Primary math solution (1st phase) by khairul alam

1. Primary Assistant Teacher Exam Question
1st
Phase-24th
May, 2019
Set: 5277
1. hw` †Z‡ji g~j¨ 25% e„w× cvq Z‡e †Z‡ji e¨envi kZKiv KZ Kgv‡j †Zj eve` e¨q e„w× cv‡e bv? [36Zg wewmGm]
K.16% L.20% M.25% N.24% DËi:L
mgvavb:
25% ‡e‡o 100 †_‡K n‡e 125 GLb LiP e„w× bv Kivi Rb¨ 100 UvKvi LiP Ki‡Z n‡e|
A_©vr LiP Kgv‡Z n‡e 25 UvKv| 125 UvKvq Kgv‡Z n‡e 25UvKv ∴100 ‡Z Kgv‡Z n‡e =
125
100
25 ×
=20%
Khairul’s Basic Math: 5th
Edition: Aa¨vq: kZKiv, c„ôv b¤^i: 293, cÖkœ b¤^i: 91 ûeû|
2. x + y = 17 Ges xy= 60 n‡j, (x – y)2
Gi gvb KZ? (wkÿK wbeÜb, wcÖwjwgbvix †U÷ K‡jR ch©vq-2015)
K. 49 L. 64 M. 36 N. 125 DËi: K
wjwLZ mgvavb:
Avgiv Rvwb(x-y)2
= (x+ y)2
- 4xy (x+y) Ges xy Gi gvb †`qv Av‡Q ZvB GB m~Î)
ev, (x-y)2
= 172
- 4×60 ( gvb ewm‡q)
ev, (x-y)2
= 289 - 240 ∴(x-y)2
= 49
gy‡L gy‡L Ki‡Z Gfv‡e fveyb = x+y= 17, xy = 60 [60 ‡K fv½‡j 12×5 = 60 Ges 12+5 = 17]
ZvB (12- 5)2
= 72
= 49 DËi: 49
Khairul’s Basic Math: 5th
Edition: Aa¨vq: gvb wbY©q, c„ôv b¤^i: 525, cÖkœ b¤^i: 14 ûeû|
3. hw` (x-y)2
= 12 Ges xy = 1 nq, Z‡e x2
+y2
= KZ? [cÖwZiÿv gš¿Yvj‡qi Aax‡b ¸ß ms‡KZ cwi`߇ii mvBevi
Awdmvi: 05]
K. 11 L. 12 M. 13 N. 14 DËi: N
mgvavb:
x2
+y2
=(x-y)2
+2xy = 12+2.1 = 12+2 = 14
Khairul’s Basic Math: 5th
Edition: Aa¨vq: gvb wbY©q, c„ôv b¤^i: 527, cÖkœ b¤^i: 26 ûeû|
4. 3wU msL¨vi Mo 6 Ges H 3wU mn †gvU 4 wU msL¨vi Mo 8 n‡j PZz_© msL¨vwUi A‡a©‡Ki gvb KZ? (BBA 94-95)
K.5 L.6 M.7 N.8 DËi:M
mgvavb:
cÖ_g 3wUi mgwó = 3×6 = 18 Avevi 4wU msL¨vi mgwó = 4×8 = 32 myZivs 4_© msL¨vwU = 32-18 = 14
Zvn‡j 4_© msL¨vwUi A‡a©K n‡e 14÷2 = 7|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: Mo, c„ôv b¤^i: 248, cÖkœ b¤^i: 15 GKB iKg|

2. 5. a-
a
1
= 3 n‡j a2
+ 2
a
1
Gi gvb KZ? (gva¨:mn:cÖ:wk:-03)
a.11 b.12 c.14 d.16 Ans:a
Solution: a2
+ 2
a
1
=a2
+
2
a
1






[ 2
a
1
‡K
2
a
1






wjL‡j GKB gvb †evSvq ]
a
1
2.a.
