‡mjm Kwgkb welqK AsK

gvgyb iwk`

cY¨ wewµ evov‡bvi Rb¨ Kwgk‡bi aviYv †ek RbwcÖq Ges G Kvi‡Y G msµvšÍ AsK wKfv‡e Ki‡Z nq Zv

Rvbv `iKvi| Kwgkb gv‡b n‡jv †Kvb †Kv¤úvbxi cY¨ †µZvi Kv‡Q hZ `v‡g wewµ Kiv n‡e Zvi GKwU

wbw`©ó kZKiv cwigvY UvKv D³ G‡R›U ev we‡µZv jvf wnmv‡e cv‡eb| GB jvf Avm‡j weµqg~j¨ †_‡K

µqg~‡j¨i we‡qvMd‡ji mv‡_ RwoZ bv, GwU m¤ú~Y© Avjv`v GKwU aviYv| †hgb, Avcbvi †Kv¤úvbxi

†gvevBj †dvb GKRb G‡R›U‡K wewµ Kivi `vwq‡Z¡ w`‡q Avcwb ej‡Z cv‡ib †h †Kvb †gvevBj †dvb‡mU

3 nvRvi UvKvi bx‡P ev 6 nvRvi UvKvi Dc‡i wewµ Kiv hv‡e bv| hZ UvKvq wewµ Ki‡Z cvi‡e Zvi 2%

Kwgkb D³ G‡R›U cv‡eb| G ai‡Yi As‡K wewfbœ ai‡Yi KvVv‡gv _vK‡Z cv‡i, †hgb:

w`b †k‡l †m 1200 UvKv Kwgkb †c‡j Ñ Zvi weµqK…Z c‡Y¨i †gvU `vg KZ wQj?

w`b †k‡l †m 1200 UvKv Kwgkb †c‡j Ñ ‡m me©wb¤œ KqwU cY¨ weµq K‡iwQj?

w`b †k‡l †m 1200 UvKv Kwgkb †c‡j Ñ ‡m m‡e©v”P KqwU cY¨ weµq K‡iwQj?

KZ¸‡jv msL¨v w`‡q ejv n‡jv bx‡Pi †KvbwU Zvi GK w`‡bi †gvU Kwgk‡bi cwigvY n‡Z cv‡i bv

(A_ev n‡Z cv‡i)|

GB Av‡jvPbvq Avgiv Dc‡ii AsK¸‡jv wKfv‡e Ki‡Z nq Zv wkL‡ev|

(K) Kwgk‡bi cwigvY ejv _vK‡j Zv †_‡K weµqK…Z c‡Y¨i †gvU `vg †ei Kiv

G ai‡Yi As‡K cÖwZwU cY¨ Avjv`v fv‡e IB G‡R›U‡K Zvi Kwgkb †hvMvb w`‡q‡Q| ‡hgb, Dc‡ii

D`vni‡Y †m 1200 UvKv Kwgkb †c‡q‡Q ejv Av‡Q| †gvevBj †m‡Ui `vg 3000 UvKvi bx‡P bq, myZivs

me‡P‡q m Í̄vq wewµ Ki‡j †m

60 UvKv Kwgkb cvq| Avevi †Kvb †m‡Ui `vg 6000

UvKvi Dc‡i bq, myZivs me‡P‡q †ewk `v‡g wewµ Ki‡j †m

120 UvKv Kwgkb cvq|

A_©vr 60 UvKv Kwgkb AR©b Kivi Rb¨ Zv‡K 3000 UvKvi cY¨ wewµ Ki‡Z nq wKsev 120 UvKv

Kwgk‡bi Rb¨ 6000 UvKvi cY¨ wewµ Ki‡Z nq| HwKK wbq‡g ejv hvq, cÖwZ 1 UvKv Kwgk‡bi Rb¨ 50

UvKvi cY¨ wewµ Ki‡Z nq|

Kv‡RB, 1200 UvKv Kwgk‡bi Rb¨ Zvi cY¨ wewµ Ki‡Z n‡e 60,000 UvKvi (DËi)

Gevi GB AsKUv cÖ¨vKwUm Kiæb: A sales person earns as commission 5% on all

sales between Tk 2000 and 6000. If in a week his commission is Tk

460,what were his total sales? (DËi 9200 UvKv)

