Student handbook maths 7 july 2017

1
Ekk/;fed f”k{kk rS;kjh dk;ZØe & ,l-,l-vkj-ih-
fo|kfFkZ;ksa ds fy, vH;kl iqfLrdk
xf.kr

1
izkDdFku
mÙkj izns”k ek/;fed f”k{kk vfHk;ku vkSj dqlqek Qkm.Ms”ku ds la;qDr iz;kl ls l= 2016&2017 esa ik¡p tuinksa&
y[kuÅ] mUuko] lhrkiqj] jk;cjsyh ,oa y[kheiqj [khjh ds 52 rFkk gjnksbZ tuin ds 25 jktdh; ek/;fed fo|ky;ksa
esa ^mn~Hko dk;ZØe* dk “kqHkkjaHk fd;k x;kA mn~Hko dk;ZØe jktdh; ek/;fed fo|ky;ksa esa d{kk&9 esa izos”k ysus okys
fo|kfFkZ;ksa ds vf/kxe Lrj dks d{kkuq:i cukus dk ,d iz;kl gS rkfd mUgsa ek/;fed ,oa mPp f”k{kk izkIr djus esa
vklkuh gks ldsA lkFk gh bl dk;ZØe ds fØ;kUo;u vkSj f”k{k.k dh xq.koÙkk c<+kus gsrq f”k{kdksa ds {kerko)Zu dk
Hkh izko/kku gSA
jk’Vªh; ek/;fed f”k{kk vfHk;ku dh uhfr;ksa ds vuq:i ,oa blds mn~ns”;ksa dh izkfIr gsrq dqlqek Qkm.Ms”ku us ^mn~Hko
dk;ZØe* dk fodkl fd;k ftls gjnksbZ tuin ds 25 jktdh; ,oa jktdh; lgk;rk izkIr ek/;fed fo|ky;ksa esa foxr
rhu o’kksZa ls lQyrkiwoZd lapkfyr fd;k tk jgk gSA blds varxZr d{kk 9 ,oa 10 ds fo|kfFkZ;ksaa ds orZeku vf/kxe
Lrj dk fu/kkZj.k dj muds lkFk dk;Z fd;k tkrk gSA lkFk gh f”k{k.k vf/kxe izfØ;k dks csgrj cukus ds fy, dqlqek
Qkm.Ms”ku }kjk fodflr fo’k; vk/kkfjr lalk/ku fo|kfFkZ;ksaa ,oa f”k{kdksa dks miyC/k djk;s tkrs gSaA
bl dk;ZØe ds varxZr f”k{kd izf”k{k.k vk;ksftr fd;s tkrs gSa rFkk fo|ky; Lrj ij f”k{kdksa dks lg;ksx iznku djus
gsrq ftyk lalk/ku lewg ¼fMfLVªDV fjlkslZ xzqi½ dk xBu fd;k tkrk gSA blls f”k{k.k dks izHkkoh cukus ds fy, fofHkUu
f”k{k.k fof/k;ksa dks le>us ,oa lh[kus esa f”k{kdksa dks lgk;rk feyrh gSA
jk’Vaªh; ek/;fed f”k{kk vfHk;ku ds mís”;ksa dh iwfrZ gsrq mÙkj izns”k ek/;fed f”k{kk vfHk;ku jkT; ds mi;qZDr tuinksa
ds p;fur fo|ky;ksa esa ^mn~Hko dk;ZØe* o vU; fo|ky;ksa esa jk’Vaªh; ek/;fed f”k{kk vfHk;ku }kjk vknsf”kr *fjesfM;y
d{kk,a* fØ;kfUor djus dk fu”p; fd;k x;k gSA mn~Hko dk;ZØe ds vUrxZr f”k{k.k eq[; :i ls pkj fo’k;ksa ¼xf.kr]
foKku] vaxzsth o fgUnh½ ij dsfUnzr gS vkSj blds fØ;kUo;u dh vof/k nks o’kZ dh gSA lkFk gh jk’Vªah; ek/;fed f”k{kk
vfHk;ku ds vUrxZr fjesfM;y d{kk,a rhu fo’k;ksa ¼xf.kr] vxzsath vkSj foKku½ ij dsfUnzr gSa vkSj blds fØ;kUo;u dh
vof/k 45 fnuksa dh gSA mÙkj izns”k ek/;fed f”k{kk vfHk;ku }kjk jkT; ds “ks’k fo|ky;ksa esa fjesfM;y d{kk,a “kq: djus
gsrq dqlqek }kjk fufeZr mnHko dk;ZØe ds lalk/kuksa dk bLrseky fd;k x;k gSA
foxr o’kZ dh rjg bl o’kZ 2017&2018 esa Hkh bl dk;ZØe dh lQyrk vki f”k{kdksa] iz/kkukpk;ksZa] fMfLVªDV fjlkslZ
xzqi ,oa LVsV fjlkslZ xzqi ds lnL;ksa dh lfØ; Hkkxhnkjh ,oa ifjJe ij gh fuHkZj gS ftl ij gesa iw.kZ fo”okl gSA ge
bl dk;ZØe dh lQyrk ds fy;s vkidks gkfnZd “kqHkdkeuk,a nsrs gSaA
;w-ih-,e-,l-,- Vhe dqlqek Vhe

33
ifjp;
;g fo|kfFkZ;ksa dh viuh vH;kl iqfLrdk gSA bldk mn~ns”; Qkm.Ms”ku dSai esa fd, tk jgs dk;ksZa dks xgjkbZ ls
lh[kus esa fo|kfFkZ;ksa dh enn djuk gSA ;g bl rjg ls cukbZ xbZ gS fd f”k{kd igys fo|kfFkZ;ksa dks dksbZ vo/kkj.kk
fl[kk,axs vkSj fQj mlds vH;kl ds fy, blesa dqN loky fn, x, gSaaA mu lokyksa dks gy djus ls fo|kfFkZ;ksa dks
mu voèkkj.kkvksa dks iDdk djus esa enn feysxhA
bl vH;kl iqfLrdk esa dbZ txg ,sls loky fn, x, gSa ftUgsa djus ds ckn d{kk esa izLrqr djuk gS rFkk ml ij lkFkh
fo|kfFkZ;ksa o f”k{kd ds lkFk ckr djuh gSA blls fo|kfFkZ;ksa dks xf.kr dh vo/kkj.kkvksa ls tqM+s vius fopkj nksLrksa o
f”k{kdks ds lkFk lk>k djus o mu ij ckrphr djus dk ekSdk feysxkA
vke rkSj ij fo|kfFkZ;ksa dks bl ij ,d fnu esa nks ckj dke djuk iM+sxkA f”k{kd fo|kfFkZ;ksa dks crk nsaxs fd mUgsa bl
ij dc dke djuk gSA
bl vH;kl iqfLrdk esa dqN loky ,sls fn, x, gSa tks f”k{kd }kjk fl[kkbZ xbZ vo/kkj.kk ds vH;kl ds fy, gSa vkSj
dqN loky ,sls gSa tks f”k{kd }kjk fl[kkbZ xbZ vo/kkj.kk dks mlds vxys Lrj ij bLrseky djus ds fy, gSA ,sls iz”u
fo|kfFkZ;ksa ds lkeus muds Kku dks FkksM+k QSykus ds fy, j[ks x, gSa rkfd os mu pqukSfr;ksa ls tw> dj viuh xf.krh;
le> dks FkksM+k vkSj fodflr dj ik,aA

4
dk;Zi=d& 1% la[;kvksa dks la[;k js[kk ij n”kkZuk
1- 36 dks la[;k js[kk ij n”kkZ,aA
2- 50] 65] 83 dks la[;k js[kk ij n”kkZ,aA
3- 600] 745] 943] 678 dks la[;k js[kk ij n”kkZ,aA
4- 3000] 5500] 7560] 8491 dks la[;k js[kk ij n”kkZ,aA ;k] vius eu ls rhu vadh; pkj la[;k,a fy[ksa o mudks
la[;k js[kk ij n”kkZ,aA

5
dk;Zi=d& 2% la[;kvksa dh tksM+ rksM+
1- 47] 50] 87] 94 dks rksM+dj fy[ksaA
2- 450] 372] 718 dks rksM+dj fy[ksaA
3- 2400] 3750] 9876 dks rksM+dj fy[ksaA
4- uhps fy[kh la[;kvksa dks feykdj cuus okyh la[;k,a fy[ksaA
3] 80] 400] 5] 20] 300] 740] 606] 60] 4] 900
5- uhps fy[kh la[;kvksa dks feykdj cuus okyh lHkh la[;k,a fy[ksaA
5000] 4] 300] 8] 7000] 100] 9] 4005] 5201] 3002] 600

6
dk;Zi=d& 3% la[;kvksa ds vkilh laca/k rFkk la[;k ds fdrus eryc
1- vius eu ls dksbZ pkj la[;k fy[ksaA muesa ls nks dks la[;k js[kk ij n”kkZ,a o ckdh nks la[;kvksa dks rksM+ dj fy[kasA
2- 3] 5] 7] 40] 70] 90 dk 10 ds lkFk laca/k n”kkZ,aA
3- 20] 600] 700] 50] 300 o 80 dk 100 ds lkFk laca/k n”kkZ,aA

4- 1000] 5000] 400] 9000] 40] 700] 3000 rFkk 900 dk 1000 ds lkFk laca/k n”kkZ,aA
5- 50000] 6000] 70000] 300] 20] 80000] 900] 10 dk 10000 ds lkFk laca/k n”kkZ,aA
6- uhps nh xbZ la[;kvksa dks 10 o 1 ds uksVksa rFkk bdkbZ o ngkbZ esa n”kkZvksA
47] 87
7- uhps nh xbZ la[;kvksa dks 10 o 1 ds uksVksa rFkk bdkbZ o ngkbZ esa n”kkZvksA
258] 641] 729] 403

7
dk;Zi=d& 4% ,d la[;k ds fdrus eryc rFkk cqfu;knh bdkbZ
1- uhps nh xbZ la[;kvksa dks 100] 10 o 1 ds uksVksa rFkk lSdM+k ngkbZ o bdkbZ esa n”kkZvksA
647] 873
2- uhps nh xbZ la[;kvksa dks 1000] 100] 10 o 1 ds uksVksa rFkk gtkj] lSdM+k ngkbZ o bdkbZ esa n”kkZvksA
3447] 8701
3- uhps nh xbZ la[;kvksa dks ngkb;ksa o bdkb;ksa esa n”kkZvksA
719 ¾
406 ¾
527 ¾
346 ¾
222 ¾
900 ¾
654 ¾
4- uhps nh xbZ la[;kvksa dks lSdM+k rFkk bdkb;ksa esa n”kkZvksA
9876 ¾
7349 ¾
8761 ¾
3001 ¾
4539 ¾