a
1
a
2
+






−
= [GLv‡b a-
a
1
Gi gvb ‡`qv Av‡Q ZvB (-) Gi m~ÎwU cÖ‡qvM Kiv n‡q‡Q Avi g‡b ivL‡eb
†fZ‡i (-) n‡j evB‡i (+) n‡e, Ges †f‡Zi (+) n‡j evwn‡i (-) n‡e|]
Khairul’s Basic Math: 5th
Edition: Aa¨vq: gvb wbY©q, c„ôv b¤^i: 528, cÖkœ b¤^i: 37 ûeû|
6. mg‡KvYx wÎfz‡Ri AwZfzR msjMœ ‡KvY `ywUi cÖ‡Z¨KwU Kx†KvY n‡e? (Z_¨ gš¿Yvjq-06) DËi:-m~²‡KvY
mgvavb:
cv‡ki wPÎwU jÿ¨ Kiæb| ∠B = 900
wKš‘ ∠A Ges ∠C Gi gvb KZ Zv ARvbv
n‡jI, ‡KvY `ywUi mgwó = 900
| myZivs G‡`i †Kvb GKwU †KvY GKvKx 900
ev Zvi †ewk n‡Z cv‡i bv,Aek¨B 900
‡_‡K Kg n‡e| ZvB Giv n‡e my²‡KvY |
Khairul’s Basic Math: 5th
Edition: Aa¨vq: wÎfzR, c„ôv b¤^i: 770, cÖkœ b¤^i: 31 ûeû|
7. ‡Kvb GKwU ¯‹z‡ji wk¶K-wk¶vwqÎxi‡`i g‡a¨ Ask gwnjv, cyiæl wk¶K‡`i 12 Rb AweevwnZ Ges Ask
weevwnZ| H ¯‹z‡ji wk¶K - wk¶vwqÎxi msL¨v KZ? (_vbv wk¶v Awdmvi cix¶v- 1999)
K.90 L.80 M.85 N.95 DËi: K
mgvavb:
cÖ‡kœ cÖ`Ë 12 nj AweevwnZ cyiæ‡li msL¨v hv nj †gvU cyiæ‡li Ask (KviY weevwnZ nj Ask)
Zvn‡j 1 As‡ki gvb n‡e = 30 Rb| GLb †gvU 30 Rb cyiæl nj mKj wkÿK - wkÿvwqÎxi Ask
(KviY Ask gwnjv ) ZvB Avgiv wjL‡Z cvwi, Ask = 30 Rb, myZivs 1 Ask = 90 Rb DËi: 90 Rb|
weKí mgvavb: †gvU = x a‡i, x. x
x
5
3
3
1
12
3
2
=
+
+ .
. 90
x =
⇒
Khairul’s Basic Math: 5th
Edition: Aa¨vq: fMœvsk, c„ôv b¤^i:118, cÖkœ b¤^i: 43 ûeû|
3
2
5
3
5
2
5
3
2
12
5 ×
3
1
3
2
3
1
hLb (a + b) Gi gvb †`qv _vK‡e ZLb (+) Gi myÎwU cÖ‡qvM Ki‡Z
n‡e wKš‘ (a − b) Gi gvb †`qv _vK‡j (-) Gi myÎwU cÖ‡qvM Ki‡Z
n‡e |
Shortcut: G ai‡bi gvb wbY©‡qi AsK Lye `ªæZ Ki‡Z n‡j GKUv welq g‡b ivL‡eb †h, wK‡mi gvb †`qv
Av‡Q? hw` (-) Gi gvb †`qv _v‡K Zvn‡j †h gvbwU †`qv _vK‡e Zvi eM© K‡i 2 ‡hvM Ki‡Z n‡e| Avevi hw` (+) Gi
gvb _v‡K Zvn‡j Zvi eM© Kivi ci 2 we‡qvM Ki‡Z n‡e| mivmwi, =32
+ 2 = 9 + 2 = 11
B C
A
900

3. 8. `yBwU µwgK msL¨vi e‡M©i AšÍi 37 n‡j, msL¨v `yBwU wbb©q Ki| [7g †kÖYx Aby : 1.2]
wjwLZ mgvavb:
