hgfpF5 .
pbfx/0f 2
olb A = {ux'F, kmfk/, tf/] L, uf]neF8] f, eG6f, v;' f{gL, hf,} cfn', l;dL} / B = {kmfk/, hf,} cfn,'
l;dL} A B kQf nufO{ eg] lrqdf k|:t't ugx'{ f];\ .
;dfwfg U
oxfF, A = {uxF,' kmfk/, tf/] L, uf]ne]8F f, eG6f, v;' f{gL, hf,}
v;' fg{ L A
cfn', l;dL}
B
B = {kmfk/, hf}, cfn', l;dL}
kmfk/
A B = {x : x ∈ A jf x ∈ B} = {uxF', kmfk/, tf]/L,
ufn] eF8] f, eG6f, v';f{gL, hf,} cfn,' l;dL} = A hf}
cfn' eG6f
;Fus} f] eg] lrqdf 5fof kf/]sf] efun] A B nfO{ uxF'
hgfp5F . l;dL
tf]/L uf]ne8F] f
ljm| ofsnfk 2
olb b'O{cf]6f ;d"x cfk;df cnlUuPsf 5g\ eg] Tof] cj:yfdf ltgLx¿sf] ;o+ fh] g s] xfn] f <
cfk;df 5nkmn u/L e]glrq;d]t agfP/ k|:t't ugx{' f];\ .
gf]6M bO' { ;dx" dWo] Pp6f ;dx" csf]{ ;d"xsf] pk;d"x 5 eg] ltgLx¿sf] ;o+ fh] g 7n' f] ;d"x
g} x'G5 . olb b'O{cf]6f ;d"x cfk;df cnluPsf 5g\ eg] ltgLx¿sf] ;+ofh] g tL ;d"xsf
;a} ;b:ox¿ ldn]/ ag]sf] ;d"x xG' 5 .
ul0ft, sIff ( 3
1.1.2 ;d"xsf] k|ltR5]bg (Intersection of Sets)
sIff 9 sf ljBfyLd{ Wo] lj1fg dg k/fpg] / ul0ft dg U
k/fpg] ljBfyLx{ ¿ lgDgfg;' f/ /x]5g\ M lj1fg ul0ft
lj1fg dg k/fpg] ljBfyL { = {/fd, l;tf, kD] af, /fd xl/
tl] Ghª, l8gf, k]Daf l;tf d~h'
ljgo} t]lGhª l8gf 8fN] df
ljgo vftg'
ul0ft dg k/fpg] ljBfyLx{ ¿ = {x/L, l;tf, d~h',
8f]Ndf, l8gf, vft'g}
dflysf ;dx" nfO{ e]glrqdf k|:tt' ubf{,
;uF s} f] eg] lrqdf lj1fg / ul0ft bj' } dg k/fpg] ljBfyL{sf] ;dx" {l;tf, l8gf} xf] . of] g} lj1fg
dg k/fpg] / ul0ft dg k/fpg] ljBfyLs{ f ;dx" sf] kl| tR5b] g (intersection) xf] .
olb A / B b'Oc{ f]6f vfnL ;dx" x¿ gePdf A / B bj' } A U
;d"xsf ;femf ;b:ox¿af6 ag]sf] ;d"xnfO{ ;d"x A / B
sf] kl| tR5]bg elgG5, o;nfO{ A B n] hgfOG5 . B
;dx" lgdf0{ f ljlwcg';f/ A B = {x : x ∈ A / x ∈
B} nl] vG5 .
o;nfO{ eg] lrqsf] k|of]u u/L lgDgfg;' f/ b]vfpg ;lsG5 . ;uF s} f] e]glrqdf 5fof kf/]sf]
efun] ;dx" A / B sf] kl| tR5]bg hgfpF5 .
pbfx/0f 3
olb P = 20 eGbf ;fgf 3 sf ckjTox{ ¿sf] ;d"x / Q = 20 eGbf ;fgf 2 sf ckjTox{ ¿sf ;dx" xg' \
eg] ;d"x P Q kQf nufO{ eg] lrqdf k|:t't ug'{xf;] \ .
;dfwfg
oxfF, P = 20 eGbf ;fgf 3 sf ckjTox{ ¿sf ;d"x = {3, 6, U
9, 12, 15, 18} P Q
Q = 20 eGbf ;fgf 2 sf ckjTo{x¿sf ;d"x = {2, 4, 39 12 4
15 10
6, 8, 10, 12, 14, 16, 18} 6 2 16
18
ca, P Q = {x : x ∈ P / x ∈ Q} = {6, 12, 18} 8
14
;uF }sf] eg] lrqdf 5fof kf/s] f] efun] P Q nfO{ hgfp5F .
4 ul0ft, sIff (
pbfx/0f 4
olb A = 20 eGbf ;fgf 2 sf ckjTo{x¿sf ;d"x / B = 20 eGbf ;fgf 4 sf ckjTo{x¿sf ;d"x xg' \
eg] A B kQf nufO{ e]glrqdf k:| tt' ugx'{ f;] \ .
;dfwfg
oxfF, A = 20 eGbf ;fgf 2 sf ckjTo{x¿sf ;dx" = {2, 4, 6, 8, U
6A
10, 12, 14, 16, 18}
B = 20 eGbf ;fgf 4 sf ckjTox{ ¿sf ;d"x = {4, 8, 12, 4 8B
12 16 10
16} 2
A B = {x : x ∈ A / x ∈ B} = ;dx" A / ;d"x B df ePsf ;femf 18 14
;b:ox¿sf] ;d"x = {4, 8, 12, 16}
e]glrqdf 5fof kf/]sf] efun] A B nfO{ hgfp5F .
ljm| ofsnfk 3
olb bO' c{ f]6f ;d"x cfk;df cnlUuPsf 5g\ eg] Tof] cj:yfdf ltgLx¿sf] kl| tR5b] g
s] xfn] f < cfk;df 5nkmn u/L k:| tt' ug'{xf;] \ .
gf6] M b'O{ ;d"xdWo] Pp6f ;d"x csf]{ ;d"xsf] pk;d"x 5 eg] ltgLx¿sf]
k|ltR5]bg pk;dx" g} xG' 5 . olb b'Oc{ f6] f ;dx" cfk;df cnlUuPsf 5g\ eg] ltgLx¿sf
kl| tR5b] g vfnL ;d"x x'G5 .
1.1.3 ;dx" x¿sf] km/s (Difference of Sets)
lj|mofsnfk 4 U
;Fu}sf] eg] lrqsf] cWoog ug'x{ f];\ M lj1fg ul0ft
lj1fg dg k/fpg] ljBfyL{ = {/fd, ;Ltf, kD] af, /fd xl/
t]lGhª, l8gf, ljgo} k]Daf l;tf d~h'
ul0ft dg k/fpg] ljBfyL{ = {xl/, ;Ltf, d~h', tl] Ghª l8gf 8fN] df
8fN] df, l8gf, vft'g} ljgo vft'g
lj1fg dfq dg k/fpg] ljBfyLs{ f] ;d"x / ul0ft dfq dg
k/fpg] ljBfyLs{ f] ;dx" nV] g'xf];\ .
oxfF ul0ftdfq dg k/fpg]n] lj1fg dg k/fpFb}gg\ . t;y{ o;nfO{ ul0ft dg k/fpg] / lj1fg dg
k/fpg] ;d"xsf] km/s elgG5 .
To:t} lj1fgdfq dg k/fpg] ljBfyLs{ f] ;d"x eGgfn] lj1fg dg k/fpg] ;dx" / ul0ft dg
k/fpg]sf] km/s eGg] a'lemG5 .
ul0ft, sIff ( 5
olb ;dx" A / ;dx" B ;j{Jofks ;dx" U sf pk;d"xx¿ x'g\ eg] ;d"x A df kg{] t/
;d"x B df gkg]{ ;dx" A sf ;b:ox¿sf] ;d"xnfO{ A / B sf] km/s (A difference
B) elgG5, o;nfO{ A – B nl] vG5 / k9\bf A / B sf] km/s cyjf A difference B
eg/] kl9G5 . o;/L g} ;d"x B df dfq kg]{ ;b:ox¿sf] ;dx" nfO{ B / A sf] km/s cyjf
B difference A elgG5 . o;nfO{ B – A n]lvG5 / k9\bf B / A sf] km/s cyjf B
difference A eg/] kl9G5 . ;d"x lgdf0{ f ljlw (Set Builder Method) cg;' f/,
A – B = {x : x ∈ A / x ∉ B} / B – A = {x : x ∈ B / x ∉ A} nl] vG5 .
e]glrqdf A km/s B / B km/s A -v_ U
A B
-s_ U
(B – A)
A B
(A – B)
(B – A)
-u_ U -3_ U
BA AB
(A – B) (B – A)
-ª_ A=B U
(A – B) (B – A)
gf6] M (A – B) / (B – A) sf] ;+of]hgnfO{ ;dldtLo km/s (Symmetric diference)
elgG5 . o;nfO{ A ∆ B n] hgfOG5 / A ∆ B = (A – B) (B – A) n]lvG5 .
6 ul0ft, sIff (
pbfx/0f 5
lbOPsf] e]glrqaf6 lgDglnlvt ;dx" x¿nfO{ ;r" Ls/0f ljlwaf6 n]Vg'xf;] \ .
-s_ A -v_ B -u_ A – B -3_ B – A
;dfwfg U
oxfF
-s_ A = {1, 3, 5, 7, 9} A B
-v_ B = {6, 7, 8, 9, 10} 56
-u_ A — B = {1, 3, 5}
3 79 10
-3_ B — A = {6, 8, 10} 1 8
2 4
pbfx/0f 6
olb U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5} / B = {4, 5, 6, 7, 8, 9, 10} eP
A — B / B — A kQf nufO{ eg] lrqdf 5fof kf/]/ k:| tt' ug{'xf];\ .
;dfwfg U
(B – A)
oxf F A – B = {1, 2, 3, 4, 5} A B
− {4, 5, 6, 7, 8, 9, 10} 6
1 7
8
= {1, 2, 3} / B – A (A – B) 2 4 9
3 5
= {4, 5, 6, 7, 8, 9,
10} – {1, 2, 3, 4, 10
5}
= {6, 7, 8, 9, 10}
;uF }sf] e]glrqdf A − B / B − A nfO{ 5fof kf/]/ bv] fOPsf] 5 .
gf6] M ;fdfGotof A − B ≠ B − A xG' 5 .
pbfx/0f 7
olb U = {x : x ≤ 30, x n] kf| sl[ ts ;ª\Vof hgfpF5},
A = {x : x n] 15 eGbf 7'nf] / 30 eGbf ;fgf] kf| sl[ ts ;ªV\ of hgfp5F } /
B = {x : x n] 1 b]lv 15 ;Ddsf] kf| s[lts ;ª\Vof hgfp5F } eg] A − B / B − A kQf nufpg'xf];\ .
ul0ft, sIff ( 7
;dfwfg
oxfF, U = {1, 2, 3, 4, ..., 28, 29, 30}
A = {16, 17, 18, ..., 27, 28, 29} /
B = {1, 2, 3, 4, ..., 13, 14, 15}
t;y,{
A − B = {16, 17, 18, ..., 27, 28, 29} – {1, 2, 3, 4, ..., 13, 14, 15}
= {16, 17, 18, ..., 27, 28, 29} = A /
B − A = {1, 2, 3, 4, ..., 13, 14, 15} – {16, 17, 18, ..., 27, 28, 29}
= {1, 2, 3, 4, ..., 13, 14, 15} = B
olb A / B cnlUuPsf (disjoint) ;d"xx¿ ePdf A – B = A / B – A = B g} xG' 5 .