8
dk;Zi=d& 5% ,d la[;k ds fdrus eryc rFkk cqfu;knh bdkbZ rFkk nksgjku
1- uhps nh xbZ lkj.kh HkjsaA
la[;k bdkb;ka ;kuh
1 dk uksV
ngkb;ka o bdkb;ka ;kuh
nl dk 10 uksV o 1
dk uksV
lSdM+k o bdkb;ka ;kuh 100
dk uksV o 1 dk uksV
gtkj o bdkb;ka ;kuh 1000
dk uksV o 1 dk uksV
26
90
82
175
973
080
404
3927
9075
8631
2580
0055
8003
9999
0660
1- uhps nh xbZ la[;kvksa dks la[;k js[kk ij n”kkZb,A
37] 753] 8642

9
1- uhps nh xbZ la[;kvksa dks rksM+dj fy[ksaA
29] 456] 3209
2- uhps fy[kh la[;kvksa dks feykdj cuus okyh lHkh la[;k,a fy[ksaA
8] 70] 400] 1] 60] 900] 630] 202] 10] 7] 800
3- 30] 500] 600] 40] 200 o 70 dk 100 ds lkFk laca/k n”kkZ,aA

10
dk;Zi=d& 6% nksckjk lewghdj.k djds tksM+uk o ?kVkuk
1- uhps fn, x, lokyksa dks la[;k,a rksM+dj tksM+sasA
v- 58 esa 37 tksM+sasA
c- 49 esa 62 tksM+sasA
l- 498 eas 342 tksM+sasA
n- 345 esa 789 tksM+sasA
;- 0987 esa 5463 tksM+sasA
j- 9456 esa 6789 tksM+sasA

11
1- uhps fn, x, lokyksa dks la[;k,a rksM+dj ?kVk,aA
v- 52 esa ls 26 ?kVk,aA
c- 94 esa ls 37 ?kVk,aA
l- 642 esa ls 489 ?kVk,aA
n- 721 eas ls 346 ?kVk,aA
;- 6456 esa ls 3897 ?kVk,aA
j- 8123 esa ls 5467 ?kVk,aA

12
dk;Zi=d& 7% HkjikbZ ds rjhds ls tksM+uk rFkk cjkcj la[;k tksM+@?kVk dj ?kVkuk
1- uhps fn, x, lokyksa dks HkjikbZ ds rjhds ls tksM+sasA
c- 59 esa 76 tksM+sasA
l- 468 esa 247 tksM+sasA
n- 251 eas 867 tksM+sasA
;- 8242 esa 9765 tksM+sasA
j- 4723 esa 5738 tksM+sasA

13
2- uhps fn, x, lokyksa esa cjkcj la[;k tksM+@?kVk dj ?kVk,aA
n- 601 eas ls 275 ?kVk,aA
;- 5364 esa ls 2476 ?kVk,aA

14
dk;Zi=d& 8% vkaf”kd tksM+ o vkaf”kd ?kVko
1- uhps fn, lokyksa dks vkaf”kd tksM+ ds rjhds ls gy djsaA
c- 58 esa 146 tksMsa+A
l- 458 esa 387 dks tksMsa+A

n- 594 esa 987 dks tksMsa+A
;- 3579 esa 4876 dks tksMsa+A
j- 2463 esa 9767 dks tksMsa+A

15
2- uhps fn, lokyksa dks vkaf”kd ?kVko ds rjhds ls gy djsaA
n- 798 esa ls 345 ?kVk,aA
;- 6579 esa ls 2312 ?kVk,aA

16
dk;Zi=d& 9% la[;k js[kk ij tksM+
uhps fn, x, lokyksa dks la[;k js[kk ij tksMsaA
v- 37 esa 65 tksMsa+A
c- 89 esa 263 tksMsa+A
l- 347 esa 278 dks tksMsa+A
n- 503 esa 769 dks tksMsa+A
;- 8643 esa 2006 dks tksMsa+A
j- 3794 esa 7843 dks tksMsa+A

17
dk;Zi=d& 10% la[;k js[kk ij ?kVko
uhps fn, lokyksa dks vkaf”kd ?kVko ds rjhds ls gy djsaA
n- 798 esa ls 345 ?kVk,aA
;- 6579 esa ls 2312 ?kVk,aA

18
dk;Zi=d& 11% tksM+ o ?kVko ds O;kogkfjd loky cukuk
tksM+ o ?kVko ds loky cuk,aA
uksV& 982] 248] 1230] gkfen] vatw rFkk iqLrdsa
¼;fn 982 iqLrds gkfen ds ikl gSa ,oa 248 iqLrds vatw ds ikl gS rks nksuks ds ikl dqy fdruh iqLrdsa gSa½
v- 982 $ 248 ¾ -------
c- 982 & 248¾ -------
l- 248 $ ------- ¾ 982
n- 982 & ------- ¾ 248
;- 982 $ ------- ¾ 1230

19
dk;Zi=d& 12% iqujko`fRr
1- 438 esa 873 dks tksM+ ds pkjksa rjhdksa ls gy djsaA
v- la[;k rksM+dj
c- vkaf”kd tksM+
l- HkjikbZ ds rjhds ls
n- la[;k js[kk ij

20
2- 1234 esa ls 965 dks pkjksa rjhdksa ls ?kVk,aA
v- la[;k rksM+dj
c- vkaaf”kd ?kVko
l- cjkcj la[;k tksM+ ;k ?kVkdj
n- la[;k js[kk ij

21
dk;Zi=d& 13% forj.k ds fu;e ls xq.kk
1- xq.kk ds lokyksa dks forj.k ds fu;e dh lgk;rk ls gy djsaA
v- 4 × 7 ¾
c- 6 × 38 ¾
l- 23 × 25 ¾
n- 36 × 14 ¾

22
2- xq.kk ds lokyksa dks forj.k ds fu;e dh enn ls gy djsaA
v- 432 × 2 ¾
c- 753 × 8 ¾
l- 415 × 14 ¾
n- 231 × 13 ¾

23
dk;Zi=d& 14% {ks=Qy dh enn ls xq.kk djuk
1- uhps fn, x, lokyksa dks {ks=Qy dh lgk;rk ls xq.kk djds fn[kk,aA
v- 4 × 3 ¾
c- 8 × 6 ¾
l- 17 × 5 ¾
n- 7 × 42 ¾

24
2- uhps fn, x, lokyksa dks {ks=Qy dh lgk;rk ls gy djds fn[kk,aA
v- 34 × 27 ¾
c- 15 × 24 ¾
l- 126 × 3 ¾
n- 345 × 38 ¾

25
dk;Zi=d& 15% x.kufof/k ds lkFk LFkkuh; eku dh enn ls xq.kk
1- uhps fn, x, loky dks gy djks o mls gy djus dk rjhdk vius “kCnksa esa fy[kksA
v- 64 × 3 ¾
c- 37 × 16 ¾
l- 613 × 12 ¾
n- 602 × 513

26
dk;Zi=d& 16 cqfu;knh bdkbZ okyh la[;kvksa dk xq.kk djuk
uhps fn, x, lokyksa dks gy djksA
v- 5 bdkbZ × 7 ngkbZ
1- rks tokc essa dqy fdruh ngkb;ka feysaxh
2- rks tokc esa dqy fdruh bdkb;ka feysaxh
3- rks tokc esa dqy fdrus lSdM+k o fdruh ngkb;ka feysaxh
c- 43 ngkbZ × 5 ngkbZ
1- rks tokc esa dqy fdrus lSdM+k o fdruh ngkb;ka feysaxh
2- rks tokc esa dqy fdruh bdkb;ka feysaxh
3- rks tokc esa dqy fdrus lSdM+k feysaxs
4- rks tokc esa dqy fdrus gtkj o fdrus lSdM+k feysaxs
5- rks tokc esa dqy fdrus nl gtkj o fdrus lSdM+k feysaxs
l- 43 lSdM+k × 3 lSdM+k
1- rks tokc esa dqy fdrus nl gtkj feysaxs
2- rks tokc esa dqy fdrus yk[k o gtkj feysaxs
3- rks tokc esa dqy fdrus lSdM+k feysaxs
4- rks tokc esa dqy fdrus nl yk[k o nl gtkj feysaxs

27
dk;Zi=d& 17% forj.k ds fu;e ls Hkkx djuk
uhps fn, x, lokyksa dks forj.k ds fu;e dh lgk;rk ls gy djsaA
v- 348 » 7 ¾
c- 405 » 4 ¾
l- 438 » 14 ¾
n- 873 » 16 ¾
;- 3546 » 3 ¾
j- 3829 » 13 ¾

28
dk;Zi=d& 18% {ks=Qy ds ekWMy dh lgk;rk ls Hkkx djuk
1-uhps fn, x, lokyksa dks gy djsaA
v- 56 » 8 ¾
c- 96 » 6 ¾
l- 218 » 4 ¾
n- 403 » 9 ¾

29
2- uhps fn, x, lokyksa dks gy djsaA
v- 263 » 14 ¾
c- 784 » 16 ¾
l- 1234 » 12 ¾
n- 2304 » 17 ¾

30
dk;Zi=d& 19% x.kufof/k dh lgk;rk ls Hkkx djuk
1- uhsps fn, x, lokyksa dks x.kufof/k dh enn ls gy djsa rFkk mls djus dk rjhdk vius “kCnksa esa fy[ksaA rjhds dks
le>kus ds fy, uksVksa ds fp= Hkh cuk,aA
v- 352 » 6 ¾
c- 673 » 8 ¾

31
2- uhps fn, x, lokykas dks x.kufof/k ds rjhds ls gy djsa rFkk mls djus dk rjhdk vius “kCnksa esa fy[ksaA rjhds dks
le>kus ds fy, uksVksa ds fp= Hkh cuk,aA
v- 7234 » 7 ¾
c- 9304 » 4 ¾

