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Bank & BCS Math Percentage Bank & BCS Math Percentage

Bank Job Publication 1 2 Bank Job Publication

01.

Percentage

Percentage (kZKiv)

kZKiv (Percentage):-

kZKiv wnmve MwY‡Zi GKwU ¸iæZ¡c~Y© Ask| wewfbœ cÖwZ‡hvwMZvg~jK cixÿvq

kZKiv Ask †_‡K cÖkœ Kiv nq| ZvB AZ¨šÍ g‡bv‡hv‡Mi mv‡_ Aa¨vqwU Abykxjb

Ki‡Z n‡e|

kZKiv k‡ãi A_© ÔcÖwZk‡ZÕ| (The term percentage means per

hundred.)

kZKiv GKwU fMœvsk hvi cÖwZ‡ÿ‡Î ni 100| (Percent is a fraction with

100 as demominator in each case.)

kZKiv kãwU‡K ms‡ÿ‡c % cÖZxK Øviv cÖKvk Kiv n‡q _v‡K| (The symbol of

percent is expressed as %)

‡hgb:- kZKiv 9 A_© 9

100 Ges 9% †jLv nq|

cÖ‡qvRbxq Z_¨:

fMœvs‡ki gvb †hgb 1 A‡cÿv †ewk n‡Z cv‡i, kZKivI †Zgwb 100% Gi †ewk

n‡Z cv‡i|

100% ej‡j m¤ú~Y© msL¨vwU eySvq| 200% ev 300% Øviv msL¨vwUi wØ¸Y I

wZb¸Y eySvq|

Formula

cY¨ `ª‡eï †ÿ‡Î:-

Formula-01t g~jë„w× cvIqvi eënvi Kgv‡bvi †ÿ‡Î-

eënvi n«v‡mi nvi = 100 g~j¨ e„w×i nvi

100 + g~j¨ e„w×i nvi

Formula-02t g~j¨n«vm †c‡j eënvi evov‡bvi †ÿ‡Î-



eënvi e„w×i nvi = 100 g~j¨ n«v‡mi nvi

100 - g~j¨ n«v‡mi nvi

Formula-03t ywU msL¨vi kZKiv nv‡ii Zzjvbvi †ÿ‡Î-

kZKiv Kg / †ewk = 100 kZKiv Kg / †ewk

100 + kZKiv Kg / †ewk

Formula-04t ªe¨g~‡jï kZKiv nvi n«vm cvIqv-

`ª‡eï eZ©gvb g~j¨ = e„w× cÖvß g~j¨ nvi †gvU g~j¨

100 †h cwigvY cY¨ Kg cvIqv wM‡q‡Q

Formula-05t ªe¨g~‡jï kZKiv nvi n«vm cvIqv-

`ª‡eï eZ©gvb g~j¨ = n«vmK…Z g~j¨ nvi †gvU g~j¨

100 †h cwigvY cY¨ ‡ewk cvIqv wM‡q‡Q

Formula-06t g~j¨ ev eënvi n«vm e„w×i †ÿ‡Î-

n«v‡mi nvi = e„w×i nvi n«v‡mi nvi

100

Formula-07t c~e©g~j¨ Ges eZ©gvb g~j¨ Abycv‡Z †Ìqv _vK‡j g~‡jï kZKiv

n«vm †ei Ki‡Z n‡j-

kZKiv g~j¨ nªvm = AbycvZØ‡qi we‡qvM dj

AbycvZ 1g msL¨v 100

cixÿv I cixÿv_©xi †ÿ‡Î:-

Formula-01t Dfq wel‡q †d‡ji nvi D‡jøL _vK‡j Dfq wel‡q cv‡ki nvi

wbY©‡qi †ÿ‡Î-

cv‡ki nvi = 100 - (1g wel‡q †d‡ji nvi + 2q wel‡q †d‡ji nvi - Dfq wel‡q

†d‡ji nvi)|

Formula-02t Dfq wel‡q cv‡ki nvi D‡jøL _vK‡j Dfq wel‡q †d‡ji nvi


‡d‡ji nvi = 100 - (1g wel‡q cv‡ki nvi nvi + 2q wel‡q cv‡ki nvi - Dfq

wel‡q cv‡ki nvi)|

Formula-03t Dfq wel‡q †dj Ges cv‡ki D‡jøL _vK‡j †gvU cixÿv_©xi msL¨v


‡gvU cixÿv_x© = Dfq wel‡q cvmK…Z QvÎ

1g wel‡q †dj + 2q wel‡q †dj + Dfq wel‡q †dj 100

Formula-04t ‡Kvb GKwU wel‡q cv‡ki nvi I †d‡ji msL¨v D‡jøL _vK‡j †gvU

cixÿv_©xi msL¨v wbY©‡qi ‡ÿ‡Î-

‡gvU cixÿv_©x = ‡d‡ji msL¨v

100 - †d‡ji nvi 100

Formula-05t Dfq wel‡q †dj D‡jøL bv _vK‡j-

‡gvU cixÿv_x© = ‡gvU cvmK…Z QvÎ

100 - (1g wel‡q †dj + 2q wel‡q †dj) 100

Convertion of Number in Decimal, Percents & Fractions

Number Decimal Percents (%) Fraction

1 0.01

1%

1100

2 0.02

2%

2100 =

150

3

0.03

3%

3100

9

0.09

9%

9100

10

0.10

10%

10100 =

110

15

0.15

15%

20

3

100

15

35

0.35 35%

20

7

100

35



100 1.00

100%

100

100= 1

120

1.20