1.1.4 ;dx" sf] k'/s (Complement of a Set)
dfgfF} ;d"x A sg' } ;j{Jofks ;d"x U sf] pk;d"x xf] . U
hxfF ;dx" A df eGbf ;dx" U df A sf ;lxt sx] L yk A
;b:ox¿ 5g\ . o:tf ;j{Jofks ;d"x U df dfq x'g]
t/ ;dx" A df gxg' ] ;b:ox¿sf] ;dx" nfO{ ;d"x A sf] U
k/" s ;dx" (Complement of Set A) elgG5 . o;nfO{
A' cyjf A cyjf Ac åf/f hgfOG5 . AA
csf]{ zAbdf sg' } ;jJ{ ofks ;dx" U / To;sf] pk;d"x A sf] km/s (difference) nfO{ Tof]
pk;dx" A sf] k/" s elgG5 . o;nfO{ ;ªs\ ]tdf A' = U − A nl] vG5 .
;d"x lgdf{0f ljlwcg;' f/,
A' = { x : x ∈ U t/ x ∉ A} n]lvG5 .
A' nfO{ e]glrqdf ;uF s} f] lrqdf h:t} 5fof kf//] b]vfpg ;lsG5 .
gf]6 M oxfF A / A' sf] ;+ofh] g hlxn] klg U x'G5 . ctM A / A' nfO{ Ps csfs{ f k/" s elgG5 .
cyf{t\ A sf] k/" s A' / A' sf] k"/s A x'G5 . A A' = U / (A')' = A
A A' s] xf]nf < ;dx" df 5nkmn u/L n]Vg'xf;] \ .
8 ul0ft, sIff (
pbfx/0f 8
olb U = {1, 2, 3, ..., 18, 19, 20}, A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} / B = {2, 4, 6,
8, 10, 12, 14, 16, 18, 20} eP lgDglnlvt ;dx" x¿sf ;b:ox¿sf] ;r" L tof/ kfg{x' f];\ .
-s_ A' -v_ B' -u_ A' B' -3_ A' B'
;dfwfg
oxfF, U = {1, 2, 3, ..., 18, 19, 20}
A = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
-s_ A' = U – A = {1, 2, 3, ..., 18, 19, 20} − {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} = B
-v_ B' = U – B= {1,2,3, ... ,18,19,20} – {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
= {1, 3, 5, 7, 9, 11, 13, 15, 17, 19} = A {1, 3, 5, 7, 9, 11, 13, 15, 17,
-u_ A' ∪ B' = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
19}
= {1, 2, 3, 4, ..., 18, 19, 20} = U
-3_ A' B' = {2, 4, 6, 10, 12, 14, 16, 18, 20} {1, 3, 5, 7, 9, 11, 15, 17, 19} = { }
pbfx/0f 9
olb U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} / A = {1, 3, 5, 7, 9} eP lgDglnlvt ;dx" x¿sf
;b:ox¿ ;"rLs/0f ljlwaf6 n]Vgx' f];\ M
-s_ A' -v_ A ∪ A' -u_ A A' -3_ A''
;dfwfg
oxfF U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} / A = {1, 3, 5, 7, 9}
-s_ A' = U − A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {1, 3, 5, 7, 9}
= {2, 4, 6, 8, 10}
-v_ A ∪ A' = {1, 3, 5, 7, 9} ∪ {2, 4, 6, 8, 10} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} = U
-u_ A ∩ A' = {1, 3, 5, 7, 9} ∩ {2, 4, 6, 8, 10} = φ
ul0ft, sIff ( 9
-3_ A'' = (A')' = U − A'
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {2, 4, 6, 8, 10}
= {1, 3, 5, 7, 9}= A
t;y{, A ∪ A' = U / A ∩ A' = φ
cEof; 1
1. lbOPsf] eg] lrqdf Fn] km6' an dg k/fpg] / V n] elnan U
dg k/fpg] ljBfyLs{ f] ;d"x hgfp5F g\ . e]glrqsf] FV
cWoog u/L lgDgfg';f/sf ;d"xx¿nfO{ ;"rLs/0f
ljlwaf6 nV] g'xf];\ M l5l/ª dfof af6'nL
bfh] ]{ cfzf 8f]Ndf
-s_ F -v_ V -u_ F ∪ V -3_ F ∩ V xl/ u0f]z ;G' tnL
2. olb U = {a, b, c, d, e, f, g, h, i, j, k}, A = {a, /fdaxfb'/ xs{;'Gb/
c, e, f, g, i, k} / B = {b, d, i, j, k, h} eP lgDg
;d"xsf ;b:ox¿ kQf nufO{ e]glrqdf k|:t't ug{'xf];\ M
-s_ (A ∩ B) -v_ (B ∪ A) -u_ A — B -3_ B — A
3. olb U = {x : x n] 1 b]lv 30 ;Ddsf k0" f{ ;Vof hgfp5F }, A = {x : x n] 1 bl] v 30 ;Ddsf 3
sf] ckjTo{ hgfp5F } / B = {x : x n] 1 b]lv 30 ;Ddsf 4 sf] ckjTo{ hgfpF5} / C ={x : x
n] 1 bl] v 30 ;Ddsf 5 sf] ckjTo{ hgfp5F } eg] lgDglnlvt ;dx" x¿nfO{ ;"rLs/0f ljlwaf6
n]Vgx' f];\ / e]glrqdf b]vfpgx' f];\ .
-s_ (A — B) -v_ (B — A) -u_ (A — C)
-3_ (B — C) -ª_ (A ∪ B)
4. olb U = {a, b, c, d, e, f, g, h, i, j, k }, A = { a, c, d, f }, B = { g, h, i} eP,
-s_ lgDg ;dx" x¿ lgdf0{ f ug{'xf;] \ M
(i) A (ii) B (iii) A ∪ B
(iv) A ∩ B (v) A ∪ B (vi) A ∩ B
-v_ k|Zg g= -s_ df agfOPsf ;d"xx¿ s'g sg' a/fa/ ;d"xx¿ xG' 5g,\ kQf nufpgx' f];\ .
5. olb U = {1 bl] v 12 ;Ddsf k"0ffª{ s\ x¿sf] ;d"x}, P = {1 bl] v 12 ;Ddsf hf/] ;ªV\ ofx¿sf]
;dx" } Q = {1 bl] v 12 ;Ddsf lahf]/ ;ªV\ ofx¿sf] ;dx" } / R = {1 bl] v 12 ;Ddsf ¿9
;ªV\ ofx¿sf] ;d"x} eP lgDglnlvt ;dx" x¿ kQf nufO{ eg] lrqdf k:| t't ug{'xf];\ M
-s_ P -v_ Q -u_ R -3_ (P ∪ R )
-ª_ P ∩ Q -5_ R=
-r_ P – Q
10 ul0ft, sIff (
6. tn lbPsf eg] lrqx¿df 5fof kfl/Psf] efun] s'g ;dx" hgfpF5, ;ªs\ t] df pQ/
nV] g'xf;] \ M
UU UU
A B A B A B A
7. olb P / Q ;jJ{ ofks ;dx" U sf k|ltR5l] bt pk;d"xx¿ eP lgDglnlvt ;d"xx¿nfO{
e]glrqdf b]vfpg'xf];\ M
-s_ P — Q -v_ Q − P -u_ (P — Q) ∪ P -3_ P ∩ (Q — P)
8. s'g} Pp6f ;j{Jofks ;dx" U / To;sf b'O{cf]6f pk;d"xx¿ X / Y agfpgx' f];\ . To;kl5
lgDglnlvt ;dx" x¿nfO{ ;"rLs/0f ljlwaf6 n]Vgx' f;] \ M
-s_ -v_ (X ∩ Y)' -u_
9. tkfOF{ k9\g] sIffdf ePsf ljBfyL{af6 lgDglnvt ;dx" x¿ agfpg'xf;] \ M
-s_ ;a} ljBfyL{sf] ;dx"
-v_ 5fqx¿sf] ;d"x /
-u_ 5fqfx¿sf] ;dx" .
oL ;d"xx¿dWo] sg' ;d"x ;jJ{ ofks ;d"x / sg' sg' ;dx" x¿ o;sf pk;d"x x'g\ < pko'St
;ªs\ ]t;lxt nV] g'xf];\ . To;kl5 oL ;a} ;dx" x¿sf k"/s ;d"xx¿ lgsfNg'xf];\ .
kl/of]hgf sfo{
:ofp / ;G' tnfdWo] tkfOFn{ fO{ sg' kmnkmn" dgk5{ egL sDtLdf 20 hgf dflg;nfO{
;f]Wgx' f];\ . :ofp dg k/fpg] dflg;x¿sf] ;dx" nfO{ A / ;'Gtnf dg k/fpg] dflg;x¿sf]
;dx" nfO{ O n] hgfpgx' f];\ . kf| Kt pQ/cg;' f/ :ofp dg k/fpg], ;'Gtnf dg k/fpg,] b'j}
kmn dg k/fpg] tyf :ofp / ;G' tnf s'g} klg kmnkmn" dg gk/fpg] dflg;x¿sf] gfdnfO{
;d"x ;ªs\ ]tdf nV] g'xf];\ / pSt hfgsf/Laf6 tnsf ;d"xx¿ lgdf{0f u/L eg] lrqdf k|:t't
ugx'{ f;] \ .
(i) A (ii) O (iii) A ∪ O (iv) A
(v) A − O (vi) O − A (vii) (O − A) ∪ ( A – O )
ul0ft, sIff ( 11
pQ/
1. -s_ {l5l/ª, bf]h]{, xl/, dfof, cfzf, u0fz] }
-v_ {af6'nL, 8fN] df, ;G' tnL, dfof, cfzf, u0fz] }
-u_ {l5l/ª, bfh] ,{] xl/, af6n' L, 8f]Ndf, ;'GtnL, dfof, cfzf, u0fz] }
-3_ {dfof, cfzf, u0fz] }
2. -s_ {i, k} -v_ U u_ {a, c, e, f, g} -3_ {b, d, j, h}
-ª_ φ / eg] lrqx¿ lzIfsnfO{ b]vfpg'xf];\ .
3. -s_ {3, 6, 9, 15, 18, 21, 27, 30} -v_ {4, 8, 16, 20, 28}
-u_ {3, 6, 9, 12, 18, 21, 24, 27} -3_ {4, 8, 12, 16, 24, 28}
-ª_ {3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21, 24, 27, 28, 30}, e]glrqx¿
lzIfsnfO{ b]vfpgx' f;] \ .
4. (i) { b, e, g, h, i, j, k } (ii){a, b, c, d, e, f, j, k }
(iii) {a, b, c, d, e, f, g, h, i, j, k }
(iv) {b, e, j, k} (v) {b, e, j, k} (vi) U
5. -s_ {1, 3, 5, 7, 9, 11} -v_ {2, 4, 6, 8, 10, 12}
-u_ {1, 4, 6, 8, 9, 10, 12} -3_ {1, 9}
-ª_ U -r_ Q -5_ {2, 3, 5, 7, 11}
6. -s_ (A − B) -v_ (B − A) -u_ B -3_ A
7-10 lzIfsnfO{ bv] fpg'xf];\ .
12 ul0ft, sIff (
kf7 2 s/ (Tax)
2.0 k'g/jnf]sg (Review)
ljBfyLx{ ¿ pko'St ;d"xx¿df a;L tnsf cj:yfx¿sf af/d] f 5nkmn ug{x' f;] \ M
-s_ ljzfnn] cfˆgf] dfl;s tnadf 1% 36fP/ kfP .
-v_ ;Ltfn] Pp6f df]afOn lsGbf 13% yk /sd ltl/g\ .
-u_ Pp6f pBf]un] cfkm"n] jif{el/ sdfPsf] s]xL kl| tzt /sd ;/sf/nfO{ a'emfof] .
-3_ kw| fgfWofksn] Pp6f sfo{j|mdsf] bl} gs a}7s eQf ?= 600 dWo] hDdf ?= 510 dfq
kf| Kt ug{'eof] .
-ª_ zlStn] cfˆgf] df]6/;fOsnsf] An'as' gjLs/0f ubf{ ?= 100 lt/] .
dflysf ;a} cj:yfx¿df s6\6L ul/Psf /sdx¿nfO{ s/x¿ elgG5 . km/s km/s zLif{ssf
km/s km/s b/df s/ tfl] sPsf] x'G5 .