awi, µwgK msL¨v `yBwU x, (x+1)
cÖkœg‡Z,
(x+1)2
-x2
= 37 ⇒x2
+2x+1-x2
= 37 ⇒ 2x=37-1 ⇒2x=36 ⇒x=
2
36
∴ x = 18
∴ msL¨v `yBwU x = 18 Ges x+1 = 18+1=19
myZivs msL¨v `yBwU h_vµ‡g, 18 I 19|
♦kU©KvU©: eo msL¨vwU =
msL¨v؇qi e‡M©i cv_©K¨ + 1
2 myZivs
2
1
37 +
=
2
38
= 19 |
†QvU msL¨vwUi m~Î =
msL¨v؇qi e‡M©i cv_©K¨ - 1
2 myZivs
2
1
37 −
=
2
36
= 18 | = 23| DËi: 19I 18
Khairul’s Basic Math: 5th
Edition: Aa¨vq: msL¨v, c„ôv b¤^i:17, cÖkœ b¤^i: 72 ûeû| GUv bZzb cÖkœ
9. GKwU †mbvevwnbxi ¸`v‡g 1500 ‰mwb‡Ki 40 w`‡bi Lv`¨ gRy` Av‡Q| 13w`b ci wKQz ˆmwbK Ab¨ RvqMvq P‡j †Mj |
evwK Lv`¨ Aewkó ‰mwb‡Ki Av‡iv 30 w`b Pj‡jv| KZ Rb ˆmwbK Ab¨ RvqMvq P‡j wM‡qwQj?
K.150 L.210 M.125 N.200 DËi: K
mgvavb:
Gai‡bi AsK mvaviY wbq‡gi gZB| ïay cÖ_‡g we‡qvM K‡i wb‡Z n‡e|
j¶¨ Kiæb: AsKwU‡Z 13 w`b c‡i wKQz ‰mb¨ Ab¨ RvqMvq wM‡q‡Q ej‡Z †evSvq †h H 13 w`b ch©šÍ mevB †L‡q‡Q|
ZvB 40w`‡bi Lvevi K‡g n‡q †M‡Q 40-13 = 27 w`‡bi|
GLb cÖ_g jvBbwU wjL‡Z n‡e
27 w`‡bi Lvevi Av‡Q = 1500 R‡bi (ˆm‡b¨i msL¨v †ei Ki‡Z e‡j‡Q ZvB Rb †k‡l)
∴1 w`‡bi Lvevi Av‡Q = 1500×27 R‡bi (27w`‡bi Lvevi 1w`‡b †L‡Z ‡ewk †jvK jvM‡e ZvB ¸Y )
∴30 w`‡bi Lvevi Av‡Q = R‡bi (1 w`‡bi Lvevi 30w`‡b †L‡Z †jvK Kg jvM‡e ZvB fvM)
= 1350Rb| GUv DËi bv| cÖ‡kœ j¶¨ Kiæb, KZRb Av‡Q †ei Ki‡Z ej‡j 1350 RbB DËi n‡Zv| wKš‘
GLv‡b DËi †ei Ki‡Z e‡j‡Q KZ Rb evB‡i †M‡Q, ZvB DËi n‡e 1500 - 1350 = 150 Rb|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: HwKK, c„ôv b¤^i: 46, cÖkœ b¤^i: 39 ûeû |
10. GKwU AvqZvKvi †ÿ‡Îi ˆ`N©¨ I cÖ‡¯’i AbycvZ 3 t 1 Ges Dnvi cwimxgv 200 wgUvi n‡j AvqZvKvi †ÿÎwUi
†ÿÎdj KZ? (NBR-2015)
K. 1575 L.1775 M.1675 N.1875 DËi: N
mgvavb:
awi, ˆ`N©¨= 3x Ges cÖ¯’ x
cÖkœg‡Z,
2(x+3x) = 200 ev, x = 25 ∴cÖ¯’=25 Ges ˆ`N©¨=3×25= 75 Zvn‡j †ÿÎdj 25×75 = 1875 ]
Khairul’s Basic Math: 5th
Edition: Aa¨vq: PZzfy©R, c„ôv b¤^i:792, cÖkœ b¤^i: 29 ûeû|
30
27
1500×
Shortcut:
1500 -
=150
30
27
1500×

4. 11. GKwU †mvbvi Mnbvi IRb 16 MÖvg| G‡Z †mvbv I Zvgvi AbycvZ 3:1| G‡Z wK cwigvb †mvbv †gkv‡j AbycvZ 4:1
n‡e? (21Zg wewmGm)
K.8MÖvg L.10MÖvg M.5MÖvg N.4MÖvg DËi:N
mgvavb:
ïiæ‡Z 3+1 = 4 Ask = 16 MÖvg wQj|
∴ 1 Ask =
4
16
=4 MÖvg| GUvB DËi| KviY bZzb
K‡i †mvbv e„w× †c‡q‡Q 1Ask = 4 MÖvg|
‡h¸‡jv‡Z 2wU Abycv‡Z GKwU ivwki gvb Same _vK‡e ‡m¸‡jv me GB wbq‡g Lye mn‡R n‡q hv‡e|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: Rule of Allegation, c„ôv b¤^i:475, cÖkœ b¤^i: 60 ûeû|
12. ‡Kvb we`¨vj‡q GKwU cixÿvq 70% wkÿv_x© MwY‡Z Ges 80% wkÿv_x© evsjvq cvm K‡i‡Q| wKš‘ 10% wkÿv_x© Dfq
wel‡q †dj K‡i‡Q| hw` Dfq wel‡q 300 Rb wkÿv_x© cvm K‡i _v‡K, Z‡e H we`¨vj‡q KZ Rb wkÿv_x© cixÿv
w`‡q‡Q? (32 Zg we‡kl wewmGm wjwLZ)
.100Rb L.200Rb M.500Rb N.600Rb DËi:M
mgvavb:
cÖ_‡g GKwU wel‡q †d‡ji nvi †ei Kiæb, ‡Kbbv Dfq wel‡q †d‡ji nvi †`qv Av‡Q 10%|
ZvB ïay MwY‡Z †dj 100-70 = 30% Ges ïay evsjvq †dj = 100-80=20%
‡gvU †dj = 30+20 -10 = 40%, GB 40% wK? GwU n‡jv †gvU †dj ( nq GK wel‡q A_ev Dfq wel‡q †dj)
Zvn‡j Dfq wel‡q cvk n‡jv 100-40% = 60% |
GLb GB 60% = 300 Rb †Kbbv 360 Rb n‡j Dfq wel‡q †gvU cvk Kiv wk¶v_©xi msL¨v|
GLb 100% Gi gvb n‡e, 300× = 500 Rb
Khairul’s Basic Math: 5th
Edition: Aa¨vq: ‡mU I †fbwPÎ, c„ôv b¤^i:725, cÖkœ b¤^i: 23 ûeû|
13. GKwU †PŠev”Pvq `yÕwU bj mshy³ Av‡Q| cÖ_g bj Øviv †PŠev”PvwU 4 wgwb‡U c~Y© nq Ges wØZxq bj Øviv 12 wgwb‡U c~Y©
nq| bj `yÕwU GK‡Î Ly‡j w`‡j Lvwj †PŠev”PvwU KZÿ‡Y c~Y© n‡e? [Sonali Bank.off. - 2014]
K.4 L.5 M.6 N.3 DËi:N
Solution:
`ywU bj GKmv‡_ 1wgwb‡U c~Y© K‡i = + ⇒ Ask|
Ask c~Y© n‡Z jv‡M = 1wgwbU∴1 ÕÕ ÕÕ ÕÕ ÕÕ = 1×3 = 3wgwbU|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: bj †PŠev”Pv I KvR, c„ôv b¤^i:216, cÖkœ b¤^i: 2 ûeû|
14. `yB AsK wewkó GKwU msL¨v, AsK؇qi ¯’vb wewbg‡qi d‡j 54 e„w× cvq| AsK `ywUi ‡hvMdj 12 n‡j msL¨vwU KZ?