120%

5

6

100

120

3

1

0.3333 33

3

1%

3

1

3

2

0.6666

66

3

1%

3

2

25 0.25 25%

4

1

50

0.50

50%

2

1

20 0.20 20%

5

1

40

0.40

40%

5

2

100

40

60

0.60

60%

5

3

80

0.80

80%

5

4

125 1.25 125%

4

5

133 1.3333 133%

3

4

150 1.50 150%

2

3

‡gŠwjK m~Îvejx:-

`ª‡eï kZKiv e„w× = cÖK…Z e„w×

Avmj cwigvY 100%

[

`ª‡eï kZKiv n«vm = cÖK…Z n«vm

Avmj cwigvY 100%

X% e„w×‡Z P Gi ewa©Z gvb, A = P (1 + X

100 )

X% n«v‡m P Gi n«vmK…Z gvb, A = P (1 - X

100 )

Formula:-

% C = F + S + FS

100

[GLv‡b,

C = Net charge;

F = First value;

S = Second value]

Questions for Bank Exam:

01. In a collage, 45% of the students are boys. If 40% of the boys

and 20% of the girls went on a picnic, what percentage of the

total students went to the picnic? [AB Bank-2014, Jamuna Bank Po- 2014]

Abyev`:- GKwU K‡j‡R QvÎQvÎxi 45% evjK| hw` 40% evjK Ges 20%

evwjKv eb‡fvR‡b hvq, Zvn‡j †gvU QvÎQvÎxi KZ kZvsk eb‡fvRb wM‡qwQj?

Formula: QvÎQvÎxi 45% evjK n‡j evwjKv n‡”Q (100- 45) % = 55%

evjK evwjKvi kZKiv msL¨vi mv‡_ eb‡fvR‡b hvIqvi kZKiv nvi c„_Kfv‡e ¸Y

Ki‡j evjK evwjKvi †gvU msL¨v cvIqv hvq| c‡i kZKiv cÖKvk Ki‡jB †gvU

QvÎQvÎxi (100) kZKiv Ask wbY©q Kiv hvq|

Solution for MCQ:-



Percentage= (Boys Boys%) +(Girls Girls%)

Total

= (45 45) +(55 22)

100 = 29

Solution for Written exam:

Suppose,

total students = 100

Given, Boy = 45

Girls = (100 – 45) = 55

Boys went to picnic = 45 of 40%

= 45 40

100

= 18

And, Girls went to picnic = 55 of 20%

= 55 20

100

= 11

So, total students went on a picnic = 18 + 11 = 29

02. In a group of people solicited by a charity, 30% contributed

Tk. 40 each 45% contributed Tk. 20 each and the rest

contributed Tk. 12 each. What percent of the total contributed

came from people who gave Tk. 40? [Bangladesh Bank AD- 2014]

Abyev`:- GKwU `vZe¨ cÖwZôv‡bi Av‡e`‡bi cwi‡cÖwÿ‡Z wKQz msL¨K e¨w³i 30%

cÖ‡Z¨‡K 40 UvKv K‡i, 45% cÖ‡Z¨‡K 20 UvKv K‡i Ges Aewkóiv cª‡Z¨‡K 12

UvKv K‡i `vb Ki‡jb| e¨w³cÖwZ 40 UvKv K‡i cÖvß `vb †gvU `v‡bi kZKiv KZ

Ask?

Shortcut Solution for MCQ:-

30 40 + 45 20 + 25 12

= 2400

30 40

2400 100%

= 50%


awi,

†gvU e¨w³i msL¨v = 100 Rb

40 UvKv nv‡i 30 R‡bi `vbK…Z UvKv nq = 30 40

= 1200 UvKv

20 UvKv nv‡i 45 R‡bi `vbK…Z UvKv nq = 20 45

= 900 UvKv

Aewkó `vZv = (100 - 45 - 30) Rb

= 25 Rb

12 UvKv nv‡i 25 R‡bi `vbK…Z UvKv = (12 25)

= 300 UvKv

‡gvU `vb = (1200 + 900 + 300) UvKv = 2400 UvKv

1200

2400 100%

= 50%

03. A student first redused a number by 20% and then increased it

again by 20%. If the difference between the last number and

the original number is 8, then the original number was;-

[Bangladesh Bank AD- 2014]

Abyev`:- GKRb QvÎ GKwwU msL¨v‡K cÖ_‡g 20% Kgv‡jv Ges Zvici G‡K 20%

ewa©Z Kij| hw` †kl msL¨v I cÖK…Z msL¨vi cv_©K¨ 8 nq, Zvn‡j Avmj msL¨vwU

KZ?