2.1 s/ (Tax)
lj|mofsnfk 1
xfd|f] bz] df kT| o]s cfly{s jif{sf] ;'?df k:| tt' ul/g] ah]6 jStJodf ;dfjz] ul/Psf] s/;DaGwL
Joj:yfnfO{ cfwf/ dfgL lgDglnlvt kZ| gx¿df ;fyLx¿lar 5nkmn ug{'xf];\ M
-s_ ;/sf/n] /fHosf] k|zf;lgs vr{, ljsf; vr{ s;/L h'6fpF5 xf]nf <
-v_ ;/sf/n] /fi6«;]js sd{rf/Lx¿nfO{ lbg] tna eQf s;/L Joj:yfkg u5{ xf]nf <
-u_ ufpF 6f]ndf jif}{lkR5] ljsf; lgdf{0fsf sfdx¿ h:t} M vfg]kfgL 6\ofª\sL lgdf{0f
tyf dd{t, ;8s lgdf0{ f tyf :t/fG] glt, l;kd"ns sfoj{ |mdx¿ cflbsf nflu ah6]
lgsf;f xg' ] u/s] f] ;'Gge' Ps} xf]nf, o:tf vrx{ ¿ sxfFaf6 h'6fOG5 <
ul0ft, sIff ( 13
s/ eg]sf] sg' } JolSt, kmd{ jf sDkgLn] sfg'gadf]lhd ;/sf/nfO{ ltg{k' g{] clgjfo{ eS' tfgL
xf] . /fHosf] cfDbfgLsf] dV' o ;f| t] s/ xf] . ;/sf/n] bz] sf] lgoldt, cfsl:ds /
ljsf;fTds ultljlw oxL s/sf dfWodaf6 k|fKt xg' ] cfDbfgLcg;' f/ ;~rfng u/]sf] xG' 5 .
To;n} ] xfdL ;a}n] clgjfo{ ?kdf s/ ltg{'k5{ . s/ ltg'{ c;n gful/ssf] st{Jo k/" f ug{'
xf] . gk] fndf kr| ngdf /x]sf s/x¿df ;jf/L s/, 3/axfn s/, eG;f/ dx;'n, cfos/,
d"No clejl[ 4 s/, ;DklQ s/, ;fdflhs ;/' Iff s/ cflb xg' \ . s/nfO{ k|ltzt (%) df
JoSt ul/G5 .
pbfx/0f M ljb]z cWoog ug{ hfg] ljBfyL{x¿n] d'b|f ;6xL ;'ljwf lbFbf ;6xL /sddf 1% s/
nfU5 .
2.1.1 cfos/ (Income Tax)
ljm| ofsnfk 2
tn lbOPsf cfos/ ;Ldf / kZ| gx¿sf ;DaGwdf cfˆgf ;fyLx¿lardf ;dx" df 5nkmn
ugx{' f;] \ / sIffsf]7fdf lgisif{ k|:tt' ugx'{ f];\ M
cfo jif{ 2077/78 sf nflu -gjf}F s/ lbj; ljzi] ffªs\ 2077 cg;' f/_
/f]huf/Lsf] cfo dfq x'g]sf nflu
Psn JolStsf nflu bDktLsf nflu
zLifs{ s/ kl| tzt zLif{s s/ k|ltzt
?= 4 nfv;Ddsf] cfodf 1% ?= 4 nfv 50 1%
xhf/;Ddsf] cfodf
4 nfveGbf a9L t/ 5 10% 4 nfv 50 xhf/eGbf 10%
nfv;Ddsf] cfodf a9L t/ 5 nfv 50
xhf/;Ddsf] cfodf
5 nfveGbf a9L t/ 7 20% 5 nfv 50 xhf/eGbf 20%
nfv;Ddsf] cfodf
a9L t/ 7 nfv 50
xhf/;Ddsf] cfodf
7 nfveGbf a9L t/ 20 30% 7 nfv 50 xhf/eGbf 30%
nfv;Ddsf] cfodf a9L t/ 20 nfv;Ddsf]
cfodf
20 nfveGbf a9Lsf] cfodf 36% 20 nfveGbf a9Lsf] 36%
cfodf
14 ul0ft, sIff (
Psnf}6L kmds{ f ¿kdf Joj;fo dfq xg' s] f nflu
Psn JolStsf nflu bDktLsf nflu
zLif{s s/ kl| tzt zLif{s s/ kl| tzt
?= 4 nfv;Ddsf] cfodf s/ gnfUg] ?= 4 nfv 50 xhf/;Ddsf] s/ gnfUg]
cfodf
4 nfveGbf a9L t/ 5 10% 4 nfv 50 xhf/eGbf a9L t/ 10%
nfv;Ddsf] cfodf 5 nfv 50 xhf/;Ddsf] cfodf 20%
30%
5 nfveGbf a9L t/ 7 20% 5 nfv 50 xhf/eGbf a9L t/ 36%
nfv;Ddsf] cfodf 7 nfv 50 xhf/;Ddsf] cfodf
7 nfveGbf a9L t/ 20 30% 7 nfv 50 xhf/eGbf a9L t/
nfv;Ddsf] cfodf 20 nfv;Ddsf] cfodf
20 nfveGbf a9Lsf] cfodf 36% 20 nfveGbf a9Lsf] cfodf
-s_ cfos/ egs] f] s] xf] <
-v_ sfgg' agfP/ xfdf| ] cfDbfgLdWo] lglZrt kl| tzt /sd ;/sf/n] p7fp5F , lsg xfn] f <
-u_ g]kfndf cfos/ Joj:yfkg ug]{ lgsfo s'g xf] <
-3_ cfGtl/s /fh:j ljefun] o; cflys{ jifs{ f nflu cfos/;DaGwL ;Ldfx¿, kf| jwfgx¿
sxfaF f6 s;/L ;lhn} cWoog ug{ ;S5 < tL k|fjwfgx¿ s] s] pNnv] ul/Psf] /x5] <
JolStut jf ;:+ yfut -pBfu] , sDkgL cflb_ n] u/s] f] cfDbfgLdf nfUg] s/nfO{
cfos/ (Income tax) elgG5 . ;/sf/sf] cfDbfgLsf] ;|f]tdWo] cfos/ klg Ps xf] .
cfos/nfO{ k|ltztdf u0fgf ul/G5 . JolStut cfos/ b/ k];f, Joj;fo / aa} flxs
l:yltcg;' f/ km/s km/s x'g] u/s] f] kfOG5 . g]kfndf cfos/sf] Joj:yfkg ug]{ sfd
cfGtl/s /fh:j ljefun] u5{ . cfGtl/s /fh:j ljefun] x/]s jif{ cfos/ u0fgf
lgod agfPsf] x'G5, h;sf] ljj/0f ljefusf] j]a;fO6 http://www.ird.gov.np af6
x]g{ ;lsG5 .
lgDglnlvt zLifs{ x¿df vr{ ubf{ s'g} klg JolStn] sdfPsf] ;DklQdf s/ 56' lbOPsf] x'G5 M
-s_ sdr{ f/L ;~ro sfi] fdf hDdf xg' uPsf] /sddf
-v_ gful/s nufgL sfi] fdf hDdf x'g uPsf] /sddf
-u_ hLjg ladfafkt lt/]sf] lkl| dod vrd{ f
-3_ wfld{s sfo{sf nflu u/]sf] vrd{ f
-ª_ rGbf lbPsf] /sddf
-r_ bu' {d eQfafkt k|fKt u/]sf] /sddf
-5_ jb} ]lzs eQfsf] 75 k|ltzt /sddf
-h_ cfi} fwL pkrf/df nfus] f] vr{df .
ul0ft, sIff ( 15
pbfx/0f 1
Ps hgf ljjflxt lzIfssf] dfl;s tna ?= 37,990 5 . cfo jif{ 2077/078 sf] cfos/
b/cg;' f/ lzIfsn] k|fKt ug{] rf8kj{ vr;{ lxtsf] 13 dlxgfsf] cfDbfgL lx;fa ubf{ jflif{s slt cfos/
ltg'k{ g{] /x]5 <
;dfwfg
oxfF dfl;s tna = ?=37990
jflif{s cfo = 13 × ?=37990
= ?=493870
ca s/of]Uo /sd ?= 493870 nfO{ cfos/ b/sf cfwf/df lgDgfg;' f/ 6'j|mo\ fP/ n]Vbf,
?= 493870 = ?=450000 + ?=43870
1% 10%
jflif{s cfos/ = ?= 450000 sf] 1% + ?=43870 sf] 10%
1 10
= ?= 450000 × 100 + ?= 43870 × 100
= ?= 4500 + ?= 4387
= ?= 8887
pbfx/0f 2
Pp6f a}ªs\ df sfd ug]{ cljjflxt sd{rf/Lsf] dfl;s tna ?= 30,000 5 . cfDbfgLdWo] jflif{s
?= 4,00,000 ;Dddf ;fdflhs ;'/Iff s/ 1% sf b/n] / ?= 4,00,000 eGbf dflysf] 10%
sf b/n] cfos/ ltgk{' 5{ . pSt sdr{ f/Ln] Ps jifd{ f 15 dlxgf a/fa/ tna kfpF5 eg] jflif{s hDdf
slt cfos/ ltg{k' 5{, kQf nufpg'xf;] \ M
;dfwfg
oxfF sdr{ f/Lsf] dfl;s cfDbfgL = ?= 30000
jflifs{ cfDbfgL = 15 × ?= 30000
= ?= 450000
oxfF s'n jflif{s cfDbfgL ?= 450000 nfO{ lbOPsf] cfos/ ;Ldfcg';f/ lgDgfg;' f/ 6j' m| \ofP/
nV] bf,
16 ul0ft, sIff (
?= 450000 = ?= 400000 + ?= 50000
1% 10%
⸫ hDdf jflifs{ cfos/ = ?= 400000 sf] 1% + ?= 50000 sf] 10%
= ?= 400000 × 1 + ?= 50000 × 10
100 100
= ?= 4000 + ?= 5000
= ?= 9000
pbfx/0f 3
gk] fndf ?=2,000 dxFuL eQf;lxt dfl;s ?= 40500 sdfpg] / jflifs{ ?=23,500
lkl| dodsf] kGw| a;{] hLjg ladf u/s] f Ps hgf ljjflxt clwst[ txdf sfo/{ t sd{rf/Ln] k|fKt
ug{] rf8kj{ vr{;lxtsf] 13 dlxgf a/fa/ Ps jif{sf] cfDbfgLsf] u0fgfdf dxª\uL eQf / rf8kj{
vr{afxs] sf] cfDbfgLdWo] 10% sdr{ f/L ;~ro sfi] fdf 5'6o\ fO;sk] l5 hDdf slt cfos/
ltg{'k5{, kQf nufpgx' f];\ . -oxfF cufl8 ki[ 7df plNnlvt cfos/ ;Ldfcg;' f/ u0fgf
ul/Psf] 5 ._
;dfwfg
oxfF dfl;s ¿kdf sdr{ f/Ln] k|fKt ug{] dxuF L eQf = ?=2,000
jflifs{ ¿kdf sd{rf/Ln] k|fKt ug]{ Ps dlxgf a/fa/sf] rf8kj{ vr{ = ?=38,500
jflif{s ¿kdf hLjg ladfafkt a'emfpgk' g]{ lkl| dod /sd = ?=23,500
dxªu\ L eQf / rf8kj{afx]ssf] sd{rf/Lsf] sn' jflif{s cfDbfgL = ?=12 × 38,500
= ?=4,62,000
;~rosfi] fdf 10% sf] b/n] hDdf x'g] 12 dlxgfsf] /sd = ?=4,62,000 sf] 10%
= ?= 462000 × 10
100
= ?=46,200
;~ro sf]ifdf hDdf xg' ] jflifs{ /sd ?=46,200 / hLjg ladf ul/Psf] jflifs{ lkl| dod
?= 23,500 df cfos/ 56' x'g] ePsfn,]
jflif{s cfos/ ofU] o /sd = ?=(4,62,000 − 46,200) − ?=23,500 + 12 × ?=2,000 + ?=38,500
= ?= 4,15,800 − ?=23,500 + ?=24,000 + ?=38,500
= ?= 3,92,300 + ?=62,500
= ?= 4,54,800
ul0ft, sIff ( 17
ca s/ of]Uo cfDbfgL ?=4,54,800 nfO{ lbOPsf] cfos/ ;Ldfcg;' f/ lgDgfg';f/ 6'jm| o\ fP/
n]Vbf,
?=4,54,800 = ?=4,50,000 + ?=4,800
1% 10%
⸫ hDdf jflif{s cfos/ = ?=4,50,000 sf] 1% + ?=4,800 sf] 10%
= ?= 450000 × 1010 + ?= 4800 × 10
100
= ?=4,500 + ?=480
= ?=4,980
To;}n,] pSt sd{rf/Ln] jflif{s ¿kdf hDdf ?=4,980 cfos/ ltg'k{ 5{ .
pbfx/0f 4
olb s'g} Joj;foLsf] jflifs{ cfodWo] ?=4,50,000 ;Dd cfos/ 5'6, ?= 4,50,001 b]lv ?= 5,50,000
;Dd 10% / ?= 5,50,001 b]lv ?=7,00,000 ;Dd 20% sf b/n] cfos/ nfUb5 eg] jflif{s
?=6,75,000 cfDbfgL xg' ] Joj;foLn] hDdf slt cfos/ ltg{k' 5,{ kQf nufpg'xf];\ .