32
dk;Zi=d& 20% la[;k js[kk ij xq.kk o Hkkx djuk
1-uhps fn, x, lokyksa dks la[;k js[kk ij gy djds fn[kk,aA
v- 5× 13 ¾

c- 12× 15 ¾
l- 16× 213 ¾
n- 36 » 4 ¾
;- 234 » 8 ¾
j- 432 » 12 ¾

33
dk;Zi=d& 21% iqujko`fRr
1- 24 × 17 dks uhps fn, x, lHkh rjhdksa ls gy djsaA
v- forj.k ds rjhds ls
c- la[;k js[kk ij
l- x.kufof/k ls
n- {ks=Qy ekWMy ls

34
2- 643 » 14 dks uhps fn, x, lHkh rjhdksa ls gy djsaA
v- forj.k ds rjhds ls
c- la[;k js[kk ij
l- x.kufof/k ls
n- {ks=Qy ekWMy ls

35
dk;Zi=d& 22% vkÑfr;ksa dh igpku o oxhZdj.k
1- uhps nh xbZ vkÑfr;ksa ij Øekad Mky nsaA blds ckn mUgsa /;ku ls ns[k dj vxys iUus ij nh xbZ lkj.kh HkjsaA

36
lkj.kh&1
lkj.kh&2
Øekad rhu dksus okyh
vkÑfr;ksa ds Øekad
pkj dksus okyh vkÑfr;ksa
ds Øekad
ikap dksus okyh vkÑfr;ksa
ds Øekad
Ng dksus okyh vkÑfr;ksa
ds Øekad
Øekad rhu Hkqtkvksa okyh
pkj Hkqtkvksa okyh
ikap Hkqtkvksa okyh vkÑfr;ksa
ds Øekad
Ng Hkqtkvksa okyh vkÑfr;kas
ds Øekad
v- pkSdksj vkÑfr ds ckjs eas rhu pkj ckras fy[ksaA
c- frdksuh vkÑfr ds ckjs esa rhu pkj ckrsa fy[ksaA
l- ikap dksus okyh vkÑfr ds ckjs esa rhu pkj ckrsa fy[ksaA

37
dk;Zi=d& 23 vkÑfr;ksa esa vUrj djuk
1-uhps nh xbZ lkjf.k;ksa esa vyx&vyx vkÑfr;ksa esa vkil eas varj crk,aA
f=Hkqt prqHkZqt
f=Hkqt ‘kV~Hkqt
f=Hkqt vk;r
vk;r oxZ

38
dk;Zi=d&24 dks.kksa ds izdkj
fn;s x;s fp=ksa esa ls vyx&vyx izdkj ds dksa.k NkaVsA dks.kksa dks NkaVdj muds uke uhsps lkj.kh esa fy[ksa ,oa izR;sd
dksa.k dh ifjHkk’kk vius “kCnksa esa fy[ksa&

39
dks.kksaa ds Øekad dks.k dk uke dks.k dh vius “kCnksa esa ifjHkk’kk

40
dk;Zi=d&25 f=Hkqt dk oxhZdj.k
1- uhps fn, x, f=Hkqtksa dks igys dks.kksa ds vk/kkj ij vkSj mlds ckn Hkqtk ds vk/kkj ij NkaVsaA igpku ds fy, igys
f=Hkqtksa ij Øekad yxk nsaA

41
v- dks.k ds vk/kkj ij f=Hkqtksa dk oxhZdj.k&
f=Hkqtksa ds Øekad f=Hkqtksa ds lewg dk uke
dks.k ds vk/kkj ij
ifjHkk’kk
f=Hkqtksa ds Øekad f=Hkqtksa ds lewg dk uke
Hkqtk ds vk/kkj ij
ifjHkk’kk
c- Hkqtk ds vk/kkj ij oxhZdj.k&

42
dk;Zi=d& 26% f=Hkqt
vius lewg esa f=Hkqtksa dh enn ls cukbZ xbZ rhu ls T;knk Hkqtkvksa okyh can vkÑfr;ksa ds fp= cukvksA ml vkÑfr
esa vkids }kjk bLrseky fd, x, f=Hkqt Hkh utj vkus pkfg,A

44
ifjp;
;g fo|kfFkZ;ksa dh viuh vH;kl iqfLrdk gSA bldk mn~ns”; lg;ksxkRed vf/kxe pj.k esa fd, tk jgs dk;ksZa dks xgjkbZ
ls lh[kus esa fo|kfFkZ;ksa dh enn djuk gSA ;g bl rjg ls cukbZ xbZ gS fd f”k{kd igys fo|kfFkZ;ksa dks dksbZ vo/kkj.kk
fl[kk,axs vkSj fQj mlds vH;kl ds fy, blesa dqN loky fn, x, gSaaA mu lokyksa dks gy djus ls fo|kfFkZ;ksa dks mu
voèkkj.kkvksa dks iDdk djus esa enn feysxhA
bl vH;kl iqfLrdk esa dbZ txg ,sls loky fn, x, gSa ftUgsa djus ds ckn d{kk esa izLrqr djuk gS rFkk ml ij lkFkh
fo|kfFkZ;ksa o f”k{kd ds lkFk ckr djuh gSA blls fo|kfFkZ;ksa dks xf.kr dh vo/kkj.kkvksa ls tqM+s vius fopkj nksLrksa o
f”k{kdks ds lkFk lk>k djus o mu ij ckrphr djus dk ekSdk feysxkA
vke rkSj ij fo|kfFkZ;ksa dks bl ij ,d fnu esa ,d ckj gh dke djuk iM+sxkA f”k{kd fo|kfFkZ;ksa dks crk nsaxs fd mUgsa
bl ij dc dke djuk gSA dbZ dke ,sls Hkh gSa tks mlh fnu iwjs uk gks ik,a ,sls esa f”k{kd cPpksa ls vH;kl iqfLrdk
esa cpk gqvk dke ?kj ls djds ykus ds fy, dgsaA
bl vH;kl iqfLrdk esa dqN loky ,sls fn, x, gSa tks f”k{kd }kjk fl[kkbZ xbZ vo/kkj.kk ds vH;kl ds fy, gSa vkSj
dqN loky ,sls gSa tks f”k{kd }kjk fl[kkbZ xbZ vo/kkj.kk dks mlds vxys Lrj ij bLrseky djus ds fy, gSA ,sls
loky fo|kfFkZ;ksa ds lkeus muds Kku dks FkksM+k QSykus ds fy, j[ks x, gSa rkfd os mu pqukSfr;ksa ls tw> dj viuh
xf.krh; le> dks FkksM+k vkSj fodflr dj ik,aA
bles dbZ txgksa ij cPpksa ds vuqHkoksa dks lk>k djus ds loky Hkh fn, x, gSaA ;s loky f”k{kdksa dks cPpksa ds vuqHkoksa
dks le>us esa enn djsaxsA

45
dk;Zi=d& 1% VSuxzke
1- uhps fn, x;s fp= esa jax Hkj nsaA pkgsa rks ,d gh jax Hkjsa vFkok vyx&vyx jax Hkj ldrs gSaA

47
vc uhps fn, x, loky dk tokc fy[ksaA f=Hkqtksa ij vius eu ls Øekad yxk nsaaA
1- f=Hkqt 1 oxZ dk dkSu lk fgLlk gS vkius dSls irk yxk;k] vius “kCnksa esa fy[ksa fp= Hkh cuk,aA

48
6- oxZ iwjs oxZ dk dkSu lk fgLlk gS vkius dSls irk yxk;k] vius “kCnksa esa fy[ksa fp= Hkh cuk,aA
7- lekarj prqHkZqt iwjs oxZ dk dkSu lk fgLlk gS vkius dSls irk yxk;k] vius “kCnksa esa fy[ksa fp= Hkh cuk,aA

49
dk;Zi=d& 2% T;kferh; vkÑfr;ksa dk la;kstu
1- dk;Zi=d&1 esa fn, x, fp= dks dkV dj ckgj fudky ysa o fdlh eksVs dkxt ij fpidk dj dkV ysaA fQj
mu lkr VqdM+ksa dh enn ls i”kq if{k;ksa] phtksa vkfn dh vkd`fr;ka cuk,aA uhps muesa ls dqN dh vkmVykbu ;kuh
:ijs[kk cuk,aA vki pkgsa rks muesa jax Hkh Hkj ldrs gSaA

50
dk;Zi=d& 3% T;kferh; vkÑfr;ksa dk la;kstu ,oa eki esa O;Dr djuk
1- uhps 16 lseh- ifjeki okys vyx&vyx vk;r cukvksA vkSj mu fp=ksa dks ns[k dj ifjeki o {ks=Qy ds ckjs
esa viuh ifjdYiuk cukvks o fy[kksA var esa vius “kCnksa esa vk;r ds ifjeki o {ks=Qy ds ckjs esa ,d lexz
ifjdYiuk fy[kksA

51
dk;Zi=d& 4% vadxf.krh; fu;eksa dks chtxfr.krh; :i esa fy[kuk
1- ?kVko ds pkj loky fy[kksA fQj ?kVkus ds fu;e dks “kCnksa esa fy[kks o mls chtxf.krh; rjhds ls fy[kksA
2- xq.kk ds pkj loky fy[kksA fQj xq.kk ds fu;e dks “kCnksa esa fy[kks o mls chtxf.krh; rjhds ls fy[kksA
3- Hkkx ds pkj loky fy[kksA fQj Hkkx ds fu;e dks “kCnksa esa o mls chtxf.krh; rjhds ls fy[kksA
4- dksbZ nks lw= fy[kksA mudk vFkZ “kCnksa esa fy[kksA mu lw=ksa dk ,d&,d mnkgj.k Hkh fy[kksA

52
dk;Zi=d& 5% fHkUu dh le>
1- uhps fn, x;s fp=ksa ds jaxhu ;k Nk;kafdr fgLls ds cjkcj fHkUu la[;k vadksa esa fy[kksA
2 uhps nh xbZ fHkUu la[;kvksa dks i<+ks o mUgsa fp= esa n”kkZvksA
3
8
2
2
3
12
7
6
9

53
3- uhps fn, x, fHkUuksa ds lerqY; fHkUu la[;k,a fy[kks o muds fp= cukvksA
4 uhps nh xbZ fHkUu la[;kvksa dks la[;k js[kk ij n”kkZ,aA
3
2
1
1
3
3
5
6
5
8
6
5
2
9

54
5- vxj fdlh fHkUu la[;k dk gj c<+k nsa rks og igys okyh la[;k ls NksVh gks tk,xh ;k cM+h vkSj D;ksa vk;r esa
cuk dj o la[;k js[kk ij le>k,aA vius “kCnksa esa fy[k dj Hkh le>k,aA
6- vxj fdlh fHkUu la[;k dk va”k c<+k nsa rks og igys okyh la[;k ls NksVh gks tk,xh ;k cM+h vkSj D;ksaA vk;r
esa cuk dj o la[;k js[kk ij le>k,aA vius “kCnksa esa fy[k dj Hkh le>k,aA