-`yB K‡i 20% n«vm- e„w× Kivi d‡j cwieZ©b,

= – 20 + 20 + (-20)(20)

100



= -4%

4 difference n‡j msL¨vwU

= 100

8 n‡j msL¨vwU = 200


Suppose,

The original number = 100

20% reduced = 100 – 100 of 20%

= 80

After, 20% increased = 80 + 80 of 20%

= 96

The difference = 100 – 96

= 4

When 4 difference then original number = 100

When 8 difference then original number = 100 8

4

= 200

04. A school has raised 75% of the amount it needs for a new

building by receiving an average donation of tk.60 from the

people already solicited. The people already solicited

represent 60% of the people the college the college will ask for

donations. If the college is to raise exactly the amount needed

for the new buliding, how much must the remaining people

donate per person? [Jamuna Bank PO- 2014]

a) tk. 25 b) tk. 30

c) tk. 40 d) tk. 50 e) tk. 60


g‡bKwi,

†gvU †jvK msL¨v = 100

60%A_©vr 60Rb †jvK 60 UvKv K‡i `vb Ki‡j,

†gvU UvKv nq= 60 60 = 3600 UvKv

evKx †jvK _v‡K = 100 – 60

= 40 Rb

cÖwZ R‡b `vb K‡i = 1200

40

= 30 Taka

Now, 75% donation = 3600 Taka

100% donation = 3600 100

75 Taka

= 4800 Taka

Remaining donation = (4800 – 3600) Taka

= 1200 Taka

Remaining donation per person = 1200

40 Taka

= 30 Taka Ans. B

05. The difference of two numbers is 20% of the larger number. If

the smaller number is 20, then the larger number is:

a) 25 b) 45 [Probasy Kalyan EO (Cash)-2014]

c) 50 d) 80


Suppose,

The larger number = x

According to the question.

x - 20 = 20% of x

or, x - 20 = 1

5 of x

or, 5x -100 = x

or, 4x = 100



x = 25 Ans. A

06. In an examination, 80% of the students passed in English, 85%

in Mathematics and 75% in both English and Mathematics. If

40 students failed in both the subjects, find the total number of

students. [Probasy Kalyan EO (Cash)-2014] 10


Only passed in English = 80 - 75

= 5%

Only passed in Mathematics = 85 - 75

= 10%

Passed in both subjects = 5+10+ 75

= 90%

Failed in both subjects =100-90=10%

When Failed students 10, then total students = 100

When Failed students 40, then total students = 100×40

10

= 400

07. A company generated revenue of Tk. 125,000 in 2012 which

was 12.5% of its gross revenue. In 2013, the gross revenue

increased by Tk. 250,000. What is the percentage increase in the

revenue in 2013? [Union Bank Ltd-2014]

a) 12.5% b) 20%

c) 25% d) 50% e) 66.3% ans. C


‡h‡nZz 2012 mv‡j †Kv¤úvwbwU Tk. 125,000 revenue K‡i

hv gross revenue Gi 12.5%

SO, revenue 12.5% gross revenue = Tk. 125,000

revenue 100% gross revenue Tk. 125000 100

12.5

= 100000 Tk.

2012 mv‡ji gross revenue = 100000 Tk.

‡h‡nZz 2013 mv‡ji gross revenue = increased by 250000

2013 mv‡ji gross revenue = 1000000 + 250000 = 1250000 Tk.

Now.

2012 Gi †ÿ‡Î 100000 Tk. gross revenue n‡j revenue 250000 Tk.

2013 mv‡ji 1250000 Tk. gross revenue n‡j revenue

= 125000 1250000

1000000 Tk.

= 156250 Tk.

2012 ‡_‡K 2013 †Z revenue increase = (156250 – 125000) Tk.

= 31250 Tk.

2012 ‡_‡K 2013 †Z revenue Gi % increase,

= 31250

125000 100

= 25%

08. A circular logo is enlarged to fit the lid of a jar. The new

diameter is 50 percent larger than the original. By what

percentage has the area of the logo increased? [AB Bank- 2014]

a) 50 b) 80

c) 100 d) 125 e) None of these


Suppose, Diameter of the jar be = d

Area = Ar2

= A(d/2)2

= A d

2

4

Then, New area = 1

4 (d + 50% of d2

)



= 1

4 (d +

d

2 )

2

= 1

4

3d

2

2

=

1

4 .

9

4 .d2

=

9

16 d2

Area increased,

= 9

16 d2

- d

2

4

= d2

9

16 -

1

4

= d2

9 - 4

16

= 5

16 d2

So, Increased in percentage =

5

16 d

2

1

4 d

2 100

= 5

16

4

1 100

= 125

Ans. D

09. The population of a certain town increases by 50 percent every

50 years. If the population in 1950 was 810, in what year was

the population 160? [Pubali Bank (SO) 2013]

a) 1650 b) 1700

c) 1750 d) 1800 e) None of Them ans. C

Abyev`:- GKwU kn‡ii RbmsL¨v cÖwZ 50 eQi AšÍi 50% e„w× cvq| hw` 1950

mv‡j RbmsL¨v 810 Rb nq Zvn‡j KZ mv‡j RbmsL¨v 160 Rb wQj?


‡Ìqv Av‡Q, cÖwZ 50 eQi AšÍi 50% e„w× cvq,

ZvB 50 eQi Av‡Mi RbmsL¨v 100 n‡j eZ©gv‡b RbmsL¨v = 100 + 50 = 150.