;dfwfg
oxfF sn' jflif{s cfDbfgL ?= 675000 nfO{ lbOPsf] cfos/ ;Ldfcg;' f/ lgDgfg';f/ 6j' |mo\ fP/
nV] bf,
?= 675000 = ?= 450000 + ?= 100000 + ?= 175000
cfos/ 5'6 10% 20%
⸫ hDdf jflif{s cfos/ = ?= 100000 sf] 10% + ?= 175000 sf] 20%
= ?= 100000 × 1010 + ?= 175000 × 20
100
= ?= 10000 + ?= 35000
= ?= 45000
18 ul0ft, sIff (
pbfx/0f 5
?=35,000 sf] 4 jif{df 10% kl| t jifs{ f b/n] ;fwf/0f Aofh slt x'G5 < pSt Aofhdf 5% s/
nufpbF f v'b ;fwf/0f Aofh slt xg' cfpF5, kQf nufpg'xf];\ .
;dfwfg
oxfF lbOPsf,]
;fjfF (P) = ?=35,000
;do (T) = 4 jif{
;fwf/0f Aofhb/ (R) = 10%
s/ = 5%
sn' ;fwf/0f Aofh = <
v'b ;fwf/0f Aofh = <
;"qaf6,
I= P×T×R
100
= 3500×4×10
100
= ?= 1,400
⸫ sn' ;fwf/0f Aofh = ?=1,400
km]l/ cfos/ = ?= 1,400 sf] 5%
= ?= 1400 × 5
100
= ?= 70
⸫ vb' ;fwf/0f Aofh = ?=1,400 − ?=70
= ?=1330
cEof; 2.1
1. gk] fndf dfl;s ?=38,000 sdfpg] / jflif{s ?=23,500 sf] hLjg ladf u/s] f Ps hgf
clwst[ txdf sfo/{ t ljjflxt sd{rf/Ln] k|fKt ug{] rf8kj{ vr;{ lxtsf] 13 dlxgf
a/fa/ Ps jifs{ f] cfDbfgL lx;fa ubf{ jflifs{ slt ?lkofF cfos/ ltb5{ g\, kQf nufpgx' f;] \ .
-cufl8 k]hdf plNnlvt cfos/ ;Ldfcg';f/ lx;fa ug'{xf];\ ._
ul0ft, sIff ( 19
2. sg' } cGt/fl{ i6o« u}/;/sf/L ;+:yfdf sfd ug{] Ps hgf sdr{ f/Ln] p;sf] s/ nfUg]
cfDbfgLdWo] ?=4,50,000 ;Dd 1%, ?=4,50,000 eGbf dfly ?=5,50,000 ;Dd 10%,
?= 5,50,000 eGbf dfly ?=7,50,000 ;Dd 20%, ?=7,50,000 eGbf dfly ?=20,00,000
;Dd 30% sf b/n] cfos/ ltgk' 5{ eg] dfl;s ?=65,000 sdfpg] pSt sd{rf/Ln]
cfDbfgLafktsf] hDdf slt s/afktsf] /sd ;/sf/nfO{ ae' mfpgk' 5,{ lx;fa ugx{' f];\ .
3. tnsf] tflnsfdf Psnf6} L kmds{ f ¿kdf Joj;fo x'g] Joj;foLsf nflu plNnlvt cfos/ ;Ldf
cWoog ug{x' f];\ M
cfDbfgL -?=_ s/ b/
cfos/ 56'
1 - 4,50,000
10%
4,50,001 - 5,50,000
5,50,001 - 7,50,000 20%
7,50,001 - 20,00,000 30%
20,00,000 eGbf dfly 36%
ca cfos/ ;Ldfcg;' f/ lgDgadf]lhdsf] cfDbfgL ug]{ Ps hgf Joj;foLn] slt cfos/
ltg{'k5,{ lx;fa ug'x{ f;] \ M
-s_ jflif{s cfDbfgL = ?=6,30,000
-v_ jflifs{ cfDbfgL = ?=9,25,000
-u_ jflif{s cfDbfgL = ?=17,88,000
-3_ jflif{s cfDbfgL = ?=22,25,000
4. a}ª\sdf hDdf u/]sf] ?=10 nfv 4 jif{df 8.5% ;fwf/0f Aofhsf b/n] lx;fa xFb' f sn'
slt Aofh x'G5 < olb pSt Aofhdf 5% cfos/ nufpFbf vb' ;fwf/0f Aofh slt xG' 5,
kQf nufpg'xf];\ .
kl/of]hgf sfo{
-s_ cfkmg\ f] ljBfnodf sfo{/t dfWolds lzIfsx¿sf] ;~ro sfi] f, gful/s nufgL sfi] f,
ladf h:tf ljifox¿nfO{ ;d6] L tnasf] jf:tljs ljj/0f lngx' f;] \ / kT| os] lzIfsn]
jflif{s cfodf slt slt ?lkofF s/ ltg'{kg]{ /x5] , lx;fa ug{x' f;] \ .
-v_ ljBfyL{sf] cfcfˆgf] 3/ kl/jf/sf] ;b:ox¿sf] gf]s/L ePdf lghx¿af6 cfDbfgL
u/s] f] lx;fa lstfa u/L jf:tljs ljj/0f lng'xf];\ / jflifs{ slt /sd s/afkt
ltg'{k5{, kQf nufpgx' f];\ .
20 ul0ft, sIff (
pQ/
1. ?=6,550 2. ?=63,500 3. -s_ ?=26,000 3. -v_ ?= 1,02,500
3.-u_ ?= 3,61,400 3. -3_ ?= 5,06,000 4. ?= 3,40,000 / ?= 3,23,000
2.1.2 d"No clej[l4 s/ (Value Added Tax)
lj|mofsnfk 1
b'O{cf6] f k;ndf Pp6} lsl;dsf Jofk6k lajm| L ubfs{ f b'O{cf]6f lanx¿sf] cWoog u/L ;f]lwPsf]
kZ| gx¿sf ;DaGwdf 5nkmn ug'x{ f];\ M
X Computer Shop, k'tnL;8s, sf7df8f+} Y Computer xfp;, kt' nL;8s, sf7df8f+}
ldlt M– 2077-10-20 ldlt M– 2077-11-23
u|fxssf] gfd M– eLdaxfb/' tfdfª uf| xssf] gfd M– c?0ff ;fksf]6f
jm| =;= ;fdfgsf kl/ b/ d"No -?=_ j|m=;= ;fdfgsf] kl/df0f b/ dN" o -?=_
ljj/0f df0f
ljj/0f
1. Nofk6k 1 56000 1×56000.00
1. Nofk6k 1 56000 1×56000.00
hDdf 56000.00
hDdf 56000.00
56' 10% 5600.00
56' 10% 5600.00 VAT 50400.00
ltg'{kg{] /sd 50400.00 nfUg] /sd
VAT 13% 6552.00
ltgk{' g{] /sd 56952.00
-s_ bO' {cf6] } landf Nofk6k lajm| Lb/ slt slt 5 <
-v_ bO' c{ f]6} landf ;dfgtf / leGgtf s] s] b]lvG5g\ <
-u_ ltg'k{ g{] d"No s'g landf a9L 5 < s] sf/0fn] a9L ePsf] xfn] f <
-3_ Tof] a9L /sd s'g zLifs{ df ltgk{' /]sf] /x5] < 5nkmn ug'{xf;] \ .
pkef]Stfn] s'g} j:t' jf ;]jfsf] d"Nodf sx] L k|ltzt yk /sd lt/]/ j:t' jf ;j] f vl/b u/L
laj|mt] f jf ;]jf k|bfosdfkmt{ ;/sf/nfO{ ltg'k{ 5{ . To:tf] yk /sdnfO{ d"No clejl[ 4 s/
(Value Added Tax) elgG5 . h;nfO{ 5f]6s/Ldf d=" c=s= jf dN" o clej[l4 s/ klg eGg]
ul/G5 . d"No clej[l4 s/ j:t' tyf ;j] fdf cfwfl/t ck|ToIf s/ xf] . xfn gk] fnsf] ;Gbed{ f
dN" o clej[l4 s/ b/ 13% /flvPsf] 5 .
ul0ft, sIff ( 21
sg' } a:t' jf ;]jf vl/b ubfs{ f] k|fKt landf cWoog ug]{ xf] eg] ;j] f z'Ns hf]8]/ cfPsf] clGtd
d"Nodf tfl] sPsf] b/ cg;' f/ d"No clej[l4 s/ nufpg] -hf8] \g]_ ul/G5 . To:t} cfoftLt j:t'
jf ;]jfsf] ;Gbed{ f 56' /sd 36fO;s]kl5 9'jfgL, ladf, sld;g, :yfgLo s/, gfkmf cflb;d]t
hf]8/] cfpg] dN" odf d"No clej[l4 s/ nufOG5 .
d"No clej[l4 s/ nufpg Jokf/Ln] /fv]sf] cªl\ st d"No, To;df ul/Psf] 5'6 36fP/ sld;g
lbg'kg]{ eP pSt /sd hf]8/] cfPsf] dN" odf d"No clej[l4 s/ /sd hf]l8G5 . o;/L d"No
clej[l4 s/ hf]l8;s]kl5 cfPsf] d"NonfO{ dN" o clejl[ 4 s/ ;lxtsf] d"No -jf:tljs d"No_
elgG5, h;sf] cjwf/0ffdf k:| 6 xg' tnsf] ˆnf] rf6{ cWoog ugx'{ f;] \ M
cª\lst d"No (Marked Price)
– 5'6 (D)
+ gfkmf (G) ljjm| o dN" o (S.P)
j|mo dN" o (C.P)
– gfS] ;fg (L) -dN" o clejl[ 4 s/ nfUg] dN" o_
d"No clej[l4 s/
d"No clejl[ 4 s/ ;lxtsf] d"No -jf:tljs dN" o_
pbfx/0f 1
lbOPsf dN" ox¿df d"No clej[l4 s/ (VAT) /sd kQf nufpgx' f;] \ M
-s_ ljjm| o dN" o (S.P.) = ?=7000 / dN" o clej[l4 s/ = 13%
-v_ cª\lst d"No (M.P.) = ?=10000, 56' = 15% / d"No clejl[ 4 s/ = 13%
;dfwfg
-s_ oxfF, ljj|mo dN" o (S.P.) = ?=7000
dN" o clejl[ 4 s/ b/ = 13%
d"No clejl[ 4 s/ /sd = <
ca, dN" o clejl[ 4 s/ /sd = ?=7000 sf] 13%
= ?= 7000 × 13
100
= ?= 910
⸫ dN" o clejl[ 4 s/ /sd = ?= 910
22 ul0ft, sIff (
-v_ oxf,F cª\lst dN" o = ?=10000
56' b/ = 15%
dN" o clejl[ 4 s/ b/ = 13%
dN" o clejl[ 4 s/ /sd = <
ca 5'6 /sd lgsfNbf,
5'6 /sd = ?=10000 sf] 15%
= ?= 10000 × 15
100
= ?=1500
dN" o clej[l4 s/ nfUg] /sd (S.P.) = ?=10000 − ?=1500
= ?=8500
ca, dN" o clejl[ 4 s/ /sd = ?=8500 sf] 13%
= ?= 8500 × 13
100
= ?=1105
⸫ d"No clejl[ 4 s/ (VAT) /sd = ?= 1,105
pbfx/0f 2
Pp6f dfa] fOn ;6] sf] cªl\ st dN" o ?= 15,000 /flvPsf] lyof,] pSt dfa] fOn ;]6df 15% 56' lbO{
13% d"No clejl[ t s/ nufpbF f ;f]sf] d"No slt k'Uof] xfn] f, lx;fa ug{'xf];\ .