55
dk;Zi=d& 6% Hkktdrk ds fu;eksa dk iz;ksx
nks feuV esa ftruh fy[k ldrs gks mruh pkj vadh; la[;k,a fy[kksA
1- nks ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa nks
dk iwjk&iwjk Hkkx pyk tkrk gSA
2- rhu ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa
rhu dk iwjk&iwjk Hkkx pyk tkrk gSA
3- ikap ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa
ikap dk iwjk&iwjk Hkkx pyk tkrk gSA

56
4- Ng ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa
Ng dk iwjk&iwjk Hkkx pyk tkrk gSA
5- lkr ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa
lkr dk iwjk&iwjk Hkkx pyk tkrk gSA
6- ukS ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa ukS
dk iwjk&iwjk Hkkx pyk tkrk gSA
7- X;kjg ls iwjk&iwjk Hkkx gks tkus okyh la[;kvksa dks igpkuus dk fu;e fy[kksA fQj os lHkh la[;k,a fy[kks ftuesa
X;kjg dk iwjk&iwjk Hkkx pyk tkrk gSA

57
dk;Zi=d& 7% lkekU;hdj.k djds fu;e cukuk
uhps fn, lokyksa dks i<+ dj fu;e fudkyks vkSj mls vius “kCnksa esa fy[kksA
1-
2-
3-
4-

5-
100 3 300× = 100 12 1200× = 100 5 500× =
8 3 24
4 3 12
× =
× =
12 5 60
6 5 30
× =
× =
16 4 64
8 4 32
× =
× =
6 5 30
5 6 30
× =
× =
10 8 80
8 10 80
× =
× =
15 6 90
6 15 90
× =
× =
(6 4 24) (7 4 28) (13 4 52)× = + × = = × =
(8 7 56) (10 7 70) (18 7 126)× = + × = = × =

58
5 mijksDr fu;eksa ds vykok xq.kk dk dksbZ fu;e fy[kks vkSj ml fu;e dks n”kkZus okyk ,d loky Hkh cukvksA
vc bl dke ds vk/kkj ij uhps fn, x, lokyksa dk mRrj fy[kks&
1- vkidks ;g djrs gq, dSlk yxk
2- vkius vius fdu&fdu nksLrksa ds lkFk lk>k fd;kA mudks dSlk yxk
3- D;k vki fu;e cuk ik;s
4- D;k vki iz”u dks i<+dj le> ik;s
5- D;k vkius dksbZ u;k fu;e Lo;a ls cuk;k
D;k vkius vius fopkjksa dks fy[kk

59
dk;Zi=d& 8% lkekU;hdj.k djds fu;e cukuk
uhps fn, lokyksa dks i<+ dj fu;e fudkyks vkSj mls vius “kCnksa esa fy[kksA
1-
2-
3-
4-
12 1 12÷ = 18 1 18÷ = 33 1 33÷ =
10 2 5÷ = 20 2 10÷ = 40 2 20÷ =
60 3 20÷ = 60 6 10÷ = 60 12 5÷ =
80 16 5÷ = 40 8 5÷ = 20 4 5÷ =

60
5- vki Hkkx ls tqMs+ de ls de nks fu;e vkSj [kksft,A rFkk mu fu;eksa dk ,d&,d mnkgj.k Hkh nhft,A
2- D;k vki fu;e cuk ik;s vkidks fu;e cukus esa D;k eqf”dy vkbZ
3- D;k vki Hkkx dk xq.kk ds lkFk laca/k dks “kCnksa esa rFkk chtxf.krh; rjhds ls fy[k ldrs gks
4- D;k vki Hkkx ls tqM+s ,d nks fu;e vkSj [kkst ik,A vkius ml fu;e dks dSls [kkstk

61
dk;Zi=d& 9% fHkUu la[;k ds dbZ eryc
1- ls D;k eryc fudky ldrs gS uhps fy[kks vkSj vius nksLr ds lkFk lk>k djksA
2- uhps nh xbZ la[;kvksa dks i<+ dj muds uhps fn, lokyksa ij fopkj djksA

• fdrus fHkUuksa dk eku ,d ls vf/kd gS
• fdrus dk eku ,d ls de gS
• fdrus fHkUUk ,d nwljs ds cjkcj gSa
vc uhps nh xbZ lkj.kh dks HkjksA
Øekad fdrus fHkUuksa dk eku ,d ls
vf/kd gS
fdrus fHkUuksa dk eku ,d ls
de gS
fdrus fHkUUk ,d nwljs ds cjkcj gSa
1
2
3
4
5
6
4
7
1
3
4
7
1
1
3
5
5
4
3
7
9
8
6
3
4
3
5
7
13
12
11
12
10
7
5
7
12
24
12
14
7
12
12
7
7
8
2

62
vf/kd gS
de gS
7
8
9
10
11
12
vius mRrj dks vius fe= ds mRrj ls tk¡p djksA vc vius eu ls nl ianzg fHkUu la[;k,a fy[kks vkSj ;gh dke
nksLrksa ls feydj djus dk iz;kl djksA uhps cuh lkj.kh dk bLrseky Hkh dj ldrs gksA
vf/kd gS
de gS
1
2
3
4
5
6
7
8

63
dk;Zi=d& 10% lgh dFkuks dh igpku
uhps dqN xf.krh; dFku fn, tk jgs gSaA muds lgh ;k xyr gksus dk dkj.k vius “kCnksa esa fy[ksaA vius rdksZa dks
le>kus ds fy, vki fp=ksa dk Hkh bLrseky dj ldrs gSaaA tSls la[;k js[kk ij la[;k fn[kkuk ;k vk;r ;k oxZ cuk
dj la[;k fn[kkuk vkfnA fQj ml dFku ds lkeus ^lgh* ;k ^xyr* “kCn fy[ksaA
1- fHkUu esa ;fn va”k leku jgs vkSj gj dks c<+k dj Øe”k% 6] 7] 8 ----- c<+k;k tk; rks fHkUu dk eku leku
jgsxkA
2- ;fn va”k vkSj gj nksuksa leku gks rks fHkUu dk eku ,d ds cjkcj gksxkA rhu pkj fHkUu la[;k,a fy[kks fQj
fp= cuk dj le>kvksA
3- fdlh Hkh la[;k dks fHkUu ds :i esa iznf”kZr dj ldrs gaSA tSls] 5] 7] 4 vkSj 9
2
5

64
4- ,d fefJr fHkUu gSA
5- vius mRrjksa dh tkap ds fy, vius fe= ds mRrj ds lkFk feyk dj ns[kksA D;k irk pyk
vc bl dke ds vk/kkj ij uhps fn, x, lokyksa ds mRrj fy[kks&
5
5

65
6- uhps fn, x, lokyksa dks gy djsaaA
D;k vki bu ikapksa lokyksa esa vkbZ fHkUuksa ds chp dksbZ laca/k ryk”k dj ldrs gSaA vki fdl urhts ij igqaps
1
60 ..............
2
of =
2
60 ............
4
of =
3
60 .............
6
of =
5
60 .............
10
of =
10
60 .............
20
of =

66
7- uhps fn, x, lokyksa dks gy djsaaA
D;k vki bu ikapksa lokyksa fHkUukas ds chp dksbZ laca/k ryk”k dj ldrs gSaA vki fdl urhts ij igqaps
2
150 ..............
3
of =
6
150 .............
9
of =
8
150 .............
12
of =
10
150 .............
15
of =
4
150 ............
6
of =

67
dk;Zi=d& 11% lerqY; fHkUu cukuk
uhps fn, lokyksa ds tokc fy[ksaA tokc ds fy, vk;r ;k oxZ dk rFkk la[;k js[kk dk Hkh bLrseky djsaaA
1- ;fn rqe fdlh la[;k dks esa tksM+rs gks rks rqEgsa 4 feysxkA og la[;k D;k gksxh crkvksA rqeus dSls irk
fd;k] mls Hkh fy[kksA fp= cuk dj Hkh le>k ldrs gksA
2- rhu vk/ks fgLls fey dj bls cukrs gSSA crkvks og la[;k fdruh gksxhA rqeus dSls irk fd;k] mls Hkh fy[ksaA
fp= cukdj Hkh le>k ldrs gksA
3- ;fn rqe 3 esa ls ?kVkrs gks rks rqEgsa dkSulh la[;k feysxh rqeus dSls irk fd;k] mls Hkh fy[kksA fp=
cukdj Hkh le>k ldrs gksA
3
4
1
4

68
4- fdlh la[;k dk leku fHkUu
10
5
gSA rqeus la[;k dk dSls irk yxk;k] mls Hkh fy[kksA fp= cukdj Hkh
le>k ldrs gksA
5- ;fn rqe bl fefJr fHkUu dks vleku fHkUu esa cnyrs gks rks rqEgsa
5
2
izkIr gksxkA rqeus la[;k dk dSls irk
yxk;k] mls Hkh fy[kksA fp= cukdj Hkh le>k ldrs gksA
6- 24 ds ,d vk/ks dk rhu pkSFkkbZ fdruk rqeus la[;k dk dSls irk yxk;k] mls Hkh fy[kksA fp= cukdj Hkh
le>k ldrs gksA
7- fdlh la[;k dk nqxquk
1
4
2
gSA crkvks og la[;k fdruh gksxhA rqeus la[;k dk dSls irk yxk;k] mls Hkh
fy[kksA fp= cukdj Hkh le>k ldrs gksA

69
8- dk rqeus ;ksxQy dSls fudkyk] mls Hkh fy[kksA fp= cukdj Hkh le>k ldrs gksA
9- fdlh la[;k vkSj 11 ds chp dk varj 4
3
5
gSA crkvks og la[;k fdruh gksxh rqeus la[;k dk dSls irk
yxk;k] mls Hkh fy[kksA fp= cukdj Hkh le>k ldrs gksA
1 1
(6 ) (2 )
2 4
× + ×

