திறனறிவும் மனக்கணக்கு நுண்ணறிவும் - 1st - chapter
திறனறிவும் மனக்கணக்கு நுண்ணறிவும் - 1st - chapter
திறனறிவும் மனக்கணக்கு நுண்ணறிவும் - 1st - chapter
Subject : Aptitude
Medium : Tamil
© Copyright
Commissioner,
Department of Employment and Training.
Aptitude
குரூப் 4
Contents
RUf;Fjy; ............................................................................................................... 3
Neuk; kw;Wk; Ntiy........................................................................................ 11
tpfpjk; kw;wk; tpfpjhr;rhuk; ......................................................................... 17
rjtPjk; .................................................................................................................. 23
jdp tl;b kw;Wk; $l;L tl;b ...................................................................... 30
II. $l;Ltl;b ....................................................................................................... 37
Neuk; & J}uk;.................................................................................................... 48
juT tpsf;fk; ..................................................................................................... 56
HCF & LCM ............................................................................................... 62
gfilfs; .............................................................................................................. 68
கேள்விேள்............................................................................................................. 69
gug;G - nfhs;ssT - R+j;jpuq;fs; ............................................................. 74
gug;gsT kw;Wk; fdmsT ............................................................................ 80
fhuztpay; .......................................................................................................... 82
2
RUf;Fjy;
tiuaiw: -
➢ RUf;Fjy; vd;gJ vspikahf;Fjy;> fzpjj;jpy;> vspik my;yJ
vspikg;gLj;Jjy; vd;gJ ntspg;ghL my;yJ gpd;dk; my;yJ fzf;Ffis
vspikahd tbtq;fspy; Fiwg;gjhFk;.
➢ BODMAS vdg;gLk; xU fzf;if vspikg;gLj;j Njitahd
nray;ghLfis xOq;fikf;fg;gl;l thpirapy; itf;fg;gLfpd;wd.
,q;F
B - Bracket (milg;Gf;Fwp)
O - of (ngUf;fy;)
D - Division (tFj;jy;)
M - Multiplication (ngUf;fy;)
A - Addition ($l;ly;)
S - Subtraction (fopj;jy;)
,aq;fzpjk; - tiuaiw : -
➢ ,aw;fzpjk; vd;gJ fzpjj;jpd; xU gphpthFk;. ,jpy; vz; fzpj
nray;ghLfs; Fwpg;gpl;l vz;fSf;Fg; gjpyhf RUf;ff; FwpaPLfSf;F kw;nwhU
Kiwahd ifahSjy;fs; gad;gLj;jg;gLfpd;wd.
1. ,uz;L vz;fspd; $Ljy; 60. NkYk; mtw;Ws; Xh; vz; kw;Nwhh; vz;iztpl 12
mjpfk; vdpy;> me;j vz;fisf; fhz;f.
a) 21, 39 b) 24, 36
c) 22, 38 d) 20 , 40
tpil: b) 24, 36
jPh;T:
x + (x + 12) = 60
2 x + 12 = 60
2x = 60 – 12
3
2x = 48
x = 48
2
rpwpavz; x=48
nghpavz; x + 12 = 24 + 12 = 36
2. ,uz;L vz;fspd; $Ljy; 116. NkYk; mtw;Ws; Xh; vz; kw;Nwhh; vz;iztpl 32
mjpfk; vdpy;> me;j vz;fisf; fhz;f.
a) 42 , 74 b) 51 , 65
c) 71 , 45 d) 38 , 88
tpil: a) 42 , 74
jPh;T:
x + ( x + 32) = 116
2 x + 32 = 116
2x = 116 – 32
2x = 84
x = 84
2
rpwpa vz; x = 42
nghpa vz; x + 32 = 44 + 32 = 74
3. ,uz;L vz;fspd; $Ljy; 80. NkYk; mtw;Ws; Xh; vz; kw;Nwhh; vz;iztpl 14
FiwT; vdpy;> me;j vz;fisf; fhz;f.
a) 38, 42 b) 30, 50
c) 28 , 52 d) 33 , 47
tpil: d) 33 , 47
jPh;T:
4
x - 14 vd;gJ rpwpa vz; vd;f
x + ( x - 14) = 80
2 x - 14 = 80
2x = 80 + 14
2x = 94
x = 94
2
4. ,uz;L vz;fspd; $Ljy; 207. NkYk; mtw;Ws; Xh; vz; kw;Nwhh; vz;iztpl 53
FiwT vdpy;> me;j vz;fisf; fhz;f.
a) 119 , 66 b) 140 , 87
c) 130 , 73 d) 148 , 95
tpil: c) 130 , 73
x + ( x - 53) = 207
2 x - 53 = 207
2x = 207 + 53
2x = 260
x = 260
2
5. Xh; vz; kw;Nwhh; vz;zpd; 12 klq;F MFk;. mtw;wpd; tpj;jpahrk; 143> vdpy;>
me;j mt;ntz;fisf; fhz;f.
a) 15 , 158 b) 12 , 155
5
c) 12, 157 d) 13 , 156
tpil: d) 13 , 156
jPh;T:
tpj;jpahrk;>
12 x - x = 143
11 x = 143
x = 143
11
Kjy; vz; x = 13
6. Xh; vz; kw;Nwhh; vz;zpd; ghjp MFk;. mtw;wpd; tpj;jpahrk; 51> vdpy;> me;j
mt;ntz;fisf; fhz;f.
a) 102 , 51 b) 106 , 53
c) 98 , 47 d) 88 , 37
tpil: a) 102 , 51
jPh;T:
Kjy; vz;iz x vd;f.
,uz;lhtJ vz;iz x vd;f.
2
tpj;jpahrk;>
x - x = 51
2
2x - x = 51
2
x = 51
2
x=51 x 2
6
2 2
804 – 6 x = 582
804 – 582 = 6 x
222 = 6 x
222 = x
6
7
gazpfsplkpUe;J ngwg;gl;l gazr; rPl;L njhif = ₹ 332
mjhtJ>
x x ₹ 7 + (40 – x ) x ₹ 11 = 332
440 – 4 x = 332
440 – 332 = 4 x
108 = 4 x
108 = x
4
500 – 8 x = 140
500 – 140 = 8 x
360 = 8 x
360 =x
8
8
₹ 2 kjpg;Gila gzj;jhs;fspd; vz;zpf;ifia x = 45
10. ₹ 20 kw;Wk; ₹ 50 kjpg;Gfis kl;LNk nfhz;l 110 gzj;jhs;fs; cs;sd. mjd;
kjpg;G ₹ 4300 vdpy;> ₹ 50 kjpg;Gila gzj;jhs;fs; vj;jid cs;sd vdf;
fhz;f.
a) 35 b) 40
c) 70 d) 60
tpil: c) 70
jPh;T:
₹ 20 kjpg;Gila gzj;jhs;fspd; vz;zpf;ifia ‘x ‘ vd;f.
₹ 50 kjpg;Gila gzj;jhs;fspd; vz;zpf;ifia ‘ 110 – x’ vd;f.
mjhtJ>
x x ₹ 20 + (110 – x ) x ₹ 50 = 4300
5500 – 30 x = 4300
5500 – 4300 = 30 x
1200 = 30 x
1200 =x
30
2 x + 1 = 83
2 x = 83 - 1
9
2 x=82
x= 82
2
x =41
x + 1=41 + 1
=42
12. mLj;jLj;J ,U ,ay; vz;fspd; $Ljy; 225 vdpy;> mt;tpU vz;fisf; fhz;f.
a) 105 , 115 b) 112 , 113
c) 100 , 125 d) 111 , 112
tpil: b) 112 , 113
jPh;T:
nfhLf;fg;l;l vz;fs; ,ay; vz;fs; kw;Wk; mLj;jLj;J tUgit.
me;j vz;fis ‘x ‘ kw;W ‘x + 1’ vd;f.
x x (x + 1 ) = 225
2 x + 1 = 225
2 x = 225 - 1
2 x = 224
x = 224
2
x = 112
x + 1= 112 + 1
x= 113
10
Neuk; kw;Wk; Ntiy
KfTiu:-
Neuk; kw;Wk; Ntiy vd;gJ xU jdpegNuh my;yJ jdpegh;fspd; FONth xU
Ntiyia Kbf;f vLf;Fk; Neuj;ijAk; mth;fs; xt;nthUtUk; nra;Ak;
Ntiyapd; nray;jpwidAk; ifahs;fpwJ.