;dfwfg
oxfF df]afOnsf] cª\lst dN" o (M.P.) = ?=15000
56' = 15%
dN" o clej[l4 s/ = 13%
d"No clejl[ 4 s/ ;lxtsf] d"No -jf:tljs dN" o_ = <
ca 56' /sd = ?=15000 sf] 15%
= ?= 15000 × 15
100
= ?=2,250
ul0ft, sIff ( 23
km]l/, dfa] fOnsf] d"No clejl[ 4 s/ nfUg] dN" o (S.P.) = ?=(15000 – 2250)
= ?=12750
d"No clej[l4 s/ /sd = ?=12750 sf] 13%
= ?= 12750 × 13
100
= ?=1657.50
⸫ dN" o clej[l4 s/;lxtsf] dN" o -jf:tljs dN" o_ = ?=12750 + ?=1657.50
= ?=14,407.50
csf]{ tl/sf
;dfwfg
oxfF, df]afOnsf] cªl\ st dN" o (M.P.) = ?=15000
56' = 15%
d"No clej[l4 s/ = 13%
d"No clejl[ 4 s/ ;lxtsf] d"No -jf:tljs dN" o_ = <
d"No clejl[ 4 s/ ;lxtsf] d"No -jf:tljs d"No_
= ?=15000 sf] (100 − 15)% × (100 + 13)%
= ?= 15000 × 8 × 113
100 100
= ?=14,407.50
pbfx/0f 3
Pp6f ;fdfgdf 15% 56' lbO{ 13% dN" o clejl[ t s/ nufpFbf vl/b stfn{ ] ?= 57630 ltgk{' 5{ eg]
pSt ;fdfgsf] cªl\ st d"No kQf nufpg'xf;] \ .
;dfwfg
oxfF dfgf,F} cªl\ st dN" o (M.P.) = ?=x
lbOPsf], 5'6 = 15%
d"No clej[l4 s/ (VAT) = 13%
d"No clejl[ 4 s/ ;lxtsf] dN" o -jf:tljs d"No_ = ?= 57630
k|Zgcg';f/ 56' /sd = ?= x sf] 15%
24 ul0ft, sIff (
= ?= x × 15
= ?=11050x 100
= ?= 3x
20
3x
dN" o clej[l4 s/ nfUg] d"No (S.P.) = ?= x – 20
= ?= 17x
20
dN" o clej[l4 s/ /sd = ?= 17x sf] 13%
20
= ?= 17x × 13
20 100
= ?=2202010x
d"No clej[l4 s/ ;lxtsf] dN" o -jf:tljs dN" o_ = ?= 17x + 221x
20 2000
= ?= 1700x + 221x
2000
= ?=21090201x
k|Zgcg;' f/,
= ?=21090201x = ?=57630
cyjf 1921x = 2000 × 57630
cyjf x = 2000 × 57630
1921
cyjf x = 60000
ctM cª\lst d"No (M.P.) = ?=60,000
csf{] tl/sf
dfgfF,} cª\lst d"No (M.P.) = ?=x
oxfF lbOPsf] 5'6 = 15%
dN" o clejl[ 4 s/ (VAT) = 13%
dN" o clej[l4 s/ ;lxtsf] dN" o -jf:tljs d"No_ = ?= 57,630
ul0ft, sIff ( 25
d"No clejl[ 4 s/ ;lxtsf] d"No -jf:tljs d"No_ = ?= x sf] (100 − 15)% × (100 + 13)%
= ?= x× 85 × 113
100 100
kZ| gcg;' f/,
?= 57630 = ?= x × 85 × 113
100 100
cyjf x = 57630 × 100 ×100
85 × 113
cyjf x = 60000
ctM cª\lst dN" o (M.P.) = ?= 60,000
pbfx/0f 4
OGkmf]6]s ;Knfo;n{ ] Pp6f lkl| G6ª d]l;g ?=2,25,000 df 13% dN" o clej[lt s/ ;lxt O;k
;Knfo;n{ fO{ lajm| L u¥of] . km]l/ O;k ;Knfo;n{ ] pSt d]l;gsf] d"Nodf ?= 6,000 9'jfgL vr{,
?=15,000 gfkmf / ?= 4,000 :yfgLo s/;lxt pkefS] tfnfO{ xf]d 8l] ne/Lsf] ;'ljwfaf6 lajm| L u¥of] . ca
pkefS] tfn] 13% d=" c=s= ltbf{ hDdf slt ?lkofF d"No clejl[ t s/ ltg'k{ nf{, kQf nufpgx' f];\ .
;dfwfg
oxf,F OGkmf]6]s ;Knfo;{sf nflu
d"No clej[l4 s/ ;lxtsf] laj|mL dN" o -jf:tljs dN" o_ = ?=2,25,000
O;k ;Knfo;{sf nflu,
OGkmf6] ]s ;Knfo;s{ f] laj|mL d"No = O;k ;Knfo;s{ f] vl/b d"No
vl/b dN" o = ?=2,25,000
9j' fgL vr { = ?=6,000
gfkmf = ?=15,000
:yfgLo s/ = ?=4,000
hDdf dN" o clej[l4 s/ nfUg] /sd = ?=2,25,000 + ?=6,000 + ?=15,000 + ?=4,000
= ?=2,50,000
ca pkefS] tfn] ltgk'{ g{] dN" o clej[l4 s/ /sd = ?=2,50,000 sf] 13%
= ?=250000 × 13
100
= ?= 32,500
26 ul0ft, sIff (
pbfx/0f 5
Pp6f k;nn] ] Pp6f ;fOsn ?= 5,800 df lsg]/ laj|mLdf /fv]sf] /x5] . p;n] j|mo dN" osf] 40%
a9fP/ cª\lst dN" o sfod u/5] . cª\lst d"Nodf 10% 56' lbO{ 13% d"No clejl[ t s/ nufpbF f
pkef]Stfn] slt dN" o ltg'{k5{ < ;fy} o; sf/fa] f/df slt k|ltzt gfkmf jf gfS] ;fg x'G5, kQf
nufpg'xf;] \ .
;dfwfg
oxfF ;fOsnsf] jm| o d"No (C.P.) = ?=5800
56' = 10%
dN" o clej[l4 s/ b/ = 13%
dN" o clejl[ 4 s/ ;lxtsf] d"No = <
gfkmf k|ltzt jf gfS] ;fg k|ltzt = <
k|Zgaf6
;fOsnsf] cªl\ st dN" o (M.P) = ?=5,800 sf] (100 + 40)%
= ?=5800 × 140
?=8,120 100
=
5'6 /sd = ?=8,120 sf] 10%
= ?=8120 × 10
?=812 100
=
⸫ dN" o clejl[ 4 s/ nfUg] d"No (S.P.) = ?=8,120 − ?=812
= ?=7,308
ca d"No clej[l4 s/ /sd = ?=7,308 sf] 13%
= ?=7,308 × 13
100
= ?= 950.04
⸫ d"No clej[l4 s/ ;lxtsf] ;fOsnsf] dN" o -jf:tljs dN" o_ = ?=7,308 + ?=950.04
= ?=8,258.04
o; sf/f]af/df la=d=" (S.P.) = dN" o clej[l4 s/ gnufpbF fsf] d"No
= ?=7,308
j|mo dN" o (C.P.) = ?=5,800
jm| o d"NoeGbf ljjm| o d"No a9L ePsfn] gfkmf x'G5 .
ul0ft, sIff ( 27
⸫ gfkmf = ?=7308 − ?=5800
= ?=1508
t;y{ gfkmf kl| tzt = Rs.1508 × 100%
Rs. 5800
= 26%
ct M pSt ;fOsnsf] sf/f]af/df 26% gfkmf eP5 .
pbfx/0f 6
k;nn] ] ?=2,000 df lsg]sf] Pp6f 38L 25% gfkmf vfP/ a]R5 eg] 13% dN" o clej[lt s/ kl5
landf pkef]Stfn] ltg'k{ g]{ /sd slt x'G5 xf]nf, kQf nufpg'xf;] \ .
;dfwfg
oxfF 38Lsf] j|mo d"No (C.P.) = ?=2000
gfkmf = 25%
dN" o clejl[ 4 s/ b/ = 13%
pkefS] tfn] ltgk{' g{] /sd -VAT ;lxtsf] dN" o_ = <
gfkmf = ?=2000 sf] 25%
= ?=2000 × 25
100
= ?=500
⸫ ljj|mo d"No (S.P.) = jm| o d"No + gfkmf
= ?=(2000 + 500)
= ?=2500
d"No clejl[ 4 s/ /sd = ?=2500 sf] 13%
= ?=2500 × 13
100
= ?=325
⸫ pkef]Stfn] ltg'{kg{] /sd = ?=2500 + ?=325
= ?= 2,825
28 ul0ft, sIff (
cEof; 2.2
1. tnsf] tflnsfsf] cfwf/df d"No clej[l4 s/ /sd kQf nufpgx' f];\ M
lj=d"= (S.P) d"No clej[l4 s/ dN" o clej[l4 s/
-s_ ?= 300 b/ /sd
13% ?= <
-v_ ?= 750 13% ?= <
-u_ ?= 6,000 13% ?= <
-3_ ?= 3,75,000 13% ?= <
-ª_ ?= 20,27,000 13% ?= <
2. tnsf] tflnsfsf cfwf/df d"No clejl[ 4 s/ gnufpFbfsf] dN" o lx;fa ug{x' f;] \ M
lj=d=" (S.P.) d"No clejl[ 4 s/ ;lxtsf] dN" o clejl[ 4 s/ b/
-s_ ?=< dN" o -jf:tljs dN" o_
13%
?= 3,616
-v_ ?= < ?= 30,510 13%
-u_ ?= < ?= 3,390 13%
-3_ ?= < ?= 57,630 13%
-ª_ ?= < ?= 1,19,328 13%
3. tnsf] tflnsfsf cfwf/df ;fdfgsf] jf:tljs d"No lx;fa ug{'xf;] \ M
cªl\ st dN" o (M.P.) 5'6 b/ d"No clej[l4 d"No clejl[ 4 s/
-s_ ?= 2,000 s/ b/ ;lxtsf] d"No
8%
13% ?= <
-v_ ?= 7,000 15% 13% ?= <
-u_ ?= 27,000 20% 13% ?= <
-3_ ?= 20,525.30 10% 13% ?= <
-ª_ ?= 1,81,500 7.5% 13% ?= <
ul0ft, sIff ( 29
4. tnsf] tflnsfsf cfwf/df cªl\ st d"No / 5'6 /sd lgsfNg'xf;] \ M
cªl\ st dN" o (M.P.) 5'6 b/ 5'6 /sd d"No dN" o clejl[ 4 s/
clejl[ 4 ;lxtsf] dN" o
-s_ ?= < 15% ?= < s/ b/
-v_ ?= < 20% ?= < ?= 57,630
-u_ ?= < 15% ?= < 13% ?= 4,520
-3_ ?= < 10% ?= < ?= 2,40,125
-ª_ ?= < 25% ?= < 13% ?= 15,225
?= 2,151.52
13%
13%
13%
5. Pp6f PnO8L 6]lnlehg ;]6sf] cªl\ st d"No ?= 37500 df 11% 5'6 lbO{ 13% VAT
nufpbF f ;f] 6]lnlehgnfO{ pkef]Stfn] slt ltg'k{ 5{ < lx;fa u/L kQf nufpg'xf;] \ .