70
dk;Zi=d& 12% bdkb;ksa esa vkilh laca/k
4]44]44]444
Åij nh xbZ la[;k esa]
1- lSdM+k dh txg okys 4 dk eku ngkbZ dh txg okys 4 dk fdruk xquk gS ----------------
2- ngkbZ dh txg okys 4 dk eku bdkbZ dh txg okys 4 dk fdruk xquk gS ----------------
3- yk[k dh txg okys 4 dk eku ngkbZ dh txg okys 4 dk fdruk xquk gS ----------------
4- djksM+ dh txg okys 4 dk eku nl gtkj dh txg okys 4 dk fdruk xquk gS ----------------
5- djksM+ dh txg okys 4 dk eku ngkbZ dh txg okys 4 dk fdruk xquk gS ----------------
6- djksM+ dh txg okys 4 dk eku yk[k dh txg okys 4 dk fdruk xquk gS ----------------
7- nl gtkj dh txg okys 4 dk eku gtkj dh txg okys 4 dk fdruk xquk gS ----------------
8- nl gtkj dh txg okys 4 dk eku ngkbZ dh txg okys 4 dk fdruk xquk gS ----------------
9- nl gtkj dh txg okys 4 dk eku lSdM+s dh txg okys 4 dk fdruk xquk gS ----------------
10- nl yk[k dh txg okys 4 dk eku ngkbZ dh txg okys 4 dk fdruk xquk gS ----------------
11- nl yk[k dh txg okys 4 dk eku gtkj dh txg okys 4 dk fdruk xquk gS ----------------
12- nl yk[k dh txg okys 4 dk eku nl gtkj dh txg okys 4 dk fdruk xquk gS -----------
13- djksM+ dh txg okys 4 dk eku lSdM+s dh txg okys 4 dk fdruk xquk gS ----------------
77]77]777
Åij nh xbZ la[;k esa]
1- bdkbZ dh txg okys 7 dk eku yk[k dh txg okys 7 dk fdruk fgLlk gS -----------------
2- yk[k dh txg okys 7 dk eku nl yk[k dh txg okys 7 dk fdruk fgLlk gS ---------------
3- gtkj dh txg okys 7 dk eku nl yk[k dh txg okys 7 dk fdruk fgLlk gS ---------------
4- lSdM+k dh txg okys 7 dk eku yk[k dh txg okys 7 dk fdruk fgLlk gS -----------------
5- nl gtkj dh txg okys 7 dk eku yk[k dh txg okys 7 dk fdruk fgLlk gS --------------
6- gtkj dh txg okys 7 dk eku yk[k dh txg okys 7 dk fdruk fgLlk gS -------------
7- lSdM+k dh txg okys 7 dk eku nl gtkj dh txg okys 7 dk fdruk fgLlk gS ----------
8- bdkbZ dh txg okys 7 dk eku nl gtkj dh txg okys 7 dk fdruk fgLlk gS -------------
9- lSdM+k dh txg okys 7 dk eku nl yk[k dh txg okys 7 dk fdruk fgLlk gS ------------
10- gtkj dh txg okys 7 dk eku nl gtkj dh txg okys 7 dk fdruk fgLlk gS --------------
bl dke ds vk/kkj ij uhps fn, x, lokyksa dk mRrj fy[kks&

71
dk;Zi=d& 13% ,d gh vad ds vyx&vyx eku
uhps nh xbZ gj la[;k esa 5 dk vyx&vyx eryc gSA vkidks ml la[;k esa 5 dk eryc irk yxk dj vius
“kCnksa esa fy[kuk gS blds lkFk gh ;g Hkh fy[kuk gS fd vkius ml la[;k esa 5 dk eryc dSls irk yxk;k
5
1
5

5
6
5 6× 7 5× 5
2 5ο
-5 .5 +5
1- 5
2- 1
5
3- 5 6×

72
4- 7 5×
5-
5
2
6- 5ο
7- -5

73
8- .5
9- +5
10 - Åij nh xbZ la[;kvksa es dkSu lh la[;k
5
10
ds cjkcj gS vkius dSls irk yxk;k
11- vki
5
100
dks n”keyo :i esa dSls fy[kksxs

74
12- D;k vki dksbZ vU; LFkku lksp ldrs gks ftlesa ik¡p dks LFkku fn;k tk lds

75
dk;Zi=d& 14% iqujko`fÙk
uhps fn, x, lokyksaa dks gy djsaA
1- ,slh la[;k cukvks ftlesa 15 lSdMs] 47 gtkj] 56 ngkb;ka rFkk 219 bdkb;ka gSaaaaA
2 la[;k 7 dks rqe vyx vyx fdruh rjg ls fy[k ldrs gks] uhps fy[kksA
3- ,d la[;k esa Ms<+ feykus ij og lok vkB gks tkrh gS rks crkvks og la[;k fdruh gS
4- uhps nh xbZ fHkUu la[;kvksa dks la[;k js[kk ij ;k vk;r esa n”kkZvksA

5- fHkUu la[;k
5
6
ds ikap lerqY; feUu cukvksA mu fHkUuksa dks vk;r rFkk la[;k js[kk ij n”kkZvksA
10
7
12
12
14
7
5
7
12
4
3
7
4
7

76
6- uhps fn, x, lokyksa dks /;ku ls ns[k dj muesa Nqik fu;e fudkyks o mls vius “kCnksa esa fy[kksA
24 x 8 =
12 x 4 =
6 x 16 =
3 x 32 =
345 + 498 =
245 + 598 =
145 + 698 =
45 + 798 =
43 + 800 =
7- uhps fn, lokyksaa dks /;ku ls i<+ksA igys mudks vkxs c<+k dj nks nks loky vkSj cukvksA fQj buesa Nqik fu;e
fudkyks o vius ”kCnksa esa fy[kksA
111 ÷ 3 = 37 37 x 3 = 111
222 ÷ 6 = 37 37 x 6 = 222
333 ÷ 9 = 37 37 x 9 = 333

77
dk;Zi=d& 15% izfr”kr rFkk fHkUu dk laca/k
uhps nh xbZ lkj.kh esa fHkUu la[;kvksa dks izfr”kr esa cnyksA vkSj izfr”kr dks fHkUu la[;k esa cnyksA
Ø- fHkUu izfr”kr bl ij dksbZ ,d O;ogkfjd ;kuh bckjrh loky cukvksA
1
2
5
2
3
20
3 75 %
4
4
10
5 15%
6
5
2
10
7 20 %
8
15
25
9 850%
10
5
2
11 375%
12
24
6
13
5
3
40

78
Ø- fHkUu izfr”kr bl ij dksbZ ,d O;ogkfjd ;kuh bckjrh loky cukvksA
14
3
9
15 16-66%

79
dk;Zi=d& 16% ,d la[;k pkj eryc
uhps fn, x, lokyksa dks gy djsa A
fHkUu izfr“kr n”keyo vuqikr
1
2
1 50 50
50%
2 50 100
×
= =
×
50
.50 .5
100
= =
1: 2
3 : 2
20
.20 .2
100
= =
70%
4
12
80%
.32
5 : 13

80
dk;Zi=d& 17% vKkr jkf”k Kkr djuk
1-
2-
3-
4-

82

83
dk;Zi=d& 18% chtxf.krh; dFku
uhps “kCnksa esa fy[kh “kkfCnd leL;k dks chtxf.krh; dFku esa cnyksA dqN leL;k,a vius eu ls cukvks o mUgsa Hkh
chtxf.krh; dFku esa cnyksA
Ø- leL;k chtxf.krh; dFku
1 fdlh la[;k dk rhu xquk ,oa nwljh la[;k dk ikap
xquk feyk dj 54 gksrk gSA
2 fdlh la[;k dk rhu pkSFkkbZ o mldk nks xquk feyk
dj ogha la[;k gks tkrh gSA
3 fdlh la[;k ds 4 xqus esa 5 tksM+us ij 30 feyrk gSA
4 fdlh la[;k dk nks ikapok fgLlk 6 gSA
5 fdlh la[;k dk 75 izfr”kr vkSj fdlh nwljh la[;k
dk 60 izfr”kr dk ;ksxQy
6 csVh dh mez dk rhu xquk vius firk dh mez ds nks
xqus ds cjkcj gSA
7 fpfM+;ksa dh la[;k dcwrjksa ls 6 xquk T;knk ysfdu
pwgksa ls rhu xquk de gS
8 fcfYy;ka pwgksa dh la[;k dk NBoka fgLlk rFkk eqfxZ;ksa
ls nqxquh T;knk gSA
9
10
11
12
13
14
15

84
dk;Zi=d& 19% chtxf.krh; dFku
uhps fy[ks chtxf.krh; dFkuksa dks “kCnksa esa fy[kks ;kuh “kkfCnd leL;k esa cnyksA dqN chtxf.krh; dFku vius eu
ls cukvks o mUgsa Hkh “kkfCnd leL;k esa cnyksA blh rjg ls dqN lw= Hkh fy[k dj mUgsa “kkfCnd leL;k esa cnyksA
Ø- chtxf.krh; dFku bckjrh ;kuh “kkfCnd loky
1 1a a÷ =
2 aaaaa 4=+++
3 acabcba +=+ )(
4 )()( cbacba ++=++
5 alxb =
6
7 dcba // =
8 aaxaxaxaxax
9 0243 =−+ cba

85
10 03/26/42/3 =−+ cabba
11
12
13
14
15
16

86
dk;Zi=d& 20% lehdj.kksa esa vKkr jkf”k dk eku fudkyuk
uhps fn, x, lokyksa dks gy djsaA
Ø- chtxf.krh; dFku bckjrh ;kuh “kkfCnd loky vKkr jkf”k dk eku fudkysa
1 15 17a ÷ =
2 5 29a + =
3
15
2
a
=
4 2 36a =
5
75
2
a
a + =
6 ( 5) 3 43a× + =
7 8 15 17a ÷ =

87
Ø- chtxf.krh; dFku bckjrh ;kuh “kkfCnd loky vKkr jkf”k dk eku fudkysa
8 2744axaxa =
9 3 26 370a − =
10
11
12
13

88
dk;Zi=d& 21% eku dh vnyk&cnyh
uhps fn, x, lokyksa dks gy djsaA dqN chtxf.krh; dFku [kqn cuk dj mudk eku fudkysaA
Ø- chtxf.krh; dFku ;fn a = 4 vkSj b = 6 rks uhps fn, x, chtxf.krh; dFkuksa dk eku irk
dhft,A
1 =+ ba
2 =+ ba 53
3
1 1
( ) ( )
4 2
a b× + × =
4 .........ab =
5 ......2)43( =−+ ba
6 ( 5) /12a b× + =