(37-Zg wewmGm wcÖwj)
(K) 57 (L) 75 (M) 39 (N) 93 DËi M
mgvavb:
Ackb †_‡K 39 msL¨vwUi AsKØq ¯’vb cwieZ©b Ki‡j 93 nq| hv 39 †_‡K 93-39 = 54 eo| ZvB 39-B DËi|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: msL¨v, c„ôv b¤^i:28, cÖkœ b¤^i: 126 ûeû|
60
100
4
1
12
1
3
1
12
4
12
1
3
=
=
+
3
1
Ae¯’vb ‡mvbv Zvgv
ïiæ‡Z wQj 3 1
‡mvbv ‡gkv‡bvi ci 4 1
‡mvbv †e‡o‡Q 1 Ask AcwiewZ©Z
Shortcut
wgwbU
3
16
12
4
12
4
12
4
=
×
=
+
×

5. 15. cÖ`Ë Dcv˸‡jvi ga¨K †KvbwU ? 12, 9, 15, 5, 20, 8, 25, 17, 21, 23, 11
K. 14 L. 12 M. 15 N. 13 DËi: M
mgvavb:
ga¨K n‡”Q µgweb¨¯Í Dcv‡Ëi ga¨c‡`i gvb| DcvË we‡Rvo msL¨K n‡j ga¨K n‡e ga¨c‡`i gvb| DcvË †Rvo
msL¨K n‡j ga¨K n‡e gvSLv‡bi c` `yBwU Mo|
Dcv˸‡jv‡K gv‡bi µgvbymv‡i mvRv‡j cvB = 5, 8, 9, 11, 12, 15, 17, 20, 21, 23, 25,
GLv‡b, c`msL¨v = 11wU| Ges Dfq cv‡k 5wU K‡i c` ivL‡j gv‡Si c`wU n‡e 5+1 = 6ô| GLv‡b 6ó c` = 15
Khairul’s Basic Math: 5th
Edition: Aa¨vq: cwimsL¨vb, c„ôv b¤^i:745, cÖkœ b¤^i: 3 m`„k
16. GKwU Køv‡mi wkÿv_©x‡`i g‡a¨ 2700 PK‡jU weZiY Kiv n‡jv| cÖ‡Z¨K wkÿv_©x K¬v‡mi †gvU wkÿv_©x msL¨vi wZb¸Y
cwigvY †c‡j wkÿv_©x msL¨v KZ? (BKB Senior oofficer - 11)
K. 45 L. 35 M.30 N.40 DËi:M
mgvavb:
awi, †gvU wkÿv_©x msL¨v = x Rb Ges cÖwZR‡bi cÖvß PK‡j‡Ui msL¨v n‡jv = 3x wU|
cÖkœg‡Z,
x×3x = 2700 ev, 3x2
= 2700 ev, x2
= 900 ∴x=30 myZivs †gvU wkÿv_©x msL¨v = 30Rb
Khairul’s Basic Math: 5th
Edition: Aa¨vq: eM© I eM©g~j, c„ôv b¤^i:155, cÖkœ b¤^i: 36 ûeû
17.
0.02
0.01
1.2
1.1
0.1
×
×
×
-Gi gvb KZ? (cÖv_:mn:wk:-10)
K.660 L.550 M.360 N.460 DËi: K
mgvavb:
GLv‡b `kwgK †Zvjvi ci msL¨v¸‡jv _vK‡e
2
1
10
12
11
1
×
×
×
×
wb‡P `kwg‡Ki ci 4wU msL¨v Ges Dc‡i `kwg‡Ki
ci 3wU msL¨v GLb wb‡P GKwU msL¨v †ewk Av‡Q ZvB Dc‡i 10 ¸Y Kiv n‡q‡Q| GLb KvUvKvwU K‡i - DËi:- 660
Khairul’s Basic Math: 5th
Edition: Aa¨vq: `kwgK I fMœvsk, c„ôv b¤^i:144, cÖkœ b¤^i: 46 ûeû
18. GKwU eM©vKvi evMv‡bi †ÿÎdj 2025 eM©wgUvi| Gi Pviw`‡K †eov Av‡Q| †eovi ‰`N¨© KZ? (mn: AvenvIqvwe`:95)
K.200 L.180 M.140 N †KvbwUB bq DËi: L
mgvavb:
GLv‡b, ‡eovi ‰`N©¨B n‡”Q cwimxgv ZvB GKevû x n‡j,
x2
=2025 ∴, x=45
Ges cwimxgv ev †eov 4x =4×45= 180
Khairul’s Basic Math: 5th
Edition: Aa¨vq: PZzf©yR, c„ôv b¤^i:799, cÖkœ b¤^i: 63 ûeû

6. 19. GK e¨vw³i RyjvB gv‡mi Avq Zvi evwK 11 gv‡mi Av‡qi mgvb n‡j, Zvi RyjvB gv‡mi Avq mviv eQ‡ii Av‡qi KZ
Ask?