6. lbOPsf] ;fdfgsf] uf| xsn] ltg{'kg]{ dN" o lx;fa ugx'{ f];\ M
-s_ cª\lst d"No = ?= 35000 -v_ cª\lst dN" o = ?= 6500
56' = 10% 56' = 7.5%
d"=c=s = 13%
d=" c=s = 13%
-u_ cªl\ st d"No = ?= 25700 -3_ cªl\ st d"No = ?= 1450
56' = 15% 56' = 22.75%
d"=c=s = 13% d"=c=s = 13%
7. olb Pp6f ljB'tLo husf] sfod ul/Psf] dN" odf 5% 56' lbO{ 13% dN" o clej[l4
s/ nufpFbf ?=1,575 x'G5 eg] ;f] husf] cª\lst d"No slt xfn] f < d"No clej[l4 s/
gnufpFbfsf] dN" o slt xf]nf, kQf nufpg'xf;] \ .
8. Ps hgf k;nn] ] ?=27,500 df lsgs] f] Pp6f ;fdfg lajm| L ug{] jm| ddf ?=35,000
cª\lst dN" o sfod u/5] g\ . pSt d"Nodf 10.5% 5'6 lbO{ 13% dN" o clejl[ 4 s/ nufO{
aR] bf,
-s_ dN" o clejl[ 4 s/ lxtsf] d"No slt xG' 5 <
-v_ o; lsl;dsf] sf/fa] f/df slt kl| tzt gfkmf jf gf]S;fg eof] xf]nf <
-u_ olb cªl\ st d"Nodf g} laj|mL ug{] xf] eg] slt k|ltzt gfkmf xG' Yof] <
30 ul0ft, sIff (
9. Ps hgf Jofkf/Ln] ?= 4,000 df lsg]/ NofPsf] 38L lajm| Lsf nflu 25% d"No a9fP/ cª\lst
dN" o lgwf/{ 0f u/5] . pSt 38Ldf 12% 5'6 lbO{ 13% dN" o clejl[ 4 s/ nufpFbf,
-s_ pkefS] tfn] ;/sf/nfO{ d"No clejl[ 4 s/ afkt slt /sd a'emfpg'k5{ <
-v_ olb 5% gfS] ;fgdf laj|mL u/]sf] eP d"No clejl[ 4 s/ ;lxtsf] dN" o slt xG' Yof] <
10. Ps hgf yfs] lajm| ]tfn] n'uf w'g] dl] ;g(washingmachine) ?=37,000df 13% dN" o clej[l4
s/ nufP/ v'bf| k;nn] fO{ lajm| L u¥of] . v'b|f k;n]n] ;f] dl] ;g 9'jfgL vr{ ?=3,000, :yfgLo s/
?=550 / ?=5,000 gfkmf;lxt pkef]Stfsf 3/df k'¥ofOlbof] eg] pkef]Stfn] d"No clej[l4
s/afkt xfnsf] b/df slt /sd lt¥of] xf]nf, kQf nufpg'xf;] \ .
kl/ofh] gf sfo{
ljBfyL{ pko'St ;dx" df ljefhg x'g'xf];\ . kT| os] ;dx" n] clxns] f] cfly{s jifs{ f] ah6]
jStJosf] cWoog ugx{' f;] \ / pSt ah]6 jStJoaf6 lgDgfg';f/sf ;r" gfx¿ ;ªs\ ng u/L
;d"xdf kl| tj]bg tof/ kfg'x{ f;] \ M
-s_ ah]6sf] cfsf/
-v_ ah6] df nufOPsf ljleGg ks| f/sf s/
-u_ s/sf b/
-3_ s/ 56' x'g] ;fdfg tyf ;j] f
-ª_ dN" o clejl[ 4 s/ b/ / nfUg] j:t'
-r_ cGo cfos/
pQ/
1. -s_ ?=339 -v_ ?=847.50 -u_ ?=6780 -3_ ?=4,23,750
-ª_ ?=22,90,510
2. -s_ ?=3,200 -v_ ?=27,000 -u_ ?=3,000 -3_ ?=51,000
-ª_ ?=1,05,600
3. -s_ ?=20,792 -v_ ?=67,235 -u_ ?=24,408 -3_ ?=20,874.23
-ª_ ?=189712.88
4. -s_ ?=60,000 -v_ ?=5,000 -u_ ?=2,50,000 -3_ ?=14,970.50
-ª_ ?=2,538.67
5. ?= 37,713.75
6. -s_ ?=35,595 -v_ ?= 6,794.13 -u_ ?= 24,684.85 -3_ ?=1,266.56
7. ?= 1,393.81 / ?=1,467.16
8. -s_ ?=35,397.25 -v_ 13.91% -u_ 27.27%
9. -s_ ?=572 -v_ ?=4,294 10. ?=6,546.80
ul0ft, sIff ( 31
sld;g / nfef+z
kf7 3 (Commission and Bonus/Dividend)
3.1 sld;g (Commission)
ljm| ofsnfk 1
sIffsf ;fyLx¿dWo]af6 tLgcf6] f ;d"x agfpgx' f;] \ . ;dx" x¿dWo] klxnf] ;dx" sf] gt] [Tj ug{]nfO{
laj|mL stfs{ f ¿kdf hUufwgL -gfd M wlg/fd_, bf;] f| ] ;dx" sf] g]t[Tj ug{]nfO{ vl/b stfs{ f ¿kdf
hUuf lng] JolSt -gfd M cflbgfy_ / t];|f] ;d"xsf] gt] T[ j ugn]{ fO{ dWo:ystfs{ f ¿kdf Ph]G6
-gfd M ;lagf_ agfO{ clego ugx'{ f];\ .
sg' } j:t' jf ;j] fsf] lajm| L stf{ / vl/b stf{sf lardf dWo:ytfsf] el" dsf lgjfx{
ug{] JolStnfO{ Ph]G6 (Agent) elgG5 . o;/L dWo:ystf{sf] e"ldsf lgjf{x
u/a] fkt lgodadfl] hd Ph]G6n] kfpg] /sdnfO{ sld;g elgG5 . Ph]G6n] To:tf] /sd
vl/b stf{ jf laj|mL stf{ jf bj' a} f6 lng ;S5 . sld;g lnbF f lbFbf lajm| L dN" onfO{
cfwf/ dflgG5 . sld;gnfO{ kl| tztdf JoSt ul/G5 . hUufsf] sf/]af/df, aª} s\ tyf
laQLo ;+:yfx¿df, ladf sDkgLx¿df, ;fdfg lsgdn] cflb h:tf cfly{s sf/fa] f/ xg' ]
Joj;fox¿df sld;gsf] u0fgf ul/G5 .
pbfx/0f 1
Ph]G6n] ?= 25,00,000 df hUuf a]lrlbPafkt 5% sld;g kfpF5g\ eg,]
-s_ PhG] 6n] sld;gafkt slt /sd kfpg] /x5] g\ <
-v_ sld;gkl5 hUufwgLsf xftdf slt /sd k5{, kQf nufpg'xf;] \ .
;dfwfg
oxfF hUufsf] laj|mL d"No = ?= 2500000
sld;g b/ = 5%
-s_ sld;gafktsf] /sd = <
-v_ hUufwgLn] kfpg] /sd = <
-s_ xfdLnfO{ yfxf 5 ls,
sld;g /sd = ?= 2500000 sf] 5%
32 ul0ft, sIff (
= ?= 2500000 × 5
100
= ?= 125000
⸫ sld;gafktsf] /sd = ?=125000
-v_ hUufwgLn] kfpg] /sd = sld;gkl5sf] d"No
= ?= 2500000 − ?=125000
⸫ hUufwgLn] kfpg] /sd = ?= 23,75,000
pbfx/0f 2
Pp6f lgdf{0f ;fdu|L k;ndf sfd ug]{ sd{rf/Lsf] dfl;s tna ?=12,000 5 . pgn] Ps dlxgfdf
?= 4,75,000 sf] lgdf0{ f ;fdu|L lajm| L u/5] g\ . olb pgn] dlxgfdf ?=19,125 sdfP5g\ eg] slt
k|ltzt sld;g afktdfq cfDbfgL u/s] f /x]5g\, lgsfNgx' f;] \ .
;dfwfg
laj|mL dN" o = ?=475000
k;nsf sd{rf/Lsf] dfl;s tna = ?=12000
sdr{ f/Lsf] sld;g;lxtsf] dfl;s cfDbfgL = ?=19125
⸫ sld;g /sd = ?= 19125 − ?=12000
= ?= 7125
sld;g /sd
ca sld;g b/ = laljm| dN" o × 100%
= 7125 × 100%
475000
= 1.5%
pbfx/0f 3
Pp6f sDkgLn] PhG] 6nfO{ lbg] sld;g b/ lgDgfg';f/ pNnv ul/Psf] 5 M
?= 1500000 ;Ddsf] laj|mLdf 0.5%
?= 1500000 eGbf dfly ?= 2500000 ;Ddsf] lajm| Ldf 1%
ul0ft, sIff ( 33
?= 2500000 eGbf dfly ?= 4000000 ;Ddsf] lajm| Ldf 1.5%
?= 4000000 eGbf dflysf] lajm| Ldf 2%
dflysf] sld;gsf] b/cg';f/ ?=60 nfvsf] laj|mLdf PhG] 6n] sld;gafkt hDdf slt /sd
kfpF5, kQf nufpg'xf];\ .
;dfwfg
oxfF laj|mL dN" o ?=6000000 nfO{ sld;gsf] ;Ldfcg;' f/ 6'jm| \ofP/ n]Vbf,
?=6000000 = ?=1500000 + ?=1000000 + ?=1500000 + ?=2000000
0.5% 1% 1.5% 2%
hDdf sld;g /sd = ?=1500000 sf] 0.5% + ?=1000000 sf] 1%
+ ?= 1500000 sf] 1.5% + ?= 2000000 sf] 2%
= ?= 0.5 + ?= 1.5
1500000 × 100 1500000 × 100
+ ?= 1000000 × 1 + ?= 2000000 × 2
100 100
= ?=7500 + ?=10000 + ?=22500 + ?=40000
⸫ hDdf sld;g /sd = ?=80,000
pbfx/0f 4
Pp6f k':ts k;ndf sfd ug{] JolStsf] dfl;s tna ?=16,000 5 . pgn] dlxgfdf ?= 5,00,000
eGbf a9Lsf] k':ts lajm| L ug{ ;sd] f pgnfO{ 2% sld;g lbg] ul/G5 . olb pSt k;nsf]
j}zfv dlxgfsf] hDdf laj|mL ?= 7,25,000 eP, sfd ug{] JolStsf] pSt dlxgfsf] hDdf cfDbfgL slt
xG' 5, kQf nufpgx' f];\ M
;dfwfg
oxfF sd{rf/Lsf] dfl;s tna = ?=16000
j}zfv dlxgfsf] lajm| L /sd = ?=725000
sld;g b/ = 2%
sd{rf/Lsf] dfl;s cfDbfgL = ? hDdf lajm| L /sd ?=7,25,000 nfO{ sld;g ;Ldfcg';f/
6'jm| o\ fP/ n]vfF},
?= 725000 = ?= 500000 + ?= 225000
34 ul0ft, sIff (
sld;g = 2%
ca sld;g /sd = ?=250000 sf] 2%
= ?=250000 × 2
100
= ?=5000
t;y{ pSt sdr{ f/Lsf] jz} fv dlxgfsf] hDdf cfDbfgL = ?=(16000 + 5000)
= ?=21,000
cEof; 3.1
1. tnsf] tflnsfsf cfwf/df sld;g /sd kQf nufpg'xf;] \ M
j|m=;= ljj/0f hDdf laj|mL dN" o sld;g b/
-s_ hUuf ?=1 s/f]8 50 nfv
-v_ 3/ ?=2 s/f]8 5%
-u_ kmf]6f]skL dl] ;g ?=4 nfv
-3_ ;]o/ sf/fa] f/ ?=5 s/f8] 25 nfv 3%
7.5%
2%
2. Ph]G6n] ?=1,40,00,000 sf] 3/ al] rlbPafkt 5% sld;g kfpF5 eg]
-s_ PhG] 6n] kfpg] sld;g /sd slt xf]nf, lx;fa ug'x{ f];\ .