89
uhps nh xbZ lkj.kh esa a rFkk b dk eku [kqn j[ksaA blds ckn chtxf.krh; dFkuksa dks gy djsaA
Ø- chtxf.krh; dFku ;fn a = ….. vkSj b = ….. rks uhps fn, x, chtxf.krh; dFkuksa dk
eku irk dhft,A
1 =+ ba
2 =+ ba 53
3
=
4 .........ab =
5 ......2)43( =−+ ba
6 ( 5) /12a b× + =

90
1 1
( ) ( )
4 2
a b× + × =

91
dk;Zi=d& 22% x.kufof/k ds rdZ dh ryk”k
1- ,d le vkSj ,d fo’ke fHkUu dk xq.kk djksA blh loky ds xq.kd o xq.; esa ckjh&ckjh ls mUgha ds lerqY; ;k
,d leku fHkUu j[k dj Hkh loky dks gy djksA vius tokc dh tkap djksA
2- ,d le vkSj ,d feJ fHkUu dk xq.kk djksA blh loky ds xq.kd o xq.; esa ckjh&ckjh ls mUgha ds lerqY; ;k
,d leku fHkUu j[k dj Hkh loky dks gy djksA vius tokc dh tkap djksA

92
3- nks vleku fHkUuksa dk xq.kk djksA blh loky ds xq.kd o xq.; esa ckjh&ckjh ls mUgha ds lerqY; ;k ,d leku
fHkUu j[k dj Hkh loky dks gy djksA vius tokc dh tkap djksA
4- nks feJ fHkUuksa dk xq.kk djksA blh loky ds xq.kd o xq.; esa ckjh&ckjh ls mUgha ds lerqY; ;k ,d leku fHkUu
j[k dj Hkh loky dks gy djksA vius tokc dh tkap djksA

93
dk;Zi=d& 23% x.kufof/k ds rdZ dh ryk”k
uhps fn, dFku dks xyr dSls lkfcr djsaxs
nks la[;kvksa dk HkkxQy] Hkktd ls NksVk gksrk gSA
vki xq.kk ds dFku dks xyr lkfcr djus ds rjhds dk bLrseky djsaA eqf”dy gks rks vius lkfFk;ksa ds lkFk fey dj
gy djsaA
xq.kk dk loky bl rjg ls gy fd;k FkkA
bl rdZ dks vkxs c<+krs gq, iwNsa fd vc vxj ge 4 dk vk/kk dj nsa rks xq.kuQy fdruk gksxk
bls ge ,sls Hkh le> ldrs gSa fd ,d cVk pkj ;kuh ,d pkSFkkbZ dks 2 ckj ysus gesa ,d pkSFkkbZ o ,d pkSFkkbZ feyk
dj ,d vk/kk feysxkA
vc vxj ge 2 dk vk/kk dj nsa rks xq.kuQy fdruk gksxk
4 3 12
4 2 8
4 1 4
1
4 2
2
1
4 1
4
1 1
2
4 2
1 1
1
4 4
× =
× =
× =
× =
× =
× =
× =
4 3 12
4 2 8
4 1 4
1
4 2
2
1
4 1
4
1 1
2
4 2
× =
× =
× =
× =
× =
× =
4 3 12
4 2 8
4 1 4
1
4 2
2
1
4 1
4
× =
× =
× =
× =
× =

94
bls ge ,sls Hkh le> ldrs gSa fd ,d cVk pkj ;kuh ,d pkSFkkbZ dks 1 ckj ysus gesa ,d pkSFkkbZ gh feysxkA
vc vxj ge 1 dk vk/kk dj nsa rks xq.kuQy fdruk gksxk
4 3 12
4 2 8
4 1 4
1
4 2
2
1
4 1
4
1 1
2
4 2
1 1
1
4 4
1 1 1
2 4 8
× =
× =
× =
× =
× =
× =
× =
× =

95
vkids fy, Hkkx dk loky bl rjg gSA
248 =÷
dk;Zi=d& 24% x.kufof/k dk rdZ le>uk
d{kk esa Hkkx dk loky bl rjg ls gy fd;k FkkA
⇒ igys bls ge xf.kr dh Hkk’kk esa j[krs gaSA
c
d
b
a
d
c
b
a
×=÷
⇒ vc uhps fn, rjhds dks viukrs gSa &
⇒ ,d xf.krh; dFku dk p;u djsa] tSls fd 6
2
1
3 =÷ .
⇒ vc
2
1
ds O;qRØe ls xq.kk djks 6
1
2
3 =×
⇒ vc 3 ds LFkku ij mlds leku ;kuh lerqY; nwljh fHkUu la[;k j[kks
⇒ vc
2
1
ds O;qRØe ls xq.kk djks
12 2 24
4 1 4
× =
⇒ leku fHkUu ikus ds fy, va”k vkSj gj dks 4 ls Hkkx nks
24 4
6
4 4
÷
=
÷
⇒ vc
2
1
ds LFkku ij blds leku ;kuh lerqY; nwljh dksbZ fHkUu j[kks
12 5
........... 6
4 10
÷ = =
⇒ vc
2
1
ds O;qRØe fHkUu ls xq.kk djks
12 10 120
4 5 20
× =
⇒ ;g gS rqEgkjs loky dk gy
120 20 6
6
20 20 1
÷
= =
÷
uhps dqN fHkUu la[;k,a nh xbZ gSaA bu fHkUu la[;kvksa dks fdlh nwljh fHkUu la[;k ls Hkkx nksA Hkkx ds fy, nks
rhu vyx&vyx rjg ds fHkUuksa dks pquksA mlds ckn ,d fHkUu pquks] bls leku fHkUu esa cnyks vkSj fQj ls Hkkx
djds ns[kksA vius mRrj dh tkap t:j djrs jgksA

1-
4
1
6

96
2-

3-
4-
5-
6-
7
5
12
10
8
9
12
15
6
5
3

97
dk;Zi=d& 25% xf.krh; izrhdksa ij izkstsDV dk;Z
xf.kr ds izrhdksa o muds vFkksZa dh lwph cukuk

98
xf.kr ds izrhdksa o muds vFkksZa dh lwph tkjh

99

100

101
1- uhps nh xbZ lkj.kh HkjksA
fHkUu izfr“kr n”keyo vuqikr
3 : 2
170 %
2- nh xbZ lkj.kh esa chtxf.krh; dFku ;k “kkfCnd leL;k fy[kksA ,d chtxf.krh; dFku rFkk ,d “kkfCnd
loky [kqn cuk dj gy djksA
1 aa =÷13
2
00 =−a
3 3 dks b ls xq.kk djds mlesa ls 6 dks a ls xq.kk djds ?kVkvksA
4 cdfj;ksa dh la[;k eqfxZ;ks dh frxquh rFkk dqRrksa dh ,d frgkbZ gSA
5
6

102
3- fHkUUkks ds xq.kk ds pkj rjg ds loky cukvks o gy djksA pkjksa rjg ds fHkUu dke esa ysus gSa & le] fo’ke] feJ]
vleku
4- fHkUuksa ds Hkkx ds pkj rjg ds loky cukvks o gy djksA pkjksa rjg ds fHkUu dke esa ysus gSa & le] fo’ke] feJ]
vleku
5- nl xf.krh; izrhd fy[k dj mudk eryc fy[kksA

103
dk;Zi=d& 27% n”keyo la[;kvksa ds lkFk xq.kk o Hkkx
v- uhps fn, x, lokyksa dks fHkUu esa cny dj xq.kk djds mRrj fudkyksA fQj mUgsa fcuk fHkUu esa cnys xq.kk djus
dk iz;kl djksA mlds ckn tokc dh tkap Hkh djksA
.05 .2
.05 .02
.05 .002
.005 .02
.005 .002
×
×
×
×
×
c- uhps nh xbZ n”keyo la[;kvksa ds Hkkx ds fy, leku rjhds dks viukvksA fQj vius tokc dh tkap Hkh djksA
15 3 5
1.5 3
1.5 .3
.15 3
.15 .03
.015 .03
÷ =
÷
÷
÷
÷
÷

104
dk;Zi=d& 28% n”keyo la[;kvksa ds lkFk tksM+&?kVko
uhps fn, x, tksM+ o ?kVko ds loky djsaaA [kkyh lkj.kh esa [kqn loky cuk dj gy djsaA loky bl rjg dk
cuk,a fd gj fgLls ls gkfly feysA
tksM+
ngkbZ bdkbZ ,d nloka
fgLlk 1
10
,d lkSoka
fgLlk
100
1
0 . 6
5 9 . 9 7
fgLlk 1
10
,d lkSoka
fgLlk
100
1
1 3 . 3
6 9 . 0 5
fgLlk 1
10
,d lkSoka
fgLlk
100
1
1 3 . 5 7
9 . 4 5
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.

105
?kVko
[kkyh lkj.kh esa [kqn loky cuk dj gy djsaA loky bl rjg dk cuk,a fd gj fgLls dks gkfly ysuk iM+sA
fgLlk 1
10
,d lkSoka
fgLlk
100
1
1 2 . 3 5
3 . 5 7
fgLlk 1
10
,d lkSoka
fgLlk
100
1
1 5 . 0 2
8 . 3 7
fgLlk 1
10
,d lkSoka
fgLlk
100
1
3 0 . 0 1
2 . 4 3
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.
ngkbZ bdkbZ ,d
nloka
fgLlk
1
10
,d
lkSoka
fgLlk
100
1
,d
gtkjok
oka
fgLlk
1000
1
.
.