Kbj;j Ntiy: -
xU Fwpg;gpl;l msT Ntiyia (W) Kbf;f Neuk; (T) vLf;Fk;. xU myF
Neuj;jpw;F nra;ag;gLk; Ntiy myFfspd; vz;zpf;if Ntiy tpfpjk; (R)
vd;W miof;fg;gLfpwJ.
vdNt> nra;j Ntiy (W) = Neuk; (T) x Ntiy tpfpjk; ( R )
#j;jpuq;fs;: -
➢ nra;j Ntiy = vLf;Fk; Neuk; x Ntiy tpfpjk;
➢ Ntiy tpfpjk; = 1
vLf;Fk; Neuk;
➢ vLf;fg;gl;l Neuk; = 1
Ntiy tpfpjk;
➢ xU Ntiyia x ehl;fspy; nra;jhy;> xU ehspy; nra;j Ntiy = 1/x
➢ nkhj;j Ntiy = ehl;fspd; vz;zpf;if x nray;jpwd;
➢ nray;jpwDk; NeuKk; xd;Wf;nfhd;W Neh;khwhd tpfpjj;jpy; cs;sd.
➢ x:y vd;gJ xU Ntiyia Kbf;f Njitg;gLk; Mz;fspd; vz;zpf;ifapd;
tpfpjk; vdpy; y:x vd;gJ mth;fs; Ntiyia Kbf;f vLf;Fk; Neuj;jpd;
tpfpjkhf ,Uf;Fk;.
➢ M1 vz;zpf;ifapyhd egh;fshy; W1 Ntiyiar; nra;a D1 ehl;fspy; xU
ehSf;F T1 kzp Neuk; Ntiy nra;a KbAk; kw;Wk; M2 vz;zpf;ifapyhd
egh;fshy; W2 Ntiyiar; nra;a D2 ehl;fspy; xU ehSf;F T2 kzp Neuk;
Ntiy nra;a KbAk; vdpy; ,uz;Lf;Fkhd njhlh;G>
M1 x D1 x T1 = M2 x D2 x T2
W1 W2
11
tpil: C) 6 ehl;fs;
jPh;T:
1
A-d; xU ehs; Ntiy = 10
1
B-d; xU ehs; Ntiy = 15
1 1
(A+B)-d; xU ehs; Ntiy = +
10 15
15+10
= 150
25
= 150
1
= 6
jPh;T:
1
A-d; xU ehs; Ntiy = 12
1
B-d; xU ehs; Ntiy = 18
1 1
(A+B) -d; xU ehs; Ntiy = +
12 18
18+12
= 216
30
= 216
5
= 36
36 1
A kw;Wk; B Nrh;e;J Ntiy nra;j ehl;fs; = (m) 7 ehl;fs;
5 5
12
jPh;T:
1
A-d; xU ehs; Ntiy = 18
1
B-d; xU ehs; Ntiy = 24
1 1
(A+B) -d; xU ehs; Ntiy = +
12 18
1 1
= 18+ 24
4+3
= 72
7
= 72
72 2
A kw;Wk; B Nrh;e;J Ntiy nra;j ehl;fs; = (m) 10 ehl;fs;
7 7
ehl;fs;
𝟔
tpil: C) 12 ehl;fs;
𝟏𝟕
jPh;T:
1
A-d; xU ehs; Ntiy = 21
13
1
B-d; xU ehs; Ntiy = 30
1 1
(A+B) -d; xU ehs; Ntiy = +
21 30
10+7
= 210
17
= 210
210 6
A kw;Wk; B Nrh;e;J Ntiy nra;j ehl;fs; = (m) 12 ehl;fs;
17 17
jPh;T :
1
(A+B) -d; xU ehs; Ntiy = 8
1
A-d; xU ehs; Ntiy = 20
1 1
B -d; xU ehs; Ntiy = -
8 20
14
5−2
= 40
3
= 40
3
= 40
40 1
B kl;Lk; jdpahf Ntiy nra;a vLf;Fk; ehl;fs = (m) 13 days.
3 3
15
10. A kw;Wk; B ,UtUk; Nrh;e;J xU Ntiyia 15 ehl;fspy; Kbg;gh;. A vd;gth;
jdpahf me;j Ntiyia 27 ehl;fspy; Kbg;ghh;. B vd;gth; jdpahf Ntiy
nra;a vj;jid ehl;fs; vLj;Jf;nfhs;thh;?
1 3
a) 39 ehl;fs; b) 37 ehl;fs; c) 33 ehl;fs; d) 40 ehl;fs;
6 4
𝟑
tpil : b) 33 ehl;fs;
𝟒
jPh;T :
1
(A+B) -d; xU ehs; Ntiy = 15
1
A-d; xU ehs; Ntiy = 27
1 1
B -d; xU ehs; Ntiy = -
15 27
9−5
= 135
4
= 135
135 3
B kl;Lk; jdpahf Ntiy nra;a vLf;Fk; ehl;fs; = (or) 33 days.
4 4
16
tpfpjk; kw;wk; tpfpjhr;rhuk;
tpfpjj;jpd; tiuaiw:-
❖ tpfpjk; vd;gJ tFj;jy; %yk; ,uz;L vz;fspd;(msTfs;) xg;gPL MFk ‘a’ kw;Wk;
‘b’ tpfpjk; “a:b” vd Fwpg;gplg;gLfpwJ. ,e;j tpfpjj;jpy; a:b, a kw;Wk; b vd;gd
cWg;Gfs; vd;Wk;, “a” vd;gJ Kd;epfo;T kw;Wk;.
tpfpjhr;rhuk;:-
17
ehd;fhtJ tpfpjk;:-
❖ a:b: :c:d my;yJ a:b = c:d, vdpy;> d vd;gJ a, b kw;Wk; c -f;F ehd;fhk; tpfpjhr;rhuk;
MFk;.