A_©vr eZ©gv‡b †jvKmsL¨v weMZ †jvKmsL¨vi 150% = 3

2

Dëvfv‡e weMZ †jvKmsL¨v eZ©gvb †jvKmsL¨vi = 1

3

2

= 2

3 .

myZivs 1950 mv‡j †jvKmsL¨v 810 n‡j,

1900 mv‡j †jvKmsL¨v wQj = 810 2

3 = 540 Rb

1900 mv‡j †jvKmsL¨v 540 n‡j,


3 = 360 Rb



3 = 240 Rb



3 = 160 Rb


GUv‡K Pµe„w× my‡ì As‡Ki m~Î w`‡q Ki‡Z cv‡ib|

CA = p( )1 + r

100

t

Or, 810 = 160( )1 + 50

100

t

Or, 810

160 = ( )1 +

1

2

t

Or, ( )3

2

4 = ( )

3

2

t

Or, t = 4.

GLb, GLv‡b t = 1 n‡jv 50 eQi|

t = 4 n‡jv 50 4 = 200 eQi n‡e|



ZvB RbmsL¨v 160 Rb wQj = 1950 – 200 = 1750 mvj Ans. C

10. A student multiplied a number by 5

3 instead of

3

5 . What is the

percentage of error in the calculation? [Rupali Bank- Junior Officer-2013]

a) 34% b) 44%

c) 54% d) 64%

Abyev`:- GK QvÎ †Kvb msL¨v‡K 5

3 Gi cwie‡Z©

3

5 Øviv ¸Y K‡i †djj| G‡Z KZ

wnmv‡ei Mowgj n‡e?


awi,

cÖ_g msL¨vwU = x

Actual number should be = 3x

5

So error number is = 5x

3

Error = (5

3 x -

3

5 x)=

16 x15

Now, 5

3 x G Error nq =

16 x15

1 G Error nq = 16

15 x

3

5x

100 G Error nq = 16

15 x

3

5x 100 = 64%


5

3 I

3

5 Gi ni 3 I 5 Av‡Q e‡j msL¨vwU = 3 5 = 15

mwVK msL¨vwU n‡e =

5

3 15 = 25 Avevi Qv‡Îi f~j msL¨vwU =

3

5 15 = 9

Error nq = (ï× msL¨v - fzj msL¨v) = (25 - 9) = 16

Now, Error % = 16

25 100% = 64% Ans. D Ans. D

11. If 35% of a number is 12 less than 50% of that number, then

the number is: [Rupali Bank- Junior Officer-2013]

a) 40 b) 50

c) 60 d) 80

Abyev`:- hw` †Kvb msL¨vi 30% H msL¨vi 50% ‡_‡K 12 Kg nq Z‡e msL¨vwU

KZ?


g‡bKwi, msL¨vwU = x

kZ©g‡Z, 35% of x = 50% of x - 12

Or, 35x

100 =

50x

100 - 12

Or, 35 x = 50 x - 12

x = 80 Ans. D

12. The area of a rectangle is 460 square metres. If the length is

15% more than the breadth, what is the breadth of the

rectangular field? [Rupali Bank- Junior Officer-2013]

a) 15 metres b) 26 metres

c) 34.5 metres d) None of these

Abyev`:- AvqZ‡ÿ‡Îi †ÿÎdj 460 m2. hw` †ÿÎwUi ˆ`N©¨ cÖ ’ n‡Z 15%†ewk

nq Z‡e †ÿÎwUi cÖ ’ KZ?


awi, cÖ¯’ = x

‰`N©¨ = x + 15% = 1.15 x

cÖkœvbymv‡i,

1.15 x x = 460

Or, x2 = 460

x = 20



cÖ ’ x = 20 m Ans. D

13. The number of marbles in Amin’s collection is 80% of the

number in Rahim’s collection. If Rahim has 80 more marbles

than Amin. how many marbles do they have altogether?

a) 720 b) 120 [Agrani Bank- Senior Officer-2013]

c) 400 d) 320

Abyev`:- ejv n‡q‡Q †h, Avwg‡bi gv‡e©j iwn‡gi gv‡e©‡ji 80% Ges iwn‡gi

gv‡e©j Avwg‡bi ‡P‡q 80 wU †ekx| Zv‡ì GK‡Î KZwU gv‡e©j Av‡Q?


awi, iwn‡gi gv‡e©j Av‡Q = x wU

Avwg‡bi gv‡e©j Av‡Q = x Gi 80% wU

kZ©vbymv‡i,

x – x Gi 80% wU = 80

Or, x - 80x

100 = 80

x = 400

iwn‡gi gv‡e©j 400 wU I Avwg‡bi gv‡e©j = (400 80%) = 320 wU

myZivs Zv‡ì GKwÎZ gv‡e©‡ji msL¨v = (400 + 320) = 720 wU Ans. A

14. In an election a candidate who gets 84% of the votes is elected

by a mojority of 476 votes. What is the total number of votes

polled? [Bangladesh Bank D- 2012]

Abyev`:- GKwU wbe©vP‡b GKRb cÖv_©x 84% †fvU †c‡q wbe©vwPZ nq Ges 476 †fvU

†ewk cvq| Zvn‡j †gvU †fvUvi msL¨v KZ?