K. L. M. N. DËi: K
mgvavb:
awi cÖwZ gv‡m 1 UvKv K‡i Avq K‡i, Zvn‡j 11gv‡mi Avq 11UvKv Zvn‡j RyjvB gv‡mi AvqI 11 UvKv GLb mviv
eQ‡ii (12gv‡mi) Avq 11+11=22 UvKv| GLb RyjvB gv‡mi Avq mviv eQ‡ii Av‡qi Ask |
Av‡iv mn‡R:
RyjvB gv‡mi Avq = x UvKv n‡j Ab¨ 11 gv‡mi AvqI x UvKv| Zvn‡j eQ‡ii 12 gv‡mi †gvU Avq
x+x = 2x UvKv | myZivs RyjvB gv‡mi Avq mviv eQ‡ii Av‡qi =
x
2
x
=
2
1
Ask |
Khairul’s Basic Math: 5th
Edition: Aa¨vq: fMœvsk, c„ôv b¤^i:119, cÖkœ b¤^i: 46 ûeû
20. `yB AsK wewkó †Kv‡bv msL¨vi A¼ `ywUi AšÍi 2; A¼ `ywU ¯’vb wewbgq Ki‡j †h msL¨v cvIqv hvq, Zv cª`Ë msL¨vi
wظY A‡c¶v 6 Kg| msL¨vwU KZ?
K.20 L.24 M.42 N †KvbwUB bq DËi: L
mgvavb:
awi, GKK ¯’vbxq AsKwU = x myZivs `kK ¯’vbxq A¼wU = x-2
Zvn‡j msL¨vwU n‡e, 10(x-2)+x = 10x-20+x = 11x-20
¯’vb wewbgq Kivi ci bZzb msL¨vwU n‡e: 10x+x-2 = 11x-2
cÖkœg‡Z,
2(11x-20) = 11x-2+6 [cÖ_g msL¨vwU‡K 2¸Y Ki‡j Zv c‡ii msL¨vi †_‡K 6 eo n‡q hv‡e ZvB c‡i 6 †hvM]
⇒22x-40 = 11x+4
⇒11x= 44
∴x = 4
myZivs msL¨vwU = 11x-20 = 11×4-20 = 44-20 = 24
cÖgvY: 24 G 2 I 4 Gi cv_©K¨ 2 | Avevi 24 †K ¯’vb e`j Ki‡j nq 42 hv Zvi wظY 48 †_‡K 6 Kg|
Khairul’s Basic Math: 5th
Edition: Aa¨vq: mij mgxKiY, c„ôv b¤^i:620, cÖkœ b¤^i: 30 ûeû
Khairuls Basic Math eB †_‡K kZfvM Kgb|
‡dmeyK: I BDwUDe: Khairuls Basic Math wj‡L mvP© w`b|
2
1
3
2
3
1
4
1
2
1
22
11
=
wUcm: KL‡bv fMœvsk mvRv‡Z ej‡j hvi mv‡_i,Gi wefw³ hy³ _v‡K ‡mB msL¨vwU‡K wb‡P wj‡L
Aci msL¨vwU‡K Dc‡i wjL‡Z nq, Ges †k‡l KvUvKvwU K‡i †h fMœvsk ˆZix nq Zv-B DËi|