/ a:b=c:d
𝑎 𝑐
=
𝑏 𝑑
ad = bc
%d;whk; tpfpjk;:-
ruhrhp tpfpjk;:-
/ x = √𝑎𝑏
18
2. a:b = 3:5, b:c = 4:9 vdpy; a:b:c = ______________
a) 10:20:43 b) 12:22:45 c) 12:20:45 d) 9:17:35
tpil: c) 12:20:45
jPh;T:
a:b = 3:5 (1)
b:c = 4:9 (2)
(1) x 4 a:b = 3x4 : 5x4
(2) x 5 b:c = 4x5 : 9x5
a:b = 12:20
b:c = 20:45
/ a:b:c = 12:20:45
19
b:c = 15:40
/ a:b:c = 6:15:35
6. a:b = 2:3, b:c = 4:5 kw;Wk; c:d = 6:7 vdpy; a:b:c:d = ______________
a) 16:24:30:35 b) 8:15:30:32 c) 12:25:30:36 d) 12:24:28:33
tpil: a) 16:24:30:35
jPh;T:
a:b = 2:3 (1)
b:c = 4:5 (2)
c:d = 6:7 (3)
(1) x 8 a:b = 2x8: 3x8
(2) x 6 b:c = 4x6: 5x6
(3) x 5 c:d = 6x5: 7x5
a:b = 16:24
b:c = 24:30
c:d = 30:35
/ a:b:c:d = 16:24:30:35
7. a:b = 2:3, b:c = 5:8 kw;Wk; c:d = 6:7 vdpy; a:b:c:d = ______________
a) 10:14:15:18 b) 8:12:15:30 c) 10:15:16:28 d) 8:12:18:27
tpil: c) 10:15:16:28
20
jPh;T:
a:b = 2:3 (1)
b:c = 5:8 (2)
c:d = 6:7 (3)
(1) x 10 a:b = 2x10 : 3x10
(2) x 6 b:c = 5x6 : 8x6
(3) x 5 c:d = 6x8 : 7x8
a:b = 20:30
b:c = 30:48
c:d = 48:56
/ a:b:c:d = 10:15:16:28
8. a:b = 4:5, b:c = 5:6 kw;Wk; c:d = 2:3 vdpy; a:b:c:d = ______________
a) 3:6:10:14 b) 3:8:10:12 c) 4:5:6:9 d) 4:6:2:3
tpil: c) 4:5:6:9
jPh;T:
a:b = 4:5 (1)
b:c = 5:6 (2)
c:d = 2:3 (3)
(1) x 2 a:b = 4x2 : 5x2
(2) x 2 b:c = 5x2 : 6x2
(3) x 6 c:d = 2x6 : 3x6
a:b = 8:10
b:c = 10:12
c:d = 12:18
a:b:c:d = 8:10:12:18
/ a:b:c:d = 4:5:6:9
9. a:b = 5:6, b:c = 9:10 kw;Wk; c:d = 4:7 vdpy; a:b:c:d = ______________
a) 5:9:10:7 b) 15:18:20:35 c) 5:10:12:15 d) 15:18:24:35
tpil: b) 15:18:20:35
jPh;T:
a:b = 5:6 (1)
21
b:c = 9:10 (2)
c:d = 4:7 (3)
(1) x 3 a:b = 5x3 : 6x3
(2) x 2 b:c = 9x2 : 10x2
(3) x 5 c:d = 4x5 : 7x5
a:b = 15:18
b:c = 18:20
c:d = 20:35
/ a:b:c:d = 15:18:20:35
10. a:b = 1:2, b:c = 2:4 kw;Wk; c:d = 3:8 vdpy; a:b:c:d = ______________
a) 3:6:12:32 b) 4:7:10:12 c) 1:2:3:8 d) 4:6:2:3
tpil: a) 3:6:12:32
jPh;T:
a:b = 1:2 (1)
b:c = 2:4 (2)
c:d = 3:8 (3)
(1) x 3 a:b = 1x3 : 2x3
(2) x 3 b:c = 2x3 : 4x3
(3) x 4 c:d = 3x4 : 8x4
a:b = 3:6
b:c = 6:12
c:d = 12:32
/ a:b:c:d = 3:6:12:32
22
rjtPjk;
tiuaiw:-
❖ rjtPjk; vd;gJ xU rjk; my;yJ xt;nthU rjk; MFk;. rjtPjj;ij p.c. vd;W
RUf;fp vOjKbAk;. % FwpaPlhdJ ngUk;ghYk; xU rjk; vd;w nrhy;Yf;F
gad;gLj;jg;gLfpwJ.
❖ xU gpd;dj;jpd; gFjpapy; 100 ,Ue;jhy;> mjid rjtPjj;jpYk; njhFjpapy; ,Ue;jhy;
tPjk; vd;Wk; Fwpg;gplg;gLfpwJ.
1
❖ v.fh. kw;Wk; 1% vd;gJ rkkhFk;. i.e., xt;nthU 100 ghfq;fspYk; xU gFjp.
100
Efh;tpd; tpisT:-
kf;fs;njhif tpisT:-
𝑅
❖ A vd;gJ B-I tpl R% mjpfkhf ,Ue;jhy; B-MdJ A-I tpl [100+𝑅 × 100]%
Fiwthf ,Uf;Fk;.
23
𝑅
❖ A vd;gJ B-I tpl R% Fiwthf ,Ue;jhy; B-MdJ A-I tpl [100−𝑅 × 100]%
mjpfkhf ,Uf;Fk;.
1.6 A = B
160
xA= B
100
B = 160 % of A
vdNt> Njitahd kjpg;G x = 160 %
3A =B
𝑥
,g;NghJ, x A=B
100
𝑥𝑋𝐴
3A = 100
3 x 100 = x
vdNt> Njitahd kjpg;G x = 300
24
tpil : C) 175
jPh;T :
A-d; 70 % = B-d; 40 %
70 40
x A = 100 x B
100
70 100
x x A =𝐵
100 40
7
A =B
4
7 𝑥𝑋𝐴
,g;NghJ, A = 100
4
7
x 100= x
4
x = 175
vdNt> Njitahd kjpg;G x = 175
jPh;T :
A-d; 80 % = B-d; 60 %
80 60
x A=100 x B
100
4
100
80
x 60 x A =𝐵
100
3
4
A = B
3
4 𝑥
,g;NghJ, A= xA
3 100
4
x 100 = 𝑥
3
400
=x
43
1
133 3 =x
1
vdNt> Njitahd kjpg;G x = 133 3
25
jPh;T :
A-d; 30 % = B-d; 20 %
30 20
x A = 100 x B
100
Here B = X % of A
30 100
x xA = 𝐵
100 20
3
A = B
2
𝑥
,g;NghJ, x A = B
100
3 𝑥𝑋𝐴
A =
2 100
3
x 100 50 =X
2
2 A = B ........................(1)
40
2A = x C
100
5
2Ax 100
40 x C
2
5A = C ....................(2)
C =A -d; X%
𝑥
5A = x A
100
5 x 100 = X
vdNt> Njitahd kjpg;G X = 500
26
7) A -d; 30 % = B -d; 10 % kw;Wk; B =C -d; 30%, C =A -d; X% vdpy;
x-d; kjpg;G ....................
a) 1000 b) 700 c) 900 d) 650
tpil : a) 1000
jPh;T :
A-d; 30 % = B-d; 10 %
30 10
x A = 100 x B
100
30 100
x xA = 𝐵
100 10
3 A = B ........................(1)
30
3A = x C
100
100
3Ax x C
30
10 A = C ....................(2)
C =A -d; X%
𝑥
10A = x A
100
10 x 100 = X
vdNt> Njitahd kjpg;G X = 1000
B =C -d; 60%
9 60
A= x C
4 100
9 100
x xA = C
4 60
15
𝐴=C ................................(2)
4
27
C =A -d; X%
15 𝑥
A = 100 x A
4
15
x 10025 = X
4
X = 375
vdNt> Njitahd kjpg;G X = 375
jPh;T :
A-d; 50 % = B-d; 30 %
50 30
xA= xB
100 100
50 100
x xA = 𝐵
100 30
5
A = B ........................(1)
3
B =C -d; 70%
5 70
A= x C
3 100
5 100
x xA = C
3 70
50
A =C ....................(2)
21
C =A -d; X%
50 𝑥
A = 100 x A
21
50
x 100 = X
21
5000
= x
21
2
X = 238 21
28
10) A -d; 70 % = B -d; 30 % kw;Wk; B =C -d; 50%, C =A -d; X% vdpy;
x-d; kjpg;G ....................
2 2 2 2
a) 454 b) 464 c) 466 3 d) 472 3
3 3
𝟐
tpil : C) 466 𝟑
jPh;T :
70 % of A = 30 % of B
70 30
xA= xB
100 100
70 100
x xA = 𝐵
100 30
7
A = B ........................(1)
3
B =C -d; 50%
7 50
A= x C
3 100
7 100
x xA = C
3 50
14
A =C ....................(2)
3
C =A -d; X%
14 𝑥
A = 100 x A
3
14
x 100 = X
3
1400
= x
3
2
X = 466 3
29
jdp tl;b kw;Wk; $l;L tl;b
jdp tl;b
➢ tl;b vd;gJ xU Fwpg;gpl;l gzj;jpd; gad;ghl;bw;fhd nrYj;jg;gLk; $Ljy;
gzk; MFk;.
➢ fld; thq;fpa gzk; mry; vd;W miof;fg;gLfpwJ
➢ tl;b kw;Wk; mrypd; $l;Lj;njhif njhif vdg;gLk;.
jdptl;b : tiuaiw:-
➢ tl;bahdJ mNj gzj;jpy; fzf;fplg;gl;lhy;> mJ jdptl;b vdg;gLk;.
➢ jdptl;b vy;yh Mz;LfSf;Fk; xNu khjphpahf ,Uf;Fk;.
➢ P vd;gJ mry; vdTk;> R vd;gJ tl;btPjk; vdTk;> T vd;gJ fhyk; vdTk;.