68% = 476

100% = 476

68 100 = 700


Suppose,

The other candidate gets = (100 – 84)% = 16%

Majority votes = (84 – 16)% = 68%

So, 68 votes get majority when total votes 100

476 votes get majority when total votes 476 100

68 = 700

15. A's income is 50% less than B's. By how much percent, B's

income is more than A's? [Bangladesh Krishi Bank Officer (Cash)-2011]

a) 33.33% b) 50%

c) 75% d) 100%


50

100-50 = 1 = 100%


Given,

A's income is 50% less than B's income

So, A's income = 50

100 × B's income =

100

100 × B's income

= 100% of B's income

and B's income = 100

50 × A's incom e=

200

100 × A's income

= 200% of A's income

B's income is (200 -100) % = 100% more than A's income. Ans. D

16. hw` wPwbi g~j¨ 20% e„w× cvIqv‡Z †Kvb GK cwigvY wPwb LvIqvq †Kgb Kgv‡j wPwb

eve` e¨q e„w× cv‡e bv? [Bmjvgx e¨vs‡Ki Awdmvi cixÿv:2008]

a) 20% b) 16%

c) 10% d) 25%



100 + g~jë„w×i nvi



= 100 20

100 + 20

= 16.67%


20% e„w×‡Z wPwbi eZ©gvb g~j¨ nq = (100 + 20) = 120 UvKv

GLb, 120 UvKv eZ©gvb g~j¨ n‡j Av‡Mi g~j¨ ev c~e© g~j¨ = 100 UvKv

100 UvKv eZ©gvb g~j¨ n‡j Av‡Mi g~j¨ ev c~e© g~j¨ = 100 100

120 UvKv

= 250

3 UvKv

wPwb LvIqv Kgv‡Z n‡e = (100 - 250

3) = 16.67% Ans. B

17. A company increases every year salary of an officer by 20%.

His salalry in the year 2001 was Tk. 26640. What was his salary

in 1999? [Sonali, Janata and Agrani Bank Officer- 08]

a) Tk. 18500 b) Tk. 20,000

c) Tk. 18840 d) Tk. 19028

Abyev`:- GKwU †Kv¤úvbx Zvi GKRb Kg©KZ©vi †eZb cÖwZeQi 20% K‡i e„w×

K‡i| 2001 mv‡j H Kg©KZ©vi †eZb 26640 UvKv n‡j, 1999 mv‡j †eZb KZ

wQj?


g‡bKwi,

1999 mv‡j †eZb = 100 UvKv


2001 mv‡j †eZb = (120 + 120 Gi 20%) = 144 UvKv

2001 mv‡j †eZb 144 UvKv n‡j 1999 mv‡j †eZb = 100 UvKv

2001 mv‡j †eZb 26640 UvKv n‡j 1999 mv‡j †eZb

= 100 26640

144 UvKv = 18500 UvKv Ans. A

18. A Bakery opened yesterday with its daily supply of 40 dozens

of rools. Half of the rolls were sold by noon, and 80% of hte

remaining rools were sold between noon and closing time.

How many dozens of rool had not been sold when the bakery

closed yesterday? [Bangladesh Commerce Bank Juniro Officer:2008]

a) 2 dozen b) 4 dozen

c) 5 dozen d) 8 dozen

Abyev`:- MZKvj †eKvix †Lvjvi 40 WRb †ivj wQj| A‡a©K †ivj `ycy‡ii g‡a¨

wewµ n‡q †Mj| Aewkó †iv‡ji 80% ci †_‡K †eKvix e‡Üi AvM ch©šÍ mg‡qi

g‡a¨ wewµ n‡q †Mj| MZKvj †eKvix e‡Üi mgq KZ¸‡jv †ivj AwewµZ wQj?


Rolls were sold by noon = 40

2 = 20 dozens

Remining rolls = (40 – 20) = 20 dozens

Rolls were sold between noon and closing time,

= (80% of 20) = 16 dozen

Rools were unsold at closing time = (20 – 16) = 4 dozen Ans. B

19. A Class of 20 girls and 30 boys arranged a picnic. However

only 30% of the girls 40% of the boys attended the picnic.

What percent of hte class attended the picnic? [Agrani Bank Officer:2008]

a) 32.5 b) 35

c) 36 d) 37.5

Abyev`:- GKwU †kÖYxi 20 Rb QvÎx I 30 Rb QvÎ GKwU eb‡fvR‡bi Av‡qvRb

Kij| 30% QvÎx Ges 40% QvÎ eb‡fvR‡b AskMÖnY Kij| kZKiv KZRb

QvÎQvÎx eb‡fvR‡b Ask MÖnY Kij?




So, Girls attended the picnic = 20 30

100 = 6

and, Boys attended the picnic = 30 40

100 = 12

Total attendance in the pcinic = 12 + 6 = 18

Total student in the class = 20 + 30 = 50

Percent of the class attended the picnic = 18

100 100= 36 Ans. C

20. If in 1997, 1998 and 1999 a worker received 10% more salary

each year than he did the previous year. How much did he

receive in 1999 than in 1997? [Bangladesh Bank Assistant Director:2001]

a) 10% b) 11%

c) 20% d) None of these

Abyev`:- GKRb kÖwgK 1997, 1998 Ges 1999 mv‡ji cÖ‡Z¨K eQi c~e© wZb

eQ‡ii A‡cÿv 10% †ewk †eZb †cj| †m 1999 mv‡j 1997 mv‡ji †P‡q KZ

†ewk †eZb †cj?


g‡bKwi,



Ges 1999 mv‡j †eZb = 110 110% = 121 UvKv

1999 mv‡j 1997 mv‡ji †P‡q †ewk †eZb †cj = (121 - 100) UvKv = 21

UvKv ‡eZb 21% e„w× †cj| Ans. D

21. The prcie of rice in the year 1995 has increased by 10% from

that of the previous year. In 1996, the price decreased by 5%.