(L) Kwgk‡bi cwigvY ejv _vK‡j Zv †_‡K weµqK…Z c‡Y¨i me©wb¤œ msL¨v †ei Kiv

AvB‡U‡gi msL¨v Kgv‡Z n‡j Zv‡K cÖwZwU AvB‡Ug †ewk `v‡g wewµ Ki‡Z n‡e| myZivs Kwgk‡bi †iÄ

Gi g‡a¨ Avgiv m‡e©v”P `vgwU we‡ePbv Ki‡ev| Zvn‡j, Dc‡ii D`vni‡Y aiv hvK w`b †k‡l Zvi Kwgkb

n‡q‡Q 1200 UvKv, †m Kgc‡ÿ KZwU †dvb †mU wewµ K‡i‡Q Rvbv hvK| m~Îg‡Z, 6000 UvKvq GKwU

†mU wewµ Ki‡j Zvi Kwgkb nq 120 UvKv| Kv‡RB, Zvi †gvU Kwgkb †h‡nZz 1200 UvKv (hv wK bv

GKwU `vgx †mU wewµi Kwgk‡bi `k¸Y), †m Avm‡j Kgc‡ÿ `kwU `vgx †mU wewµ K‡i‡Q| `kwUi bx‡P

†Kvb fv‡eB m¤¢e bq, KviY †m‡ÿ‡Î Zvi cÖwZwUi Mo g~j¨ 6000 UvKvi Dc‡i P‡j hvq Ges †Kv¤úvbxi

kZ© j•Nb Kiv nq|

GB D`vni‡Y ‡gvU Kwgk‡bi cwigvY 1200 UvKv aivq wnmveUv †ewk mnR n‡q †M‡Q| aiv hvK, w`b †k‡l

Zvi †gvU Kwgkb 1200 UvKvi †P‡q 10 UvKv Kg (gv‡b 1190 UvKv)| Zvn‡j †m me‡P‡q `vgx 6000

UvKvi †mU 9Uv wewµ K‡i UvKv Kwgkb †c‡q‡Q| Aewkó

UvKv Kwgkb †c‡q‡Q †h †mUwU wewµ K‡i Zvi `vg

UvKv| A_©vr †m‡ÿ‡ÎI IB

G‡R›U †gvU Lvbv †dvb †mU wewµ K‡i‡Q|

(M) Kwgk‡bi cwigvY ejv _vK‡j Zv †_‡K weµqK…Z c‡Y¨i m‡e©v”P msL¨v †ei Kiv

G ai‡Yi AsK¸‡jvI wVK Dc‡ii †`Lv‡bv wbq‡g Ki‡Z n‡e| wewµZ †m‡Ui msL¨v evov‡bvi Rb¨

Avcbv‡K Aek¨B †m¸‡jv m Í̄vq †Q‡o w`‡Z n‡e| Kv‡RB Dc‡ii D`vni‡Y g‡b Kiæb G‡R›UwU Zvi

AbygwZi wbPzZg `vg 3000 UvKvq cÖwZwU †mU wewµ Ki‡jv| Zvn‡j GKwU †mU wewµ Ki‡j Zvi Kwgkb

_v‡K UvKv| A_©vr, 60 UvKv †c‡Z Zv‡K 1wU †mU wewµ Ki‡Z nq, †mB wnmv‡e

1200 UvKv IVv‡bvi Rb¨ †m wewµ K‡iwQj

wU †mU| Gi †ewk msL¨K †mU wewµ Kiv m¤¢e

bq, KviY †m‡ÿ‡Î Zv‡K cÖwZ wcm †mU Aby‡gvw`Z wb¤§Zg `vg 3000 UvKviI bx‡P wewµ Ki‡Z n‡e|

(N) Kwgk‡bi †gvU cwigvY n‡Z cv‡ibv Ggb msL¨vwU‡K Ackbmg~n †_‡K wPwýZ Kiv|

Dc‡ii D`vni‡Y †h‡nZz wb¤§Zg `vg 3 nvRvi UvKv, D”PZg `vg 6 nvRvi UvKv Ges wewµZ †m‡Ui msL¨v