S.I. vd;gJ jdptl;b vdTk; vLf;f Ntz;Lk;.
vdpy;
jdptl;b =PTR
100
Njhif =P 1 + TR
100
30
2. mh;[Pd; xU tq;fpapypUe;J Mz;Lf;F 5% tl;b tPjk; ₹ 5000 – If; fldhfg;
ngw;whh;. %d;W Mz;Lfspd; Kbtpy; mth; nrYj;j Ntz;ba tl;biaAk; nkhj;jj;
njhifiaAk; fhz;f.
a) ₹ 350> ₹ 5350 b) ₹ 650, ₹ 5650
c) ₹ 750> ₹ 5750 d) ₹ 950> ₹5950
tpil: c) ₹ 750> ₹ 5750
jPh;T:
,q;F>
mry; ( P ) = ₹ 5000
tl;b tPjk; ( R )= 5%
fhyk; ( N ) = 3 Mz;Lfs;
jdptl;b = PNR
100
= 5000 x 3 x 5
100
jdptl;b = ₹ 750
njhif = mry; + jdptl;b
= 5000 +750
= ₹ 5750
31
P=15,000
vdNt> tpf;Nd\; fldhfg; ngw;wj; njhif ₹15>000 MFk;.
32
tpil: b) ₹ 2000
jPh;T:
,q;F>
tl;b tPjk; ( R ) = 5 %
fhyk; ( N ) = 5 Mz;Lfs;
jdptl;b = PNR
100
500 =Px5x5
100
100 20
500 x 100 = P
5x5
P =2,000
vdNt> md;T fldhfg; ngw;wj; njhif ₹ 2>000 MFk;.
33
8. xU Fwpg;gpl;lj; njhifapd; kPjhd jdptl;l 5 Mz;Lfspy; Mz;Lf;F 9% tPjk; ₹
4016.25 MFk; vdpy; mriyf; fz;lwpaTk;.
a) ₹ 8925 b) ₹ 8875
c) ₹ 8575 d) ₹ 8635
tpil: a) ₹ 8925
jPh;T:
,q;F>
mry; njhifia ‘ P ‘ fhz;f
tl;b tPjk; ( R ) = 9 %
fhyk; (N ) = 5 Mz;Lfs;
jdptl;b = ₹ 4016.25
PNR =4016.25
100
P x 5 x 9=4016.25
100
P =4016.25x 100
5x9
80325
P= 401525
5x9
P=8925
vdNt> mry; ₹ 8925 MFk;.
34
= 8200 x 2 ½ x 17.5
100
41
P= 82 x 5 x 17.5
2
jdptl;b= ₹ 3587.5
36
II. $l;Ltl;b
$l;Ltl;b : tiuaiw: -
➢ Muk;gj; njhif kw;Wk; Ke;ija fhyfl;lq;fspy; nrYj;jg;gl;l tl;b
,uz;bd; mbg;gilapy; fzf;fplg;gLk; fld; my;yJ itg;Gj;njhiff;fhd
tl;b $l;Ltl;b vdg;gLk;.
➢ “tl;b kPjhd tl;b” vd;W miof;fg;gLk;. $l;Ltl;b mNj topapy;
nray;gLfpwJ.
➢ vjph;fhyj;jpy; mry; kw;Wk; tl;bapd; nkhj;j njhif – jw;Nghija mry;
njhif = $l;Ltl;b
➢ tl;b Mz;Lf;F xU Kiw> miuahz;Lf;F xU Kiw kw;Wk; fhyhz;Lf;F xU
Kiw Mfpa Kiwfspy; fzf;fplg;glyhk;.
➢ Mz;Lf;F xU Kiw>
Njhif =P 1+ R N
100
,q;F>
P= mry;
N= Mz;Lfspd; vz;zpf;if
R= tl;btPjk;
➢ miuahz;Lf;F xU Kiw>
njhif =P 1 + R/2 2N
100
➢ fhyhz;Lf;F xU Kiw>
njhif =P 1 + R /4 4N
100
1. Mz;Lf;F 6% tPjk; 2 Mz;LfSf;F ₹ 10000 nfhz;L Mz;LNjhWk; ngWk;
$l;Ltl;biaf; fz;lwpaTk;.
a) ₹ 936 b) ₹ 1136
c) ₹ 1036 d) ₹ 1236
tpil: d) ₹ 1236
jPh;T:
,q;F>
mry; = ₹ 10000
fhyk; = 2 Mz;Lfs;
tl;btPjk; = 6%
37
njhif = P 1+ R N
100
= 10000 1 + 6 2
100
= 10000 100 + 6 2
100
= 10000 106 2
100
= 10000 x 106 x 106
100 100
njhif = ₹ 11236
$l;Ltl;b = njhif – mry;
= 11236 – 10000
$l;Ltl;b = ₹ 2136
100
= 1200 1 + 6 2
100
= 1200 100 + 6 2
100
= 1200 106 2
100
= 1200 x 106 x 106
100 100
= 33708
25
38
njhif = ₹ 1348.32
$l;Ltl;b = njhif - mry;
= 1348.40 - 1200
$l;Ltl;b = ₹ 148.42
39
tpil: d) ₹ 1080.56
jPh;T:
,q;F>
mry; (P) = ₹ 10000
fhyk; (N) = 1 Mz;L 3 khjq;fs; (m) 1 3/12 Mz;Lfs;
( m) 1 ¼ Mz;Lfs;
tl;btPjk; ( R ) = 8½ %
tl;b = PNR
100
= 10000 x 1 x 8 ½
100
= 100 x 1x 17
2
= ₹ 850
njhif = tl;b +mry;
= 850 + 10000
= ₹ 10850
2- tJ Mz;bw;F> mry; vd;gJ Ke;ija Mz;bd; njhifahf ,Uf;Fk;.
($l;Ltl;bahf ,Ue;jhy;)
mry; (P) = ₹ 10850
fhyk; (N) = 3 khjq;fs; (m) 3/12 ( m) ¼ Mz;Lfs;
tl;btPjk; ( R ) = 8 ½ %
tl;b = PNR
100
= 10850 x ¼ x 8 ½
100
= 10850 x 17 x 1
100 x 2 x 4
= 3689
16
tl;b = ₹ 230.5625
nkhj;j tl;b = 850 + 230.5625
= ₹ 1080.5625
1 Mz;L 3 khjq;fSf;Fg; gpwF toq;fg;gLk; $l;Ltl;b ₹ 1080.56.
40
5. Mz;Lf;F 16% $l;Ltl;bapy; 5 Mz;LfSf;F ₹ 13500 KjyPL nra;ag;gLfpwJ.
Kjy; Mz;bd; ,Wjpapy; njhifiaf; fz;lwpaTk;.
a) ₹ 15660 b) ₹ 17890
c) ₹ 19535 d) ₹ 20990
tpil: a) ₹ 15660
jPh;T:
,q;F>
mry; (P) = ₹ 13500
tl;btPjk; ( R ) = 16 %
Kjy; Mz;L Kbtpy; fpilf;Fk; njhif>
njhif = P 1+ R N
100
= 13500 1 + 16 1
100
= 13500 116
100
= 13500 x 116
100
njhif = ₹ 15660
6. Mz;Lf;F ve;j $l;Ltl;b tPjj;jpy; ₹ 12600 vd;gJ 2 Mz;Lfspy; ₹ 15246
MfpwJ.
a) 12.5% b) 10%
c) 15% d) 17.5%
tpil: b) 10%
jPh;T:
Mz;Lf;F tl;btPjj;ij R% vd;f.
,q;F>
mry; ( P ) = ₹ 12600
njhif = ₹ 15246
fhyk; ( N ) = 2 Mz;Lfs;
njhif = P 1+ R N
100
15246 =12600 1 + R 2
100
2
15246 = 1 + R
12600 100
41
121 = 1+ R 2
100 100
121 = 1+ R
100 100
11 = 1+ R
10 100
11 - 1 = R
10 100
11 - 10 = R
10 100
1 = R
10 100
R = 100
10
R = 10%
/ Mz;Lf;F tl;btPjk; 10% MFk;.