In 1996 what was the increase in price with respect to that of

1994? [Bangladesh Bank Assistant Director:2001]

a) 4.5% b) 5%

c) 5.5% d) None of these

Abyev`:- 1995 mv‡j Pv‡ji g~j¨ c~e© wZb eQ‡ii †P‡q 10% e„w× †cj| 1996

mv‡j Zv 5% K‡g †Mj| 1994 mv‡ji mv‡c‡ÿ 1996 mv‡j g~j¨ KZ e„w× †cj?


g‡bKwi,

1994 mv‡j Pv‡ji g~j¨ wQj = 100 UvKv

1995 mv‡j Pv‡ji g~j¨ `vovq = (100 + 10) = 110 UvKv

Ges 1996 mv‡j Pv‡ji g~j¨ `vovq = {100 - (110 Gi 5%)} UvKv

= 104.5 UvKv

Pv‡ji g~j¨ e„w× †cj = (104.5 - 100)% = 4.5% Ans. A

Question for BCS & Others exam:-

01. wPwbi `vg 20% K‡g †Mj, wKš‘ Bnvi eënvi 20% e„w× ‡cj| G‡Z wPwb eve`

e¨q kZKiv KZ evo‡jv ev Kg‡jv? [wcGmwm KZ©„K wba©vwiZ 12wU c`-2001, †Rjv cÖv_wgK wk¶v Awdmvi

wcwUAvB Gi mycvwib‡Ub‡W›U wcwUAvB Gi mnKvix mycvwib‡Ub‡W›U-2005, RvZxq mÂq cwi`ß‡ii mnKvix cwiPvjK-2009]

a) 5% eo‡jv b) 5% Kg‡jv

c) 4% eo‡jv d) 4% Kg‡jv


20 + 20 + (-20)(20)

100 = - 4%


awi,

cwiev‡i wPwb jv‡M x †KwR I cÖwZ‡KwRi `vg y UvKv

†gvU LiP = xy UvKv



wPwbi `vg 20% Kg‡j UvKvq K‡g .2y UvKv

cªwZ †KwRi cwiewZ©Z `vg = (y -.2y) = .8y UvKv

cybivq, wPwbi eënvi 20% evo‡j x †KwR‡Z ev‡o .2x ‡KwR

cwiewZ©Z eënvi = (x +.2x) †KwR = 1.2x †KwR

cwiewZ©Z †gvU LiP = (.8y × 1.2x) =.96xy UvKv

wPwb eve` e¨q Kg‡e = xy - .96xy = .04xy UvKv A_©vr 4% Ans. D

02. hw` †Kv‡bv eM©‡¶‡Îi cÖ‡Z¨K evûi cwigvY 10% e„w× cvq, Z‡e Zvi †¶Îdj

kZKiv KZ e„w× cv‡e? [cwi‡ek I eb gš¿Yvj‡qi cwi‡ek Awa`ß‡i wdìe Bb‡fw÷‡MUi Ges wimvP©

A¨vwm‡÷›U-2006, wcGmwmi mnKvix cwiPvjK Ges cvm‡cvU© A¨vÛe Bwg‡MÖk‡b mnKvix cwiPvjK-2006]

a) 18% b) 20%

c) 21% d) 22%


10+10+1010

100 = 21%


awi,

e‡M©i evûi ˆ`N © = x GKK

e‡M©i †¶Îdj = x2 eM© GKK

cÖwZ evû e„w× cvq = x Gi 10

100 GKK

= x10

GKK

evûi cwigvY = x + x10

GKK

= 11x

10 GKK

myZivs bZzb e‡M©i †¶Îdj = 121x

2

100 eM© GKK

†¶Îdj e„w× = 121x

2

100 - x2

= 21x

2

100 eM© GKK

kZKiv e„w× cvq =

21x

2

100

x2 ×100 %

= 21x

2

100x2 ×100

= 21% Ans. C

03. hw` hw` †Z‡ji g~j¨ 25% e„w× cvq Z‡e †Z‡ji eënvi kZKiv KZ Kgv‡j †Zj eve`

LiP e„w× cv‡e bv? [cwi`k©K (RvZxq ivR¯^ †evW©) wb‡qvM-2010; 23Zg wewmGm; †ijI‡qi mnKvix Kgv‡Û›U

cixÿv-2000; cÖv_wgK wkÿv Awa`ß‡ii wnmve mnKvix c‡` wb‡qvM cixÿv-2011; evsjv‡`k M¨vm wdì †Kv¤úvbx mnKvix

eë¯’vcK c‡` cixÿv- 2011]

a) 30% b) 20%

c) 15% d) 25%



100 + g~jë„w×i nvi

= 100 25

100 + 25

= 20%


25% e„w×‡Z †Z‡ji g~j¨ nq = (100 + 25) = 125 UvKv

125 UvKv eZ©gvb g~j¨ n‡j Av‡Mi g~j¨ ev c~e© g~j¨ = 100 UvKv

100 UvKv eZ©gvb g~j¨ n‡j Av‡Mi g~j¨ ev c~e© g~j¨ = 100 100

125= 80 UvKv

myZivs Kgv‡Z n‡e =( 100 Ñ 80) = 20% Ans. B

04. hw` ‡Kvb cixÿvq wkÿv_x© 80% MwY‡Z Ges 70% evsjvq cvm Ki‡jv| Dfq wel‡q



cvm Ki‡jv 60% Dfq wel‡q kZKiv KZ Rb †dj Ki‡jv?