0 Ges 1 Gi gvSvgvwS wKQz n‡Z cv‡ibv, IB G‡R›U mvivw`‡b GKwU †mUI wewµ Ki‡j Zvi Kwgkb

Kgc‡ÿ 60 UvKv (

) n‡e| Aek¨ GKwU †mUI wewµ Ki‡Z bv cvi‡j Zvi Kwgkb

n‡e 0 UvKv| Kv‡RB, 0 Gi eo wKš‘ 60 Gi †QvU †Kvb msL¨vB n‡e IB G‡R‡›Ui GKw`‡bi AMÖnY‡hvM¨

Kwgk‡bi cwigvY|

Gevi Avgiv wfbœ Av‡iKwU wPÎ †`wL †hLv‡b G‡R›U D”PZg I wb¤§Zg `v‡gi gv‡S B”QvgZ †h †Kvb `v‡g

Zvi cY¨ wewµ Ki‡Z cv‡ib bv eis Zv‡K GKwU kZ© gvb‡Z nq| †mB kZ© n‡jv, `vg¸‡jv 100 UvKv jvd

w`‡q w`‡q ev‡o| gv‡b, cÖ_gUv 3000 UvKv, Zvi c‡iiUv 3100 UvKv, Zvic‡iiUv 3200 UvKv BZ¨vw`|

Zvn‡j Avgiv cÖ_g PviwU m¤¢ve¨ `v‡gi Rb¨ GiKg GKUv wPÎ cvB:

`vgmg~n 3000 3100 3200 3400

2% Kwgkb gvb 60 62 64 68

wbR¯̂ Kwgkb gvb

†_‡K b~¨bZg

Kwgkb gvb 60

we‡qvM K‡i cÖvß

msL¨v

60-60 = 0 62-60 = 2 64-60 = 4 68-60 = 8

Gevi 0, 2, 4, 8 GB wmwi‡Ri w`‡K ZvKv‡jB Avcwb ey‡S hv‡eb w`b †k‡l Zvi m¤¢ve¨ Kwgkb †Kgb n‡Z

cv‡i| me¸‡jvB †Rvo msL¨K| myZivs 60 Gi †Kvb ¸wYZ‡Ki mv‡_ hw` †e‡Rvo †Kvb msL¨v †hvM Kiv

nq Zvn‡j Zv n‡e Am¤¢e Kwgkb| †hgb n‡e GiKgB GKwU Am¤¢e Kwgkb|

Av‡iKwU cÖ¨vKwUm Kiæb: Avjg mv‡ne Zvi cY¨¸‡jv †KejgvÎ 800, 1200 Ges 2000 UvKvq wewµ

Ki‡Z cv‡ib Ges weµqg~‡j¨i Dci 10% Kwgkb †fvM K‡ib| w`b †k‡l Zvi Kwgkb bx‡Pi †KvbwU n‡Z

cv‡i bv? (A) 600 (B) 680 (C) 640 (D) 700 (E) 760

Avjg mv‡n‡ei Rb¨ Avgiv †UwejwU ˆZix Ki‡Z cvwi Gfv‡e:

`vgmg~n 800 1200 2000

10% Kwgkb gvb 80 120 200

wbR¯̂ Kwgkb gvb

†_‡K b~¨bZg

Kwgkb gvb 80

we‡qvM K‡i cÖvß

msL¨v

80-80 = 0 120-80 = 40 200-80 = 120

myZivs, 80Õi †h †Kvb ¸Yd‡ji mv‡_ 0 A_ev 40 A_ev 120 (hv Aek¨ 40 Gi wZb¸Y) †h †Kvb

¸wYZK †hvM K‡i Zvi †gvU Kwgkb cvIqv hv‡e| weRMwYZ e¨envi K‡i GUv‡K A_©vr

m~Î w`‡q cÖKvk Kiv †h‡Z cv‡i| GB m~‡Îi evB‡ii †Kvb msL¨v Zvi †gvU Kwgkb n‡Z

cv‡i bv| Gevi As‡K †`Iqv Ackb¸‡jvi w`‡K ZvKv‡j †`Lv hvq †Kej 700 msL¨vwU‡K

Gfv‡e cÖKvk Kiv hvq bv| Kv‡RB GUvB n‡jv DËi|