100
34347 = 1+ R 2
3000 100
42
11449 = 1+ R 2
10000 100
11449 = 1+ R
10000 100
107 = 1+ R
100 100
107 - 1 = R
100 100
107 - 100 = R
107 100
7 = R
10 100
R = 7%
/ tl;btPjk; ( R ) = 7%
100
35123.20 = 25000 1 + R 3
100
35123.20 = 1+ R 3
25000 100
35123.20 x 100 = 1+ R 3
2500000 100
43
21952 = 1+ R 3
15625 100
3 21952 = 1+ R
15625 100
28 = 1+ R
25 100
28 - 1 = R
25 100
28 - 25 = R
28 100
3 = R
25 100
3 x 100 = R
25
R = 12
/ tl;btPjk; ( R ) = 12 %
100
8820 = 1+ R 2
8000 100
441 = 1+ R 2
400 100
441 = 1+ R
400 100
44
21 = 1+ R
20 100
21 - 1 = R
20 100
21 - 20 = R
20 100
1 = R
20 100
100 = R
20
R = 5
/ tl;btPjk; ( R ) = 5 %
100
26620 = 1+ R 3
20000 100
1331 = 1+ R 3
1000 100
3 1331 = 1+ R
1000 100
11 = 1+ R
10 100
45
11 - 1 = R
10 100
11 - 10 = R
10 100
1 = R
10 100
100 = R
10
R = 10
/ tl;btPjk; ( R ) = 10 %
11. 6 2/3 % Mz;L tl;bapy;> Mz;Lf;F xU Kiw tl;bf; fzf;fplg;gl;lhy;
vj;jid Mz;Lfspy; ₹ 3375 MdJ ₹4096 Mf khWk;.
a) 2 Mz;Lfs; b) 3 Mz;Lfs;
c) 1.5 Mz;Lfs; d) 1 Mz;L
tpil: b) 3 Mz;Lfs;
jPh;T:
,q;F>
mry; ( P ) = ₹ 3375
njhif = ₹ 4096
tl;btPjk; = 6 2/3 %
Mz;Lf;F xUKiw tl;b vdpy;>
njhif = P 1+ R N
100
4096 = 3375 1 + 6 2/3 N
100
4096 = 3375 1 + 20/3 N
100
4096 = 3375 1 + 20 N
300
4096 = 3375 1 + 1 N
15
4096 = 3375 16 N
15
4096 = 16 N
3375 15
16 3 = 16 N
15 15
46
N = 3
/ Mz;Lfs; = 3 Mz;Lfs;
100
100
3362 = 3200 1 + 5 N
200
3362 = 3200 205 N
200
3362 = 3200 41 N
40
3362 = 41 N
3260 40
1681 = 41 N
1600 40
41 2 = 41 N
40 40
N = 2
/ Mz;Lfs; = 2 Mz;Lfs;
47
Neuk; & J}uk;
1. Q vd;gth; fpof;F Nehf;fp gazpf;fpwhh;. M vd;gth; tlf;F Nehf;fp gazpf;fpwhh;.
S kw;Wk; T vd;gth;fs; vjph;j; jpirapy; gazpf;fpd;wdh;. T vd;gth; Q-tpd; tyJ
Gw;j;jpy; gazpf;fpwhh;. gpd;tUtdtw;wpy; vJ cz;ik?
a) M kw;Wk; S vjph;j; jpirfspy; gazpf;fpd;wd.
b) S Nkw;F Nehf;fp gazpf;fpwhh;.
c) T tlf;F Nehf;fp gazpf;fpwhh;.
d) M kw;Wk; S xNu jpirapy; gazpf;fpd;wd.
48
5. xU ntapy; ehspy;> khiy 4 kzpf;Fg; gpwF> uNk\; gs;spapypUe;J jpUk;gpf;
nfhz;bUe;jNghJ> mtd; khkh vjph;j;jpirapy; tUtijf; fz;lhd;. mtDila khkh
mtDld; rpwpJ Neuk; Ngrpdhh;. khkhtpd; epoy; tyJ gf;f ,Ug;gijg; ghh;j;jhd;.
mth;fs; NgRk; NghJ mtdJ khkh ve;j jpiria Nehf;fp ,Ue;jhh;.
a) tlf;F b) njw;F
c) fpof;F d) NghJkhd juTfs; ,y;iy
7. mNyhf; vd;gth; fpof;F Nehf;fp 30 kPl;lh; ele;J gpd;> tyJGwk; jpUk;gp 40 kPl;lh;
ele;jhh;. mth; kPz;Lk; tyJGwk; jpUk;gp 50 kPl;lh; ele;jhh;. mth; jdJ
njhlf;fg;Gs;spapypUe;J ve;j jpiria Nehf;fp nry;fpwhh;?
a) njw;F b) Nkw;F c) njd;Nkw;F d) njd;fpof;F
49
10. xU ehs; kjpak;> Nghahypy; cs;s vk;. [p. Nuhl;by; kdp\hTk; khJhpAk;
NeUf;F Neh; Ngrpf; nfhz;bUe;jdh;. kdp\htpd; epoy; khJhpapd; ,lJgf;fk; rhpahf
,Ue;jhy;> kdp\h ve;j jpiria Nehf;fp ,Ue;jhh;?
a) tlf;F b) njw;F
c) fpof;F d) NghJkhd juT ,y;iy
11. ‘X” Neuhf njw;F Nehf;fp elf;f Muk;gpj;jhh;. mth; 5 kPl;lh; J}uk; ele;J>
,lJGwk; jpUk;gp 3 kPl;lh; J}uk; ele;jhh;. gpd;dh; tyJgf;fk; jpUk;gp kPz;Lk; 5 kPl;lh;
J}uk; ele;jhh;. ‘X” ,g;NghJ ve;jj; jpiria Nehf;fp ,Uf;fpwJ?
a) tlfpof;F b) njw;F
c) njw;F d) njd;Nkw;F
14. xU igad; tlf;F Nehf;fp irf;fpis Xl;bdhd;. gpwF> ,lJGwk; jpUk;gp 1 fp.kP
Xl;b> kPz;Lk; ,lJGwk; jpUk;gp 2 fp.kP Xl;bdhd;. mth; jdJ njhlf;fg;
Gs;spapypUe;J Nkw;Nf rhpahf 1 fp.kP. Muk;gj;jpy; mth; tlf;F Nehf;fp vt;tsT
J}uk; gazk; nra;jhh;?
a) 1 fp.kP b) 2 fp.kP c) 3 fp.kP d) 5 fp.kP
50
15. utp vd;gth; jpNal;lUf;F vjpNu ,Uf;Fk; gy;fiyf;fofj;jpw;F nry;y
tpUg;gg;gLfpwhh;. mth; fpof;fpy; cs;s jdJ tPl;bypUe;J njhlq;fp xU
flitg;gFjpf;F tUfpwhh;. rhiyapd; ,lJKidapy; jpNal;lUk;> Neuhf
kUj;JtkidAk; cs;sd. vdpy;> gy;fiyf;fofk; ve;j jpirapy; cs;sJ?
a) tlf;F b) njw;F
c) fpof;F d) Nkw;F
16. xU vyp fpof;F Nehf;fp 20’ Xb gpd; tyJGwk; jpUk;gp 10’ Xb tyJg;Gwk; jpUk;gp
9’ Xb> kPz;Lk; ,lg;Gwk; jpUk;gp 5’ xLfpwJ. gpd; ,lJGwkhf 12’ Xb filrpapy;
,lJGwk; jpUk;gp 6’ xLfpwJ. ,g;NghJ> vyp ve;j jpiria Nehf;fp ,Uf;fpwJ?
a) fpof;F b) Nkw;F
c) tlf;F d) njw;F
51
20. mD[; vd;gth; R+hpaid jdJ gpd;Gwk; gLkhW Nehf;fp elf;fj; njhlq;fpdhh;.
rpwpJ Neuk; fopj;J> mth; ,lJGwk; jpUk;gp> gpd;dh; tyJGwk; jpUk;gpdhh;. gpd;dh;>
kPz;Lk; ,lJGwk; jpUk;gpdhh;. mth; ,g;NghJ ve;j jpirapy; nry;fpwhh;?
a) tlf;F (m) njw;F b) fpof;F (m) Nkw;F
c) tlf;F (m) Nkw;F d) njw;F (m) Nkw;F
52
3.
4.
6. (a)
7. (C)
8. (C)
53
9. (a) kjpak; R+hpad; Nkw;fpy; cs;sJ. vdNt epoy; fpof;fpy; cs;sJ. ,g;NghJ>
fpof;F jpirahdJ khJhpapd; ,lJGwk; cs;sJ. vdNt> khJhp njw;F
Nehf;fp ,Uf;fpwhh;. vdNt> khJhpia NeUf;F Neh; ghh;j;j kdp\h tlf;F
Nehf;fp ,Uf;fpwhh;.