[22Zg wewmGm, Dc‡Rjv mnKvix wkÿv Awdmvi cixÿv- 2006, A_©gš¿bvj‡q AwWUi

c‡` wb‡qvM cixÿv-2011, 6ó mnKvix RR wb‡qvM cixÿv- 2011]

a) 15% b) 10%

c) 12% d) 11%


†d‡ji nvi = 100 - (1g wel‡q cv‡ki nvi + 2q wel‡q cv‡ki nvi-Dfq

wel‡q cv‡ki nvi)

= 100 -(80 + 70 - 60) = 100 - 90 = 10%


ïay MwY‡Z cvm K‡i = 80% - 60% = 20%

ïay evsjvq cvm K‡i = 70% - 60% = 10%

myZivs yB welq wg‡j †gvU cvm K‡i = 20% + 10% + 60% = 90%

Dfq wel‡q †dj K‡i = (100 - 90)% = 10% Ans. C

05. hw` ‡Kvb ¯‹z‡j 70% wkÿ_x© Bs‡iRx‡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 360 Rb wkÿv_©x cvm

K‡i Z‡e H ¯‹z‡j KZRb wkÿv_©x cixÿv w`‡q‡Q? [15, 20 I 23Zg wewmGm,]

a) 500 Rb b) 450 Rb

c) 700 Rb d) 600 Rb




= 360

30 + 20 + 10 100

= 600 Rb


ïay Bs‡iRx‡Z †dj K‡i (100 - 70)% - 10% = 20%

Ges ïay evsjvq †dj K‡i (100 - 80)% - 10% = 10%

`yB wel‡q †gvU †dj K‡i = (20 + 10)% + 10% = 40%

myZivs yB wel‡q †gvU cvm K‡i = 100 - 40 = 60%

60 Rb cvm K‡i 100 R‡bi g‡a¨

360 Rb cvm K‡i 100 360

60 = 600 Rb Ans. D

06. cÖwZwU 3600 UvKv K‡i ywU †Pqvi weµq Kiv n‡q‡Q| GKwU 20% jv‡f Ges

AciwU 20% ¶wZ‡Z weµq Kiv n‡q‡Q| me wgwj‡q KZ †jvKmvb n‡q‡Q?

[18Zg wewmGm, cÖv_wgK mnKvix wk¶K-2012 (†gNbv)]

a) jvf †jvKmvb wKQzB nqwb b) 900 UvKv

c) 300 UvKv d) 600 UvKv


‡Pqvi yBwUi weµqg~j¨ = 3600×2 = 7200 UvKv

20% jv‡f, weµqg~j¨ 120 n‡j µqg~j¨ = 100 UvKv

weµqg~j¨ 3600 n‡j µqg~j¨ = 3600×100

120 UvKv = 3000UvKv

weµqg~j¨ 80 n‡j µqg~j¨ = 100 UvKv

weµqg~j¨ 3600 n‡j µqg~j¨ = 3600×100

80 UvKv = 4500UvKv

‡gvU µqg~j¨ = 3000+4500=7500 UvKv

†gvU †jvKmvb = 7500 - 7200 = 300 UvKv Ans. C

07. GKwU AvqZ‡¶‡Îi ˆ`N¨© 20% evov‡bv n‡jv Ges cÖ¯’ 20% Kgv‡bv n‡jv|

†¶Îdj –

[cwiKíbv gš¿Yvjq Ges cÖevmx Kj¨vY I ê‡`wkK Kg©ms¯’kvb gš¿Yvj‡qi mnKvix cwiPvjK-2006, mve †iwR÷ªvi-2003]

a) AcwiewZ©Z _vK‡e b) 4% Kg‡e

c) 4% evo‡e d) 2% Kg‡e


awi, ˆ`N© = 100 GKK

†¶Îdj = 10000 eM© GKK



myZivs AvqZ‡¶‡Îi ˆ`N©¨ 20% evov‡j, ˆ`N© = 120 GKK

Ges AvqZ‡¶‡Îi cÖ¯’ 20% Kgv‡j, cÖ ’ = 80 GKK

†¶Îdj =(120×80) = 9600 eM© GKK

†¶Îdj K‡g = (10000-9600) eM© GKK

= 400 eM© GKK

10000 eM© GK‡K †¶Îdj K‡g = 400 eM© GKK

100 eM© GK‡K †¶Îdj K‡g = 400×100

10000 = 4 eM© GKK Ans. B

08. hw` Pv‡ji g~j¨ 12% K‡g hvIqvq 6,000 UvKvq c~e©v‡cÿv 1 KyB›Uvj Pvj †ewk cvIqv

hvq| 1 KB›Uvj Pvj Gi eZ©gvb g~j¨ KZ?