106
dk;Zi=d& 29% vioR;Z rFkk viorZd
uhps fn, lHkh lokyksa ds tokc “kCnksa esa fy[ksaA tokc fy[kus ds ckn ml tokc dk dkj.k Hkh fy[ksaA
1- D;k 4 ds lHkh vioR;Z le la[;k,¡ gS
2- 1 dks lkekU; xq.ku[kaM ;kuh lekioR;Z D;kas dgrs gS
3- D;k 4 ds lHkh vioR;Z 2 ds Hkh vioR;Z gS
4- D;k 10 ds lHkh vioR;Z 2 vkSj 5 ds Hkh vioR;Z gS
5- 1] 2 ]3] 4] 5] vkSj 6 esa ls dkSu 12 dk viorZd ugha gS
6- D;k 12] 12 dk vioR;Z ;k viorZd gS ;k nksuksa gS
7- rhu la[;k gSa & 2] 6] 3
crk,a dkSu fdldk viorZd gS vkSj dkSu fdldk viorZd
nksuksa esa vkil esa D;k laca/k gS

107
dk;Zi=d& 30% vHkkT; xq.ku[kaM rFkk okfrZd loky
1- uhps fy[ks lokyksa ds tokc nksA
v- vc bu iz”uksa ds mRrj nsus dk iz;kl djksA
1- lcls NksVh vHkkT; la[;k dkSu lh gS
2- D;k le la[;k,¡ vHkkT; la[;k gksrh gS
3- 1 vkSj 100 ds chp esa fdruh vHkkT; la[;k,¡ gS 25 ;k 26
4- D;k 1 vHkkT; la[;k gS vius mRrj dk dkj.k crkvksA
c- vc uhps fn, x, xf.krh; dFkuksa ij /;ku nks vkSj uhps fn, x, lokyksa ds mRrj nksA
12 2 2 3
60 2 2 5 3
100 2 2 5 5
72 2 2 2 3 3
96 2 2 2 2 2 3
91 13 7
= × ×
= × × ×
= × × ×
= × × × ×
= × × × × ×
= ×
1- vioR;kZs ds D;k fo”ks’k xq.k gksrs gSa
2- bl izfØ;k dks D;k dgrs gSa D;k bldk dksbZ [kkl uke Hkh gS
3- gesa ;g lh[kus dh D;ksa vko”;drk gS

108
2- uhps fn, x, bckjrh lokyksa dks i<+ks] le>ks vkSj gy djksA bu okfrZd iz”uksa ds mRrj irk djksA D;k rqEgas
y?kqRke lekioR;Z dh vo/kkj.kk irk gS] rc rks ;s loky rqEgkjs fy, fcydqy gh vklku gSa!
v- jatw ikWp fnu esa ,d ckj iqLrdky; tkrh gSA latw pkj fnuksa esa ,d ckj iqLrdky; tkrh gSA vkt os iqLrdky;
esa feysA os vxyh ckj dc feysaxs
c- nknh ek¡ Vksdjh esa vke ys tk jgh FkhA ,d lkbfdy lokj us mUgsa VDdj ekj nhA Vksdjh fxj iM+hA nksuksa
us vke dks bdV~Bk fd;kA vkneh us pqipki vkeksa dh fxurh dh vkSj iwNk& rqEgkjh Vksdjh esa fdrus vke
Fks nknh us dgk& eSa ugha tkurh ysfdu ;fn eS bls 6 ds lewg esa j[kwa rks blesa 5 cp tk;saxsA vkSj ;fn eSa
bls 5 ds lewg esa j[krh gwa rks pkj cp tkrs gSaA ;fn bls eSa pkj ds lewg esa j[krh gw¡ rks 3 cpsaxsA vkneh us
lkspk vkSj cksyk& geus lkjs vke bdV~Bs dj fy, gaSA vc rks crkvks] Vksdjh esa fdrus vke Fks rqe rks crk
gh nksxs] rks tYnh crkvks& nknh dh Vksdjh eas fdrus vke Fks
l- vkeksa dh D;k la[;k gksxh ;fn nknh ek¡ dgrh& ;fn eaS bls 6 ds lewg esa j[kw¡ rks 4 cp tkrs gaSA 5&5 ds
lewg cukÅa rks 3 cp tkrs gSa vkSj ;fn 4 dss lewg esa j[kwa rks 2 cprs gSa vkSj 3 ds lewg esa j[kus ij 1
vke cp tkrk gSA
n- Vksdjh esa fdrus vke gksxsa ;fn nknh ek¡ dgrh& ;fn eSa lHkh vkeksa dks 6] 5] 4 ] 3 vkSj 2 ds lewg esa j[kwa
rks 1 vke cprk gSA

109
dk;Zi=d& 31% y?kqRre lekioR;Z rFkk egRre lekiorZd
v- ;gk¡ dqN la[;k,¡ nh x;h gSA muesa ls nks nks la[;kvksa dk tksM+k cuk dj ml tksM+s dk y- l- vkSj e- l- nksuks
rjhdksa ls Kkr djksA
48, 50, 75, 120, 96, 80, 150, 160...

110
c- nks ;k rhu la[;kvkas dks pquksA blds y- l- vkSj e- l- dk vuqeku yxkvks] mls gy djks] fQj vius vuqeku ls
gy dk feyku djksA

111
dk;Zi=d& 32% iw.kkZdksa ds lkFk lafØ;k,a
v- bu dFkuksa dks iwjk djks&
1- nks /kukRed la[;kvksa dk ;ksx-----------------------------------------------------------------------------------------------------------
2- nks _.kkRed la[;kvksa dk ;ksx----------------------------------------------------------------------------------------------------------
3- ,d _.kkRed vkSj ,d /kukRed la[;k dk ;ksx-------------------------------------------------------------------------
4- nks /kukRed la[;kvksa dk vUrj------------------------------------------------------------------------------------------------------------
c- Åij dh rjg ?kVko dh fØ;kvksa ds fy, fu;e fy[kksA
1-
2-
3-
4-
l- Åij dh rjg xq.kk dh fØ;kvksa ds fy, fu;e fy[kksA
1-
2-
3-
4-
n- Åij dh rjg Hkkx dh fØ;kvksa ds fy, fu;e fy[kksA
1-
2-
3-
4-
nks /ku la[;kvksa dk xq.kuQy ,d /kukRed la[;k esa dSls cny tkrk gS
bl fu;e dks bl rjg ls lR;kfir fd;k tkrk gS tSlk fd d{kk esa f”k{kd us rqEgsa le>k;k Hkh gksxkA
bl ckr dks le>us ls Ikgys dh rhu vo/kkj.kkvksa dks ;kn dj ysuk pkfg,A ;s mijksDr fu;e dks lkfcr djus esa
enn djsxhA
1a a= × ;g 1 dh fo”ks’krk gS
( )a b c ab ac+ = + forj.k dk fu;e
1, 2, 3, 4, 5.... = +1, +2, +3, +4, +5.... lHkh izk—frd la[;k,¡ ;k fxufr;k¡ /kukRed gksrs gSA

112
uhps lR;kiu fn;k x;k gS A izR;sd pj.k esa mi;ksx esa ykbZ x;h vo/kkj.kkvksa dks igpkuus dk iz;kl djksA
( )11()11( −×=+×− )
vc rqe uhps fn, x, loky dks lR;kfir djksA
1)1()1( +=−÷−
( 1) ( 1) 0
1 1 0
1( 1 1) 1(0)
(1 ( 1) 1 ( 1) 0
1 1 0
1( 1 1) 1(0)
( 1 1) ( 1 1) 0
............. ( 1 1) 0
............. ( 1) 0
( 1) ( 1) 0
( 1 1) 1
− + + =
− + =
− + =
× − + × + =
− + =
− − + =−
− × − + − × + =
+ − × + =
+ − =
+ + − =
− × − = +

113
dk;Zi=d& 33% f=Hkqt ls tqM+h igsfy;ka
1- f=dks.k dh dqy la[;k Kkr djus dh dksf”k”k djksA vius mRrj dks nksLrksa ds lkFk lk>k djksA D;k muds Hkh
mRrj ogh gSa
2- cuk,a fp= igsyh
1- ,d f=Hkqt cuk;sA vc fdlh dks.k ls mlds lkeus okyh js[kk dks feykrs gq, ,d js[kk [khsfp, fp= 1A vc
f=Hkqtksa dh la[;k dh x.kuk djksA D;k ;g 3 gS
2- vc nwljs fp= dks ns[kks blesa ,slh gh js[kk nks dks.kksa ls [khaph xbZ gS A f=Hkqtksa dh la[;k dh x.kuk djksA
D;k rqeus blesa Nqis gq, iSVuZ dks tkuk
3- vc bUgha dks.kksa ls ,d&,d js[kk vkSj [khpksa fp= & 3A irk djksa fd ;g iSVuZ lgh gS ;k ugha
fp= 1 fp= 2 fp= 3
viuk urhtk fy[kksA

114
4- fdlh f=Hkqt ds vk/kkj dks.k ls rhu js[kk,¡ [khpksaA fp= dks vius fe= dks fn[kkvksa vkSj dgks fd os dqy
f=Hkqtksa dh la[;k irk djsaA
3- ,slk f=Hkqt cukvks ftlds nks dks.k ledks.k gksaA
4- ,slk f=Hkqt cukvks ftlds lHkh dks.k vf/kd dks.k gksaA
5- f=Hkqt dh Hkqtkvksa o dks.kksa ds chp laca/kksa dks fy[kksA

115
dk;Zi=d& 34% chth; O;atdksa dk tksM] ?kVko rFkk in
1- fuEufyf[kr dk foLrkj djdsa fy[ksa
2- ;gk¡ dqN chtxf.krh; dFku gSaA mUgsa /;ku ls ns[ksaA uhps fn, pj.kokj funsZ”kksa ds vuqlkj vH;kl djsa&
⇒ mRrj dk vuqeku yxkb;sA
⇒ pj “a” dk eku 2 j[ksaA
⇒ vius mRrj dk eku Kkr dhft,
⇒ vkids fdrus mRrj lgh gSa ---------------------------
⇒ D;k vki xyr mRrj okys lokyksa ds fy, nksckjk iz;kl djuk pkgrs gSa
⇒ vkius blls D;k lh[kk
⇒ vius lkfFk;ksa ds lkFk vius lh[ks x, fu’d’kksZa ds ckjs esa ppkZ djsaA mu fu’d’kksZa dks uhps fy[ksaA
3- vc fuEufyf[kr iz”uksa ds mRrj irk djus dk iz;kl djsa&
1- 3 lkbfdy $ 2 “kVZ
2- 6 cksry $ 4 feBkbZ
3- 10 eksckby Qksu $ 5 eksckby Qksu
4- ........34 =+ ba
5- ......45 =+ aa
5
5
4
....................................
5 ....................................
4 ..................................
(5 ) ...............................
b
b
b
b
=
=
=
=
3 2
3 2
3 2
( ) ( ) 3 2 ........
( ) ( ) ( ) ( ) .........
( ) ( ) 3 2 ........
( ) ( ) ( ) ( ) ........
( ) ( ) ( ) ( ) .........
a a a a a a a
a a a a a a a
a a a a a a a
a a a a a a a
a a a a a a a
+ + + + = + =
× × × × = × =
+ + − + = − =
× × − × = − =
× × + × = + =