10. (a) kjpak; R+hpad; Nkw;fpy; cs;sJ. vdNt epoy; fpof;fpy; cs;sJ.
,g;NghJ> fpof;F jpirahdJ khJhpapd; ,lJGwk; cs;sJ. vdNt> khJhp
njw;F Nehf;fp ,Uf;fpwhh;. vdNt> khJhpia NeUf;F Neh; ghh;j;j kdp\h
tlf;F Nehf;fp ,Uf;fpwhh
11. (b)
13. (a) R+hpad; fpof;fpy; cjpf;fpwJ. vdNt> fhiyapy;> epoy; Nkw;F Nehf;fp
tpOfpwJ. ,g;NghJ> Nfhghypd; tyJGwj;J fk;gj;jpd; epoy; tpOfpwJ. vdNt>
Nfhghypd; tyJgf;fk; Nkw;F. vdNt> mth; njw;F Nehf;fp ,Uf;fpwhh;.
14. (b) njspthf $wpdhy;> rpWtd; A-,ypUe;J B-f;F gpd;dh; C kw;Wk; D tiu
,Wjpahf rthhp nra;jhd;. D vd;gJ A-f;F Nkw;Nf ,Ug;gjhy;>
Njitg;gLk; J}uk; AB = CD = 2 fp.kP
54
15. (a) fpof;fpy; cs;s jdJ tPl;bypUe;J njhlq;fp> utp Nkw;F Nehf;fp efh;fpwhh;.
mg;NghJ> ,lJGwk; ,Uf;Fk; jpiuauq;fk;> njw;fpy; ,Uf;Fk; Neuhf Kd;dhy;
,Uf;Fk; kUj;Jtkid Nkw;F Nehf;fp ,Uf;Fk;. vdNt> gy;fiyf;fofk;
tlf;Nf ,Uf;Fk;.
17. (c) ,q;Nf> xt;nthU jpirAk; 900 + 450 = 1350 efUk; (vjph;fbfhu jpirapy;)
18.
55
20. njspthf> fPNo fhl;lg;gl;Ls;sgb mD[pd; ,uz;L rhj;jpakhd ,af;fq;fs;
cs;sd.
juT tpsf;fk;
jpirfs; (Nfs;tpfs;:1-5) nfhLf;fg;gl;l Nfs;tpfSf;Fg; gjpyspf;f gpd;tUk;
ml;ltizia gbf;fTk;. MW ghlq;fspy; VO khzth;fs; ngw;w kjpg;ngz;fs; :
(Max,Mark
Meera 100 80 50 90 90 60
Subodh 80 70 80 100 80 40
Kunal 90 70 60 90 70 70
Soni 60 60 65 80 80 80
Richu 50 90 62 80 85 95
Irene 40 60 64 70 65 85
Vgay 80 80 35 65 50 75
56
3. vy;yhg; ghlq;fspYk; vj;jid khzth;fs; 60S my;yJ mjw;F Nkw;gl;l kjpg;ngz;fs;
ngw;Ws;sdh;?
(a) 64 (b) 65
(c) 75 (d)64.24
5. ve;j ghlj;jpy; xl;Lnkhj;j rjtPjk; rpwe;jJ?
60 Branded
50 Assembled
40
30
20
(a) 30 (b) 20
(c) 40 (d) 35
57
8.nkhj;j Kj;jpiuaplg;gl;l kw;Wk; nkhj;j Nrh;f;fg;gl;l fzpdpfSf;F tpw;fg;gLk;
tpj;jpahrk; vd;d?
(a) 75000 (b) 750000
(c) 175000 (d) Cannot be determined
Government
Year Private
2007-2008 3900 -
2008-2009 29400 -
2009-2010 90000 -
58
13. 2011-12-k; fhyfl;lj;jpy; jdpahh; ,iza chpikahsh;f;Fk; muR ,iza
chpikahsh;fSf;Fkhd tpfpjk; vd;dthf ,Uf;f Ntz;Lk;?
Total
Company Years
ZIR 75 80 83 86 90 91 505
PEN 25 30 35 40 42 45 217
vSIO 85 87 89 91 92 96 540
17. S10 epWtdj;jpw;F Ke;ija Mz;il tpl ve;j Mz;L cw;gj;jpapy; rjtPjk;
mjpfhpg;G my;yJ Fiwg;G mjpfkhf ,Ue;jJ?
59
18. Kjy; %d;W tUlq;fis xg;gpLifapy; fle;j %d;W tUlq;fspy; ve;j
epWtdk; ruhrhp cw;gj;jp Fiwthf cs;sJ?
No Change 25% 5%
60
13. thrpg;G rjtPjk; ----120000-- 100 ≈5%
230000 +12000
ePq;fs; mij vspa fbdkhd Ntiy jPh;f;f KbAk;. njhlh;e;J ,uz;L Mz;LfSf;F
,ilNa cw;gj;jp nra;ag;gl;l myFfspd; NtWghl;ilf; fhz;f. 2013 Kjy; 2014
tiuapyhd tpj;jpahrk; mjpfgl;rk;> ,e;j Mz;Lfspy; cw;gj;jp fpl;lj;jl;l xNu
khjphpahf ,Uf;Fk;. vdNt> 2014 Mk; Mz;by; SIO Ke;ija Mz;Lfis tpl
cw;gj;jpapy; mjpfgl;r mjpfhpg;igg; gjpT nra;jJ.
First Last
Company three
three
years years
TP 358 349
PEN 90 127
279
SIO 261
61
17. nfhLf;fg;gl;l Kjy; ,uz;L Mz;Lfspy; epWtdq;fspd; nkhj;j cw;gj;jp =863
927=1790
kPz;Lk;> fle;j ,uz;L Mz;Lfspy; MW epWtdq;fspd; nkhj;j cw;gj;jp = 989
991=1980
vdNt Njitahd rjtPjk; = 1790x100 = 90.40%
1980
18. Njitahd NtWghL
jPh;T :
gpd;dj;jpd; hcf = njhFjpapdHCF
gFjpapd; LCM
kP.ngh.t (4, 2, 6, 2)
2 4, 2, 6, 2
2, 1, 3, 1
HCF (4, 2, 6, 2) = 2
LCM (9, 5, 8, 5)
2 9, 5, 8, 5
9, 1, 8, 1
kP.rp.k (9, 5, 8, 5) = 5X9X8
= 360
4 2 6 2 2
kP.ngh.t , 5, , =
9 8 5 360
𝟏
= 𝟏𝟖𝟎
62
3 2 3 1
2) , , , ,tw;wpd; HFC fhz;f
8 9 5 3
1 1 1 1
a) b) c) d) 360
45 90 180
1
tpil: d) 360
jPh;T :
gpd;dj;jpd; HCF = njhFjpapdHCF
gFjpapd; kP.rp.k
HCF (3, 2, 3, 1) = 1
LCM (8, 9, 5, 3)
3 8, 9, 5, 3
8, 3, 5, 1
LCM (8, 9, 5, 3) = 3X8X3X5
= 360
3 2 3 1 1
HCF , , , =
8 9 5 3 360
4 8 6
3) , , ,tw;wpd; HCF fhz;f
9 27 45
4 2 2 4
a) b) c) d) 45
135 135 45
2
tpil: b)
135
jPh;T :
gpd;dj;jpd; HCF = njhFjpapd; HCF
gFjpapdLCM
HCF (4, 8, 6)
2 4, 8, 6
2, 4, 3
1, 2, 3
HCF (4, 8, 6) = 2
LCM (9, 27, 45) = 3X3X3X5
= 135
4 8 6 2
HCF , , =
9 27 45 135
4 10 20
4) , , ,tw;wpd; HCF fhz;f
9 21 63
2 2 2 2
a) b) c) d) 189
21 31 63
63
2
tpil: c) 63
jPh;T :
gpd;dj;jpd; HCF = njhFjpapdHCF
gFjpapdLCM
HCF (4, 10, 20)
2 4, 10, 20
2, 5, 10