-v_ 3/wgLn] kfpg] /sd slt xf]nf, kQf nufpg'xf;] \ .
3. Pp6f df]6/;fOsn ;f]?ddf ?= 20,000 dfl;s lx;fan] tna kfpg] 10 hgf :6fkmx¿ 5g\ .
pgLx¿n] dfl;s sn' lajm| Lsf] 0.25% sld;g kfpg] /x5] g\ . olb c;f]h dlxgfdf hDdf
?= 35,00,000 sf] sf/f]af/ eP5 eg]
-s_ pSt ;f]?dn] sld;gafkt sdr{ f/LnfO{ hDdf slt ?lkofF lbgk' g{] /x]5, lx;fa
ug{xf;] \ .
-v_ Ps hgf sd{rf/Lsf] cfDbfgL pSt dlxgfsf] tnadf slt k|ltztn] jl[ 4 x'g] eP5 <
4. Pp6f Knfl:6shGo ;fdfg pTkfbs sDkgLn] ?=6,00,000 ;Ddsf] laj|mLdf 1%,
?=6,00,000 nfveGbf a9L ?= 10,00,000 ;Ddsf] laj|mLdf 1.5% / ?=10,00,000
eGbf dflysf] laj|mLdf 2% sld;g lbg] /x]5 eg] tn lbOPsf sf/fa] f/df ljj|m]tfn] k|fKt
ug{] sld;g lgsfNgx' f];\ M
-s_ ?=4,45,600 -v_ ?=7,25,000 -u_ ?=15,75,000
ul0ft, sIff ( 35
5. Pp6f s:d]l6s k;ndf sfd ug]{ sdr{ f/Lsf] dfl;s tna ?=17,000 5 . p;n] hDdf
laj|mL /sddf sx] L k|ltzt sld;g kfp5F . olb dªl\ ;/ dlxgfdf ?=10,00,000 lajm| L
u//] p;n] tna;lxt hDdf ?=30,000 cfDbfgL u/5] eg] k;naf6 slt kl| tzt sld;g
kfPsf] /x]5, kQf nufpg'xf;] \ .
kl/of]hgf sfo{
glhss} f] Pp6f sDkgL jf k;ndf hfgx' f;] \ . ToxfFsf sd{rf/Lx¿;uF jf dflns;uF
lgDglnlvt s'/fx¿sf af/d] f ;f]wk'5 ug'{xf];\ M
-s_ lajm| Lsf kf| jwfg
-v_ sd{rf/Lsf nflu laj|mLafktsf] yk ;l' jwfsf] of]hgf
pQ/
1. -s_ ?= 7,50,000 1. -v_ ?= 6,00,000 1. -u_ ?=30,000 1. -3_ ?=10,50,000
2. -s_ ?=7,00,000 2. -v_ ?=1,33,00,000 3. -s_ ?=87,500 3. -v_ 43.75%
4. -s_ ?=4,456 4. -v_ ?=7,875 4. -u_ ?=23500 5. 1.3%
36 ul0ft, sIff (
3.2 nfefz+ (Bonus)
lj|mofsnfk 1
lj=;=+ 2077 k;' 14 ut] gofF klqsf bl} gsdf ks| flzt æsdr{ f/LnfO{ 6 s/f8] nfefz+ ljt/0f
ub{} cfon lgudÆ zLifs{ sf] ;dfrf/sf] ;Dkflbt c+z o; k|sf/ 5 M
cfon lgudn] sdr{ f/LnfO{ nfef+z ljt/0f ug{] ePsf] 5 . gfkmf ePsf] jif{ nfefz+ ljt/0f
ug]{ sfg'gL kf| jwfgnfO{ 6]s/] lgud Joj:yfkgn] sdr{ f/LnfO{ nfefz+ ljt/0f ug]{ lg0f{o
u/]sf] xf] . t/ sd{rf/LnfO{ nfef+z v'jfpg lgudn] ;/sf/sf] cg'dlt lngk' 5{ .
cfon lgudn] b'O{ cfly{s jif{ (2075/076 / 2076/077) sf] nfefz+ afkt 5'6\ofPsf]
29 s/f]8 9 nfv 86 xhf/ ?lkofFaf6 sl/a 6 s/f8] ?lkofF sdr{ f/LnfO{ ljt/0f ug{
nfus] f] xf] . lgudsf] cflwsfl/s 6«8] o'lgogsf cWoIf uf]kfn /fOs{ f cg;' f/ ;xfos:t/sf
sdr{ f/LnfO{ 2 dlxgf 15 lbgsf] / clws[t jf ;fe] Gbf dflyNnf] :t/sf sdr{ f/LnfO{
2 dlxgfsf] tna a/fa/sf] /sd nfef+z ljt/0f ug]{ lg0f{o ePsf] 5 .
nfefz+ Pg] n] vb' gfkmfsf] 1 kl| tzt xg' cfpg] /sd ;fj{hlgs ;+:yfgsf sd{rf/LnfO{
nfef+zafkt ljt/0f ug{ kfpg] Joj:yf u/s] f] 5 . Pg] n] clwstd 3 dlxgfsf] tna a/fa/
sf] /sd Ps cflys{ jif{df sdr{ f/Ln] nfef+zafkt kfpg] Joj:yf;d]t u/s] f] 5 . lgudn]
nfefz+ af6 56' o\ fPsf] /sdaf6 sd{rf/LnfO{ ljt/0f u/L afsF L /sdsf] 80% ;/sf/L
sf]ifdf / 20% lgudsf] sNof0fsf/L sf]ifdf hDdf ug'{kg{] 5 . bj' } sfi] fdf 22 s/f]8
?lkofFeGbf a9L /sd lgudn] hDdf ug]{ 5 .
dflysf] ;dfrf/sf] c+z cWoog u/L tnsf k|Zgx¿sf] pQ/ lbgx' f];\ M
-s_ sDkgLn] nfefz+ lsg lbG5 xfn] f <
-v_ s]nfO{ cfwf/ dfgL nfef+z ljt/0f ul/Psf] x'G5 xfn] f <
-u_ s] sDkgLn] d'gfkmf sdfpg g;Sbf klg nfef+z ljt/0f u5{ <
s'g} sd{rf/Ln] cfkm" sfo/{ t ;+:yfaf6 lgoldt ¿kdf kfpg] kfl/>lds -tna_sf
cltl/St pSt sd{rf/Ln] cfkm" sfo{/t ;:+ yfn] gfkmf sdfpg ;s]sf] jf a9L gfkmf sdfpg
;s]sf sf/0fn] sfo{/t sdr{ f/LnfO{ pSt gfkmfsf] lglZrt kl| tzt /sd jflif{s ¿kdf Psdi' 6
k|fT] ;fxg :j¿k k|bfg ul/g] /sdnfO{ nfefz+ (bonus) elgG5 . gk] fnsf] ;Gbed{ f xg] {] xf] eg]
gk] fn ljBt' \ kf| lws/0f, g]kfn 6l] nsd, gk] fn cfon lgud, gk] fn vfgk] fgL ;:+ yfg, ljleGg
aª} \sx¿nufot cGo lghL ;+:yfgx¿n] d'gfkmf u/]df To:tf ;+:yfgx¿df sfd ug{] sd{rf/Lx¿n]
Pg] lgodcg;' f/ jflifs{ ¿kdf Psdi' 6 nfef+z (bonus) kfpg] u5g{ \ .
ul0ft, sIff ( 37
pbfx/0f 1
Pp6f pBfu] n] Ps jifd{ f ?= 40,00,000 d'gfkmf u/]5 . d'gfkmf u/s] f] /sdsf] 60% /sd
To; pBfu] df sfo{/t 80 hgf sdr{ f/LnfO{ gub nfefz+ (bonus) :j¿k a/fa/ /sd ljt/0f
ug]{ lg0f{o u/]5 eg] k|To]s sdr{ f/Ln] pSt jif{ slt /sd nfefz+ afkt k|fKt ug{] /x5] g\,
kQf nufpgx' f];\ .
;dfwfg
hDdf d'gfkmf u/s] f] /sd = ?= 40,00,000
ljt/0f ul/g] nfef+z (bonus) /sd = ?= 40,00,000 sf] 60%
= ?= 4000000 × 60
100
= ?= 24,00,000
hDdf sdr{ f/L ;ªV\ of = 80 hgf
Ps hgf sdr{ f/Ln] kfpg] nfefz+ = ?= 2400000
80
= ?=30,000
ctM kT| o]s sd{rf/Ln] pSt jif{df tna afx]s ?=30,000 nfefz+ (bonus) k|fKt u5g{ \ .
pbfx/0f 2
Pp6f xf]6nn] Ps jif{df ?= 50,00,000 dg' fkmf u/5] . d'gfkmfsf] sx] L k|ltzt ;f] xf]6ndf sfo{/t 55
hgf sfdbf/nfO{ a/fa/ ?=50,000 sf b/n] nfefz+ (bonus) ljt/0f u/]5 eg] ;f] xf]6nn] dg' fkmfsf]
slt kl| tzt nfefz+ ljt/0f u/]sf] xfn] f, lx;fa ug'{xf];\ .