116
6- .......52 33
=+ aa
7- igys nks iz”u esa ge phtksa dks D;ksa ugha tksM+ ldrs
8- vfUre nks iz”uksa ds ckjs esa D;k fopkj gS
9- D;k 23
,aa leku in gS ;k vleku in
10- ;g dSls irk djksxs
D;k vki bl vo/kkj.kk ij vius fe= dh le> dks tk¡puk pkgrs gS mlds le{k rdZ nsa fd 23
,aa leku in gSa
vkSj bl lanHkZ esa mlds rdZ ij /;ku nsaA

117
dk;Zi=d& 35% fHkUu ls izfr”kr
1- uhps fn, x, pj.kokj funsZ”kksZa dk ikyu djrs gq, iz”uksa ds mRrj nks&
1- izR;sd Js.kh dh nks fHkUu la[;k,a fy[kks& le fHkUu] fo’ke fHkUu vkSj feJ fHkUu
2- mUgsa izfr”kr esa cnyks
3- rc 5 n”keyo la[;k,a fy[kks
4- mUgsa izfr”kr esa cnyksA
5- mRrj dks ns[kksA D;k vo/kkj.kk cu jgh gS] viuh dkih esa fy[kksA
6- bl vo/kkj.kk ij vius fe= ds lkFk ppkZ djksA

118
2- fHkUu dks izfr’kr esa cnyks o izfr’kr dks fHkUu esa cnyksA
Ø- fHkUUk la[;k izfr”kr cnyus dk rjhdk
1
2
1
2 50 %
3 80 %
4
5
3
5 10%
6 75 %
7
5
1
8 125 %
9
4
3
10 25 %
11
5
2
12
5
4
13
2
2

119
dk;Zi=d& 36% fuf”pr izfr”kr
uhps fn, x, lokyksa ds tokc fy[ksaA
1- fuEu dFkuksa dks ns[ksa vkSj fn, x, lokyksa dk mRrj nsa&

1- 240 dk 55% Kkr djus dk lcls vklku rjhdk D;k gS
2- 240 dk 80% rqe dSls Kkr djksxs
3- fdrus rjhdksa ls rqe 240 dk 95% Kkr dj ldrs gks
4- ,sls gh T;knk ls T;knk iz’u cukvks vkSj vius nksLrksa ds lkFk gy djrs gq, bu rjhdksa ij ppkZ djksA
50% 5% 10%
30 5 6
60 10% 6
÷ =
÷ =
× =
10% 3 30%
6 3 18
60 30% 18
× =
× =
× =
50% 10% 60%
60 50% 30
60 10% 6
60 60% 36
+ =
× =
× =
× =
50% 10% 40%
60 50% 30
60 10% 6
60 40% 30 6 24
− =
× =
× =
× = − =
1)50 10% ..........
2)60 ......... 12
3).......... 25% 30
4)......... ......... .......
× =
× =
× =
× =

120
dk;Zi=d& 37% ykHk o gkfu
1- rkfydk ns[kksA fjDr LFkkuksa dh iwf= djus dk iz;kl djksA ;gk¡ dqN ladsr fn;s x;s gSa
Cost price Profit Loss Selling price
400 15% .....................
550 10% .....................
.................... 15% 690
500 .................... 600
................... 15% 340
vius eu ls nks ykHk okys o nks gkfu okys loky cukvks o mUgsa gy djksA vius gyksa dks nksLrksa dks fn[kk dj irk
djks fd os lgh gSa ;k ughaA
100%
100% (15%)
100 15% 115%
115%
CP CP
P SP
CP SP
× =
+ =
+ =
× =

121
dk;Zi=d& 38% lk/kkj.k C;kt
1- **C;kt dh nj 8 izfr”kr gS** dFku dk D;k eryc gS
2- ;fn ge 1000 #i, cSad esa tek djrs gSa tks 8 izfr”kr dk C;kt nsrk gS A rks ge ,d o’kZ ds i”pkr
fdrus #i, ik;saxs
3- ge 4000 #i, dk yksu ;kuh dtkZ cSad ls ysrs gSa] tks 9 izfr”kr dk C;kt ysrk gSA ,d o’kZ ds ckn gesa
fdruk #0 C;kt okil djuk gksxk
4- ge 2000 #i, dk yksu cSad ls ysrs gS] tks 9 izfr”kr dk C;kt ysrk gSA nks o’kZ ds ckn gesa fdruk #0
C;kt okil djuk gksxk
5- ;fn ge 2000 #i, dk yksu cSad ls 18 izfr”kr C;kt dh nj ls ysrs gSa rks] ,d o’kZ ds ckn gesa fdruk #0
C;kt okil djuk gksxk
6- vki vfUre rhu iz”uksa ls D;k le>s

122
7- ;g rhu la[;kvksa ds xq.kuQy ls dSls lacaf/kr gS
8- D;k rqe C;kt dh x.kuk djus ds fy, lw= cuk ldrs gks
dk;Zi=d& 39% lk/kkj.k C;kt dh x.kuk
uhps fn, rjhds ls vkids f”k{kd us vkids lkFk dke fd;k FkkA
,d dFku fy;kA
P = 1000 rupees; N = two years; R = 8%
ge tkurs gSa fd mRrj 160 #i;s gaSA
bl dFku dks mRrj lfgr ,sls fy[krs gSa%
vxj gekjs ikl le; ugha fn;k x;k gks rc bl lw= dks fuEu izdkj ls fy[krs gq, le; dk irk dj ldrs gSa%
vc fuEufyf[kr lokyksa dks gy djks&
vc ,sls ikap iz”u cukb;s] mRrj Kkr dhft,] ,d lwpuk dks fNikb;s vkSj vius fe= ls mls irk djus dks dgsaA
vkSj vki fe= ds cuk,a ikap loky ysdj uhps gy dhft,A
tc vki iz”u cuk jgsa gksa rks bls vkSj dfBu djus ds fy, fuEu rjhdksa dk iz;ksx djsaaA
v- o’kZ dh la[;k dks eghus esa cnfy,&
1 efguk =
1
12
o’kZ
2 efguk =
1
6
o’kZ
82
100
160
2
100
1000
160
××=
××=
P
R
160 10 8
160 10 8
160 80
1 1
160 80
80 80
2 1
2
2
N
N
N
N
N
N
N
= × ×
= × ×
= ×
× = × ×
= ×
=
=

123
73 fnu =
1
5
o’kZ
146 fnu =
2
5
o’kZ bR;kfn
c- C;kt dh nj dks fefJr fHkUu esa cnydj loky cuk,a&
1
8
2
%
vkids cuk, loky o mlds gy
1-
2-
3-
4-
5-
dk;Zi=d& 40% lk/kkjk.k C;kt dh x.kuk
vius fdlh nksLr }kjk cuk, gq, ikap loky ysdj gy dhft,A
1-

124
2-
3-
4-
5-
1- Qk#[k vkSj lq”khy ds chp ds okrkZyki dks i<+ksA cgl dks iwjk djus esa lq”khy dh enn djksA
Qk:[k% 100 izfr”kr eryc
100
100
, D;k eaS lgh gwa
lq”khy% gk¡] rqe fcydqy lgh gksA
Qk:[k% ;fn fHkUu dk va”k vkSj gj leku gksrk gS rks eku 1 gksrk gSA
lq”khy % gk¡] blesa dksbZ lansg ughaA
Qk:[k% blfy, lkS izfr”kr eryc gS 1- ;fn rqe xf.kr esa lkS izfr”kr vad ikrs gks rks bldk eryc gS rqeus
dsoy 1 vad izkIr fd;kA D;k rqe lger gks
lq”khy % D;k ugha] rqe xyr gks D;ksafd--------------------------------------------------------------------------------------------------------

125
2- nks la[;k,a yksA mudk y-l- rFkk e-l- fudkyksA vc mu nksuksa la[;kvksa dk xq.kuQy fudkyksA vc muds y-l
rFkk e-l- dk xq.kuQy fudkyksA
3- la[;kvksa rFkk y-l- rFkk e-l- ds xq.kuQy dks ns[kksA rqe fdl urhts ij igqaprs gks
4- nks la[;kvksa dk e- l- 3 gSA mudk y-l- 120 gSA muesa ls ,d la[;k 24 gS rks nwljh la[;k D;k gksxh
5+- 0-6 dks 0-7 ls xq.kk djds ns[kksA xq.kuQy nksuksa la[;kvksa ls de D;ksa vkrk gS dkj.k le>kvksA
6- nks chtxf.krh; dFku fy[kks ftuesa pkjksa lafØ;kvksa ;kuh tksM+ ?kVko xq.kk o Hkkx dk bLrseky fd;k x;k gksA
fQj mu dFkuksa dks “kkfCnd leL;k esa cny dj fy[kksA
7- 180 dk 75% fudkyus dk vklku rjhdk crkvksA
8- vxj vki 15750 :i, dk dtkZ nks lky ds fy, 7-5 izfr”kr lkykuk dh nj ij ysrs gSa rks vkidks nwljs lky
ds vkf[kj esa fdruk C;kt nsuk iM+sxk

4
This Teaching-Learning material is part of Kusuma Foundation’s Secondary School Readiness
Programme (SSRP) and its scale up supported by Uttar Pradesh Madhyamik Shiksha Abhiyan
(UPMSA) through its Udbhav Programme and state wide remedial programme. This material has
been developed by Kusuma Foundation with support from subject experts and consultants and is
intended for use by students, teachers and teacher educators of secondary schools in Uttar Pradesh.
The material also draws upon existing curricula, education materials and manuals, the experience
and views of teachers and also includes original material. The material has been finalised after review
and endorsement by the State Resource Group (SRG) set up by UPMSA.
The material and its contents may not be sold or used for any commercial purpose. The manual and
its contents may be reproduced and used for educational purposes. Permission for reproduction and
use may be obtained from Kusuma at udbhav@kusumatrust.org or info@kusumafoundation.co.in
Funded by the Kusuma Trust UK (www.kusumatrust.org)
© 2017 Kusuma Trust UK
Kusuma believes that every child and young person has the potential to transform
and improve their life. Our mission is to facilitate and increase access to education
and other life opportunities for children and young people. Kusuma enables children
and young people to realise their potential. Our focus is to improve education
outcomes, and understand and address major barriers in education.
Kusuma Foundation (www.kusumafoundation.in) :
State office, Hardoi
Ist Floor, Surendra Pal Pathak Complex, Civil line, Hardoi,
Uttar Pradesh-241001, Contact Number: +91-05852-235010
Registered Office, New Delhi
A-21, Third Floor Green Park main, Aurbindo Marg,
New Delhi - 110016, Contact Number: +91-11-41500321|22|24

Student handbook maths 7 july 2017

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Student handbook maths 7 july 2017