HCF (4, 10, 20) = 2
LCM (9, 21, 63)
3 9, 21, 63
3 3, 7, 21
7 1, 7, 7
1, 1, 1
LCM (9, 21, 63) = 3X3X7
= 63
4 10 20 2
HCF , , =
9 21 63 63
2 4 5 7
5) , 9, 6, ,tw;wpd; HCF fhz;f
3 12
1 1 1 1
a) b) c) d) 36
3 6 12
1
tpil: d) 36
jPh;T :
gpd;dj;jpd; HCF = njhFjpapd; HCF
gFjpapd; LCM
HCF (2, 4, 5, 7) = 1
LCM (3, 9, 6, 12)
3 3, 9, 6, 12
2 1, 3, 2, 4
1, 3, 1, 2
LCM (3, 9, 6, 12) = 3X2X3X2
= 36
2 4 5 7 1
HCF , , , =
3 9 6 12 36
64
1 3 5 7
6) , , , ,tw;wpdHCF fhz;f
2 4 6 8
1 1 2 2
a) b) c) d) 49
24 48 25
1
tpil: a) 24
jPh;T :
gpd;dj;jpd; HCF = njhFjpapd; HCF
gFjpapd; LCM
HCG (1, 3, 5, 7) = 1
LCM (2, 4, 6, 8)
2 2, 4, 6, 8
2 1, 2, 3, 4
1, 2, 3, 2
HCF (2, 4, 6, 8) = 2X2X3X2
= 24
1 3 5 7 1
HCF , , , =
2 4 6 8 24
3 6 9
7) , , ,tw;wpd; HCF fhz;f
5 10 20
3 3 3 3
a) b) c) d) 20
16 5 10
3
tpil: d) 20
65
3 6 9
8) , , ,tw;wpd; HCF fhz;f
4 7 8
3 3 3 3
a) b) c) d) 32
28 56 25
3
tpil: b) 56
jPh;T :
gpd;dj;jpdHCF = njhFjpapdHCF
gFjpapdLCM
HCF (3, 6, 9)
3 3, 6, 9
1, 2, 3
HCF (3, 6, 9) = 3
LCM (4, 7, 8)
4 4, 7, 8
1, 7, 2
LCM (4, 7, 8) = 4X7X2
= 56
3 6 9 3
HCF , 7, =
4 8 56
2 4 6 8
9) , 5, 7, ,tw;wpdHCF fhz;f
3 9
2 2 2 2
a) b) c) d) 125
945 385 215
2
tpil: a) 945
jPh;T :
gpd;dj;jpdHCF = njhFjpapdHCF
gFjpapdLCM
HCF (2, 4, 6, 8)
2 2, 4, 6, 8
1, 2, 3, 4
HCF (2, 4, 6, 8) = 2
LCM (3, 5, 7, 9)
3 3, 5, 7, 9
1, 5, 7, 3
1, 1, 7, 9
66
LCM (3, 5, 7, 9) = 3X5X7X9
= 945
2 4 6 8 2
HCF , , , =
3 5 7 9 945
3 5 7
10)16 , , ,tw;wpdHCF fhz;f
12 8
1 1 1 1
a) b) c) d) 48
8 16 24
1
tpil: d) 48
jPh;T :
gpd;dj;jpdHCF = njhFjpapdHCF
gFjpapdLCM
HCF (3, 5, 7) = 1
LCM (16, 12, 8)
2 16, 12, 8
2 8, 6, 4
2 4, 3, 2
2, 3, 1
HCF (16, 12, 8) = 2X2X2X2X3
= 48
3 5 7 1
HCF , , =
16 12 8 48
67
gfilfs;
gfilfs; vd;gJ mjd; midj;J Kfq;fspYk; ntt;NtW vz;fisf; nfhz;l
xU fdrJukhFk;. vz;fs; nghJthf 1 Kjy; 6 tiu xw;iw ,yf;fkhf ,Uf;Fk;.
gfilapd; vz;fs;:-
vjph;Kfq;fspy; cs;s vz;zpd; $l;Lj;njhif vg;NghJk; 7-f;F rkkhf
,Uf;Fk;. vz; 1 vd;gJ vz; 6-f;F vjpNu ,Uf;Fk;. vz; 2 vd;gJ vz; 5-f;F
vjpuhdJ. vz; 3 vd;gJ vz; 4-f;F vjpuhdJ.
1+6=7
2+5=7
3+4=7
gfilfspd; tiffs;:-
epiyahd gfil:-
gfilfis cUl;Lk;NghJ> ,uz;L gfilfspd; Kfg;gf;fq;fspy; cs;s
vz;fs; xd;Wf;nfhd;W nghUe;jtpy;iy vd;why;> mit epiyahd gfil vd;W
miof;fg;gLfpd;wd.
rhjuz gfil:-
xd;W my;yJ xd;Wf;F Nkw;gl;l vz;fs; ,uz;L gfilfSf;F ,ilapy;
nghUe;jpdhy; mJ rhjhuz gfil vdg;gLk;.
tif 1:-
,uz;L gfilfs; xNu Nkw;gug;igf; nfhz;bUf;Fk; NghJ> ,uz;L
gfilfspYk; vz;fspy; xd;W nghJthdjhf ,Ue;jhy;> ,uz;L gfilfspd;
kPjKs;s Nkw;gug;GfSk; xd;Wf;nfhd;W vjpNu ,Uf;Fk;
tif 2:-
,uz;L gfilfspy; ve;j ,uz;L vz;fSk; xNu khjphpahf ,Ue;jhy;>
,uz;L gfilfspYk; cs;s kPjKs;s %d;whtJ vz; xd;Wf;nfhd;W vjpNu ,Uf;Fk;.
68
tif 3:-
,uz;L gfilfspYk; ntt;NtW epiyfspy; nghJthd xU cWg;G
,Ue;jhy;> vjph; Nkw;gug;igg; ngw gfilia fbfhu jpirapy; Row;WfpwJ.
கேள்விேள்
1. ve;j vz; Nfs;tpf;Fwpf;F gjpyhf khw;w Ntz;Lk;?
tpil:- c) 228
jPh;T :-
(3 + 12) x 9 = 15 x 9
= 135
(7 + 4)x 15 = 11 x 15
= 165
III ly
(9 +3)x19 = 12 x 9
= 228.
69
tpil: a)16
jPh;T :-
8x2 = 16
1x6 = 6
4x9 = 36
3x6 = 18
III ly
7x4 = 28
2x8 = 16
3. tpLgl;l tl;lk; ahJ ?
tpil :
jPh;T :
70
tpil :- b) 5
jPh;T :
5+9 = 1 4
17 + 11 = 2 8
III ly
19 + 26 = 4 5
a) 10 b) 5 c) 8 d) 4
tpil:- d) 4
jPh;T :
(3 x 8) ÷ (4 x 2) = 24 ÷ 8
= 3
(9 x 8) ÷ (3 x 12) = 72 ÷ 36
= 2
III ly
(4 x 16) ÷ (8 x 2) = 64 ÷ 16
= 4
6. ve;j vz; 2 -f;F vjpNu tUfpwJ?
a) 3 b) 6 c) 4 d) 5
71
tpil :- d) 5
jPh;T :-
a) 3 b) 5 c) 6 d) 2/3
tpil : a) 3
jPh;T :-
4-d; vjph; vz; 3 MFk;.
a) 4 b) 1 c) 2 d) 3
tpil : b) 1
jPh;T :-
6 1, 2, 3, 4, 5,
72
2, 3, 4 kw;Wk; 5 vz;fs; 6-f;F mUfpy; ,Ug;gjhy; 6-f;F vjph; Kfj;jpy; cs;s
vz;.1 MFk;.
jPh;T:-
kQ;rs; epwj;ij Xl;ba epwq;fs; MuQ;R> ePyk;> rptg;G> kw;Wk; Nuh]; vdNt
Cjh> kQ;rs; epwj;jpw;F vjpNu ,Uf;Fk;.
a) D b) B c) C d) F
tpil :- a) D
jPh;T :-
A B, C, D, E, F
A vd;W vOj;jpd; mUfpy; cs;s vOj;Jf;fs; B, C, E kw;Wk; F MFk;. vdNt
D vd;gJ A vOj;jld; Kfj;jpw;F vjpnu cs;s vOj;jhFk;.
73
gug;G - nfhs;ssT - R+j;jpuq;fs;
rJuk;
gug;G = a2 r.myFfs;.