;dfwfg
xf]6nsf] hDdf jflif{s dg' fkmf = ?=5000000
kl| t sd{rf/L ljt/0f ul/Psf] nfef+z (bonus) = ?=50000
hDdf sd{rf/L ;ª\Vof = 55 hgf
nfefz+ (bonus) :j¿k ljt/0f ul/Psf] hDdf /sd = 55 × ?=50000
= ?=2750000
⸫ nfef+z (bonus) b/ = ?= 2750000 × 100%
5000000
= 55%
38 ul0ft, sIff (
3.3 nfefz+ (Dividend)
ljm| ofsnfk 2
lj=;+= 2077 r}q 14 ut] uf/] vfkq cgnfOgdf k|sflzt æ6l] nsdsf] nfefz+ kfl/tÆ zLif{ssf]
;dfrf/sf] ;Dkflbt cz+ o; k|sf/ 5 M
g]kfn b/' ;~rf/ sDkgLn] cflys{ jif{ 2076/77 sf] d'gfkmfaf6 k|lt ;]o/ 40 ?lkofFsf b/n]
;o] /wgLnfO{ gub nfef+z ljt/0f ug]{ k:| tfj kfl/t u/]sf] lyof] .
dflysf] ;dfrf/ c+z cWoog u/L tnsf kZ| gx¿sf] pQ/ lbg'xf];\ M
-s_ ;]o/ egs] f] s] xf] <
-v_ tkfOF{ cyjf tkfO{sF f] kl/jf/df sg' } ;b:on] s'g} sDkgLsf] ;]o/ vl/b uge'{ Psf] 5 <
-u_ nfefz+ egs] f] s] xf] < s]nfO{ cfwf/ dfgL sDkgLn] nfefz+ ljt/0f u5{ <
-u_ sDkgLn] kT| o]s jif{ u/]sf] d'gfkmfsf] s]xL lx:;f ;o] / wgLx¿nfO{ ljt/0f ug]{ u5,{
tkfOF{n] To:tf] /sd kf| Kt ug{e' Psf] 5 <
sg' } sDkgL jf gfkmfd"ns ;+:yfdf ;o] / nufgL u/]sf cfwf/df ;+:yfn] sdfPsf] gfkmf
/sdsf] s]xL kl| tzt /sd ;o] /wgL (share holder) nfO{ kb| fg ul/G5 eg] pSt
/sdnfO{ nfefz+ (dividend) elgG5 . nfef+z ljt/0f ubf{ ;:+ yfgsf] v'b gfkmfdWo]
5'6\ofOPsf] lglZrt kl| tzt /sdnfO{ ;o] / ;ª\Vofn] efu u/]/ ljt/0f ul/G5 . o:tf]
nfefz+ (dividend) bO' { lsl;dsf] xG' 5 M -s_ gub nfefz+ (cash dividend) / -v_ ;]o/
nfefz+ (share dividend) .
pbfx/0f 3
olb Pp6f n3'ljQ sDkgLdf ?=100 sf b/n] 600000 lsQf ;]o/ /x5] / pSt ;+:yfn] Ps jifd{ f
?=7,40,00,000 d'gfkmf u/]5 . olb ;+:yfn] dg' fkmfsf] 20% gub nfefz+ (cash dividend)
;o] / wgLx¿nfO{ ljt/0f ug{] lg0f{o u/]5 eg] pSt sDkgLsf] 60 lsQf ;o] / x'g] JolStn] slt nfefz+
(cash dividend) k|fKt u5,{ kQf nufpgx' f];\ .
;dfwfg
oxfF hDdf dg' fkmf = ?=74000000
ljt/0f ul/g] hDdf gub nfefz+ = ?=74000000 sf] 20%
= ?= 74000000 × 20
100
= ?=14800000
ul0ft, sIff ( 39
kml] /, hDdf lsQf ;ªV\ of = 600000
1 lsQf ;o] /sf] gub nfefz+ = ?= 14800000
600000
= ?=24.66
ct M 60 lsQf ;o] / xg] JolStn] pSt sDkgLaf6 k|fKt ug{] nfef+z = 60 × ?=24.66
= ?=1,480
cEof; 3.2
1. tnsf] tflnsfsf cfwf/df nfef+z lx;fa ug{'xf;] \ M
sDkgL dg' fkmf nfefz+ b/
-s_ ?=60 nfv
-v_ ?= 2 s/f8] 50 nfv 25%
-u_ ?=80 nfv 67.5%
-3_ ?=9 s/f8] 48%
55%
2. Pp6f sk8f pBfu] n] lj=;=+ 2076 ;fndf ?=5 nfv 60 xhf/ d'gfkmf u/5] . dg' fkmf
u/s] f] /sdsf] 60% /sd cfˆgf] pBfu] df sfd ug]{ 105 hgf sdr{ f/LnfO{ gub nfefz+
:j¿k ljt/0f ug]{ lg0fo{ u/]5 eg] kT| os] sd{rf/n] slt slt /sd k|fKt ug]{ eP5g\,
kQf nufpg'xf;] \ .
3. Pp6f ladf sDkgLn] dg' fkmfsf] b'O{ ltxfO /sd cfˆgf 150 hgf sdr{ f/Lx¿nfO{ a/fa/
?= 40,000 sf b/n] nfefz+ :j¿k ljt/0f ug{] lg0f{o u/]5 eg] To; jif{ ;f] sDkgLsf]
hDdf dg' fkmf slt /x]5 <
4. tn lbOPsf] tflnsfaf6 s'n nfef+z (Total dividend) / kl| t ;o] / lsQf nfef+z
(Per share dividend) lx;fa ug{x' f;] \ M
sDkgL hDdf ;o] / lsQf nfefz+ (dividend) b/ vb' gfkmf
-s_ ?=5000000
-v_ 450000 40% ?=120000000
-u_ 11562486 55.5% ?=52060000
-3_ 32850000 23.5% ?=2756736894
216325030 60%
5. olb ;o" {nIdL ;xsf/L ;+:yfdf ?=100 sf b/n] 13,63,497 lsQf ;o] / lyof] . ddtfsf]
pSt ;xsf/L ;:+ yfdf 350 lsQf ;o] / 5 . ;:+ yfn] Ps jif{df ?=1 s/f8] 20 nfv d'gfkmf
40 ul0ft, sIff (
sdfP5 / ;]o/ wgLx¿nfO{ dg' fkmfsf] 45% gub nfef+z lbg] lg0f{o u/]5 eg] ddtfn]
slt gub nfefz+ (dividend) kfpFl5g\, kQf nufpgx' f;] \ .
6. ?=100 kg{] 22,39,440 lsQf ;]o/ ePsf] Pp6f ladf sDkgLn] jflifs{ ?=1,52,05,674
d'gfkmf u/5] . ;f] sDkgLsf] ;~rfns ;ldltaf6 dg' fkmfsf] 65% gub nfefz+
(cash dividend) lbg] lg0f{o eP5 eg] 280 lsQf ;]o/ ePsf] Ps hgf ;o] / wgLn]
hDdf slt gub nfef+z kfp5F g\ xf]nf, lx;fa ugx'{ f;] \ .
kl/ofh] gf sfo{
cfˆgf] sIffsf7] fsf ;fyLx¿nfO{ 5 cf]6f ;d"xdf ljefhg u/L ljleGg 5 cf6] f ;fj{hlgs
jf lghL ;+:yfgx¿n] cfˆgf sdr{ f/LnfO{ ljt/0f ug{] nfef+z (bonus) / sg' } 5 cf]6f
sDkgLsf] ;]o/cg;' f/ ljt/0f x'g] nfefz+ (dividend) nfO{ sIffsf]7fdf k:| t't ugx'{ f;] \ .
pQ/
1. -s_ ?=1,5,00,000 1.-v_ ?=1,68,75,000 1. -u_ ?= 38,40,000
1. -3_ ?= 4,95,00,000 2. ?=3,200 3. ?= 90,00,000
4. -s_ ?=20,00,000 / ?= 4.44 4. -v_ ?= 6,66,00,000 / ?=5.70
4. -u_ ?=1,22,34,100 / ?=0.37 4.-3_?=1,65,40,42,136 / ?=7.65
5. ?=1,386.14 6. ?=1,235.77
ul0ft, sIff ( 41
3/fo;L cªs\ ul0ft
kf7 4 (Household Arithmetic)
4.0 k'g/jnf]sg (Review)
tnsf k|Zgx¿df 5nkmn u/L ;dfwfg ug'{xf];\ M
-s_ 25 cf6] f sfkLsf] d"No ?=500 k5{ eg] Pp6f sfkLsf] dN" o slt k5{ <
-v_ Ps bhg{ sfkLsf] d"No ?=600 k5{ eg] 7 cf6] f sfkLsf] d"No slt x'G5 <
-u_ ?=500 sf] SofNs'n]6/df 2% 5'6 lbFbf slt /sd 5'6 xG' 5 < 5'6kl5sf] dN" o slt
xG' 5 <
-3_ cfkm";uF ePsf] ?=750 df 10% /sd yKg] xf] eg] slt ?lkofF x'G5 <
P]lss lgod, 5'6 /sd, yk /sd;DaGwL lx;fax¿ cluNnf sIffx¿df cWoog ul/;ss] f 5f}F .
h;sf] ko| fu] af6 xfdf| bl} gs hLjgdf 3/df vkt ul/g] lah'nL, kfgL, 6]lnkmf]g lansf] dx;'n
ltg]{ an] fdf ul0ftLo cfwf/et" lj|mofx¿af6 lx;fa ug{ ;xh xG' 5 .
ljBt' \ dx;'n, kfgLsf] dx;n' , 6l] nkmf]g dx;'n, 6\ofS;L ef8f cflb h:tf 3/fo;L vr{x¿
cfˆgf] df]afOn ;]6df xg' ] PK; jf sDKo6' / ;6] sf] ko| f]u u//] cgnfOg (online) dfWodaf6
klg e'StfgL ug{ ;lsG5 . cfhsfn ;"rgf k|ljlwn] ubf{ ljleGg dx;n' x¿, zN' sx¿ eS' tfgL
ug{ ;DalGwt sfofn{ odf ef}lts ¿kdf pkl:yt eO{ 3G6f}F kª\lStdf /xg'kg{] afWofTds
cj:yfsf] cGTo xb'F } uPsf] 5 .
4.1 lahn' Lsf] vkt;DaGwL 3/fo;L vrs{ f] lx;fa
(Household expenses for use of electricity)
lj|mofsnfk 1
g]kfn ljB't\ k|flws/0fn] pknAw u/fpg] ljBt' \ ;]jfafkt nfUg] dx;'n b/ ljBt' \ ld6/
Ifdtfcg';f/ km/s km/s ¿kdf ljlgodfjnL 2077 df lgDgfg';f/ pNnv] ul/Psf] 5 M
42 ul0ft, sIff (
ls=jf=306f 5 PlDko/ 15 PlDko/ 30 PlDko/ 60 PlDko/
-ol' g6_
;j] f zN' s OghL{ z'Ns ;j] f z'Ns OghL{ zN' s ;]jf zN' s OghL{ zN' s ;j] f zN' s OghL{ zN' s
0 – 10 -?=_ -?=_ -?=_ -?=_ -?=_ -?=_ -?=_ -?=_
0 – 20 30 gnfUg] 50 4 75 5 125 6
21 – 30 75 7 100 7 150 7
31 – 50 30 3 100 8.50 125 8.50 175 8.50
51 – 150 50 7 125 11 150 11 200 11
151 – 250 75 8.50 150 12 175 12 225 12
251 – 400 100 10 175 13 200 13 250 13
125 11 200 14 225 14 275 14
400 eGbf 150 12
dfly 175 13
dflysf] dx;'n b/ / ;Fus} f] lan cWoog u/L tnsf] kZ| gx¿ ;DaGwdf sIffsf7] fdf ;fyLx¿lar
5nkmn ugx{' f];\ M
gf]6 M lsnf]jf6nfO{ 5f6] s/Ldf ls=jf= nl] vG5 .
-s_ lbOPsf] lah'nLsf] lan s'g dlxgfsf] xf] <
-v_ ;f]xL dlxgfdf o; landf slt ol' g6 ljB't\ vkt ePsf] b]Vg
;lsG5 <
-u_ o; lancg';f/ ;]jf zN' safkt slt ltg{'kg{] b]lvG5 <
-3_ landf OghL{ z'Ns slt p75] <
-ª_ lancg';f/ slt Ifdtfsf] ld6/ h8fg ul/Psf] /x]5 <
-r_ tkfO{Fsf] 3/df s'g Ifdtfsf] ld6/ h8fg ug{'ePsf] 5 <
-5_ tkfO{sF f] 3/df h8fg ul/Psf] ld6/sf] Gog" td dx;n' s;/L
lx;fa ug'{xG' 5 <
-h_ dflysf] dx;n' b/ tflnsfdf ;j] f zN' s (service charge)
eGgfn] s] a'lemG5 < OghL{ z'Ns (energy charge) eGgfn]
s] al' emG5 <
-em_ tkfO{nF fO{ ld6/ l/8/n] xfn ko| f]udf NofOPsf] :jrflnt
d]l;gaf6 lbg] landf s'g sg' ljj/0fx¿ pNnv] ul/Psf] xG' 5 <
-`_ tkfOFn{ ] ld6/ l/8/af6 kf| Kt uge{' Psf] landf plNnlvt dx;n'
s;/L lx;fa ul/Psf] xf]nf <
ul0ft, sIff ( 43
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