Rw;wsT = 4a r.myFfs;.
nrt;tfk;
gug;G = l x b r.myFfs;.
Rw;wsT = 2 (l + b) myFfs;.
b %iytpl;lk; = √𝑙 2 + 𝑏 2 myFfs;.
l
Rw;wsT = 2 𝜋𝑟 2 r.myFfs;.
miu tl;lk;
Rw;wsT = r (𝜋 + 2) r.myFfs;.
74
tl;lf;Nfhzg; gFjp
𝜃
gug;G = 𝜋𝑟 2 x r.myFfs;.
360
Rw;wsT = 2 r + l r.myFfs;.
Rw;wsT = a + b+ c r.myFfs;.
s = a + b+ c myFfs;.
2
Rw;wsT = 2a + 2 √ 𝑎2 − ℎ2 myFfs;.
rkgf;f Kf;Nfhzk; √3
gug;G = 𝑎2 r.myFfs;.
4
Rw;wsT = 3a myFfs;.
√3
cauk; = a myFfs;
4
75
வலது கேோண முக்கேோணம் gug;G = 1/2 x b x h r.myFfs;.
d Rw;wsT = h + b + d myFfs;.
d c Rw;wsT = AB + BC + CD + DA myFfs;.
a b
Rw;wsT = 2 (a + b) myFfs;
rha;rJuk;
gug;G = 1/2 x d1 x d 2 r.myFfs;.
Rw;wsT = 4a myFfs;
76
3 ghpkhz tbtq;fs;
tisgug;G = 2h (l + b) r.myFfs;
nkhj;j gug;G = 2(lb +bh+ lh) r.myFfs;
Nfhsk; nfhs;ssT =
4
𝜋𝑟 3 f.myFfs;.
3
tisgug;G = 4 𝜋𝑟 2 r.myFfs;
miuf;Nfhsk; nfhs;ssT =
2
𝜋𝑟 3 f.myFfs;.
3
tisgug;G = 4 𝜋𝑟 2 r.myFfs;
77
cUis
nfhs;ssT = 𝜋𝑟 2 h f.myFfs;.
1
nfhs;ssT = 𝜋𝑟 2 h f.myFfs;.
3
r = mbg;gf;fj;jpd; Muk;
78
cs;sPlw;w cUis nfhs;ssT =
4
𝜋 (R2- r2) f.myFfs;.
3
tisgug;G = 2 𝜋ℎ (R+r) r.myFfs;
nkhj;j gug;G = 2𝜋 (R+r) (R-r+h) r.myFfs;
cs;sPlw;w cUis
4
nfhs;ssT = 𝜋 (R3- r3) f.myFfs;.
3
cs;sPlw;w miuf;Nfhsk;
2
nfhs;ssT = 𝜋 (R3- r3) f.myFfs;.
3
nkhj;j gug;G = 3 𝜋R2 + 𝜋r2 r.myFfs;
or
𝜋 (3R2 + r2)
79
gug;gsT kw;Wk; fdmsT
I. rJuk;
1. xU rJu tbtkhd jghy; tpy;iyapd; Rw;wsT 10 nr.kP. vdpy; mjd; gf;f msitf;
fhz;f.
jPh;T:-
4xS = 10
S = 10/4
S = 2.5 nr.kP
tpil: b) 32 nr.kP
jPh;T:-
= 4x8
S = 32 nr.kP
tpil: d) ₹1120
jPh;T:-
80
nfhLf;fg;gl;lit>
= 4 x 14
S = 56 kP
= ₹1120
jPh;T:-
= 4 x 11
= 44 nr.kP
= (11)2
= 121 nr.kP 2
5. xU rJu tbt G+q;fhtpd; Rw;wsT 40kP vdpy; G+q;fhtpd; xU gf;fj;jpd; msT vd;d?
NkYk; G+q;fhtpd; %iytpl;lk; fhz;f.
81
jPh;T:-
nfhLf;fg;gl;lJ,
4xS = 40
40
S = 4
rJuj;jpd; gf;fk; = 10 kP
= 10√2 kP
fhuztpay;
1. gpd;tUk; xt;nthU Nfs;tpapYk;> nfhLf;fg;gl;l khw;wpypUe;J njhlh;Gila nrhy;
my;yJ vz;izj; Njh;e;njLf;fTk;.
tpil: c) Fsk;
jPh;T:-
tpil: c) njhy;ypay;
jPh;T:-
tpil: c) u\;ah
82
jPh;T:-
a) fplq;F b) MAjf;fplq;F
tpil: b) MAjf;fplq;F
jPh;T:-
tpil: b) kUe;jfk;
jPh;T:-
tpil: c) jpUfp
jPh;T:-
jPh;T:-
83
Viii) rpk;nghdp: ,ir: : ________________ : _______________
tpil: b) Clfk;
tpil: d) tuyhW
jPh;T:-
a) NEDOIUTCA b) NEOIDUTCA
c) NEDUOITCA d) NEODIUTCA
tpil: d) NEODIUTCA
jPh;T:-
H U M B L E
E H U B M
mNjNghy;>
E D U C A T I O N
N E O D I U T C A
84
3. xU Fwpg;gpl;l nkhopapy;> MADRAS vd;gij NBESBT vd Fwpaplg;gl;lhy;> BOMBAY
vd;gjd; FwpaPL vd;d?
a) CPNCBX b) CPNCBZ
c) CPOCBZ d) CQOCBZ
tpil: b) CPNCBZ
jPh;T:-
M A D R A S
+1 +1 +1 +1 +1 +1
N B E S B T
mNjNghy;>
B O M B A Y
+1 +1 +1 +1 +1 +1
C P N C B Z
4. xU Fwpg;gpl;l nkhopapy;> OPERATION vd;gij NODQBUJPO vd Fwpaplg;gLfpwJ
vdpy; INVISIBLE vd;gij vt;thW Fwpaplyhk;?
a) JOWJTJCMF b) JOWJTHAKD
c) HMUHTJCMF d) HMUHTHAXD
tpil: c) HMUHTJCMF
jPh;T:-
O P E R A T I O N
-1 -1 -1 -1 +1 +1 +1 +1 +1
N O D Q B U J P O
mNjNghy;>
I N V I S I B L E
-1 -1 -1 -1 +1 +1 +1 +1 +1
H M U H T J C M F
85
5. xU Fwpg;gpl;l FwpaPl;by;> FAVOUR vd;gij EBUPTS vd Fwpaplg;gLfpwJ vdpy;
DANGER vd;gij vt;thW Fwpaplyhk;?
a) CBFFDS b) CBMHDS
c) EBFHDS d) EBHHFS
tpil: b) CBMHDS
jPh;T:-
F A V O U R
-1 +1 -1 +1 -1 +1
E B U P T S
mNjNghy;>
D A N G E R
-1 +1 -1 +1 -1 +1
C B M H D S
a) NOTECFREP b) NOITCEFREP
c) NIOCTEFREP d) NOITCEFERP
tpil : b) NOITCEFREP
jPh;T:-
I N S T I T U T I O N
N O I T U T I T S N I
mNjNghy;>
P E R F E C T I O N
N O I T C E F R E P
a) DOOSGSEN b) DOOGSESN
c) DOOGSSEN d) DOGOSSEN
86
tpil: c) DOOGSSEN
jPh;T :-
P R O D U C E D
D O R P D E C U
mNjNghy;>
G O O D N E S S
D O O G S S E N
a) RNRETU b) RNETRU
c) RNERTU d) RENRTU
tpil: c) RNERTU
jPh;T:-
S I L E N T
S T I N L E
mNjNghy;>
R E T U R N
R N E R T U
a) UKRKU b) UKRKS
c) WKRKU d) WKRKS
tpil: b) UKRKS
87
jPh;T:-
B O X E R
-1 +2 -1 +2 -1
A Q W G Q
mNjNghy;>
V I S I T
-1 +2 -1 +2 -1
U K R K S
a) XVRPA b) QBKJA
c) LPRTU d) JQDKB
tpil: d) JQDKB
jPh;T:-
L O G I C
-1 -1 -1 -1 -1
B H F N K
mNjNghy;>
C L E R K
-1 -1 -1 -1 -1
J Q D K B
88