[11Zg wewmGm, cvm‡cvU© GÛ Bwg‡MÖk‡bi mnKvix cwiPvjK cixÿv-2003]

a) 750 UvKv b) 75 UvKv



`ª‡eï eZ©gvb g~j¨ = e„w× cÖvß g~j¨ nvi †gvU g~j¨

100 ‡h cwigvY cY¨ Kg cvIqv wM‡q‡Q

= 12 6000

100 1 = 720 UvKv


GLb, K Gi †eZb 135 UvKv n‡j L Gi †eZb = 100 UvKv

K Gi †eZb 100 UvKv n‡j L Gi †eZb = 100 100

135 = 78.07 UvKv

Ans. D

09. A trader raised the price of his product by 10%, and then he

lowered the enhanced price by 10%. Compared to the latest

price the first price has been - [evwYR¨ gš¿Yvjqi Aaxb evsjv‡`k U¨vwid Kwgkb wimvP© Awdmvi-2010]

a) lowered by 1% b) kept equal

c) enhanced by 1% d) enhanced by 4%


10 - 10+ 10(-10)

100 = -1

Decreased/ lowered by 1%


Suppose,

The cost price be x.

Here, at the first case, x+10% of x = 1.1x

and at the second case, 1.1x - 10% of 1.1x = 0.99x = latest price

x-0.99x = 0.01x

So, the latest price has been lowered by 2% compared to the first

price.

Ans. A

10.

g›`vi Kvi‡Y kÖwgK‡ì ‰`wbK †eZb 50% n«vmKiv nq| 1 eQi ci ˆ`wbK †eZb

80% e„w× Kiv nq| g›`vi c~‡e© ‰`wbK †eZb 100 UvKv n‡j eZ©gv‡b kÖwg‡Ki

ˆ`wbK †eZb KZ? [cÖv_wgK mnKvix wk¶K-2010 (wZZvm)]




50 + 80 + (-50)80

100 = -10%

100-10 1

100 = 90


50% n«v‡m †eZb nq = (100-50) = 50 UvKv

g›`vi c‡i kÖwgK‡ì ˆ`wbK †eZb = 50 UvKv

80% e„w×‡Z, †eZb = (100+80) = 180 UvKv



c~‡e©i †eZb 100 UvKv n‡j eZ©gvb †eZb = 180 UvKv

c~‡e©i †eZb 50 UvKv n‡j eZ©gvb †eZb 180×50

100 UvKv = 90 UvKv Ans. C

11. Avj‡gi eqm Kg‡ji eq‡mi 80% n‡j Kg‡ji eqm Avj‡gi eq‡mi -

[cÖv_wgK mnKvix wk¶K-2010 (K‡cvZv¶)]

a) 125% b) 116%

c) 80% d) 20%


g‡bKwi,

x n‡jv Avj‡gi eqm, Avi y n‡jv Kg‡ji eqm

x = 80%y

x = 80

100 y

y = 100

80 x

y= 100×100

80×100 x =

125

100 x

y =125%x Ans. A

12. hw` MZKvj †kqv‡ii `vg 25% †e‡owQj| wKš‘ AvR 25% K‡g‡Q| †kqv‡ii `vg †gvU

KZ †e‡o‡Q ev K‡g‡Q? [mgvRKj¨vY Awdmvi (mgvR gš¿Yvjq) wb‡qvM-2010]

a) 6

1

4 % K‡g‡Q b) 6

1

4 % ‡e‡o‡Q

c) 4

1

2 % K‡g‡Q d) 4

1

2 % ‡e‡o‡Q


n«v‡mi nvi = e„w×i nvi n«v‡mi nvi

100 =

25 35

100 = 6

1

4 %


e„w×i c~‡e© `vg = 100 UvKv

MZKvj wQj = 125 UvKv

100 UvKvq K‡g 25 UvKv

125 UvKvq K‡g 25 125

100 =

125

4

AvR‡K n‡q‡Q = 125 - 125

4 =

375

4

`vg K‡g = 100 - 375

4 =

25

4 = 6

1

4 K‡g Ans. A

13. GKwU Nwo I GKU †PB‡bi g~j¨ GK‡Î 500 UvKv| Nwoi g~j¨ 10% I †PB‡bi

g~j¨ 5% e„w× †c‡j ewa©Z g~j¨ 545 UvKv nq| Nwoi g~j¨ KZ?

[cÖv_wgK cÖavb wk¶K-2009 (†Mvjvc)]




500+5001

20 = 525,

Difference = 545-525 = 20

Nwoi g~j¨ = 20

5 100 =

20100

5 = 400


awi,

Nwoi g~j¨ = x UvKv

‡PB‡bi g~j¨ = (500 - x) UvKv

Nwoi bZzb g~j¨ = x + 10

100 x UvKv

= 11x

10 UvKv



‡PB‡bi bZzb g~j¨ = (500-x) + 5

100 (500-x) UvKv

=

525-21x

20 UvKv

kZ©g‡Z,

11x

10 +

525-21x

20 = 545 - 525

Or, 22x-21x

20 = 20

x = 400 Ans. A

14. GKwU AvqZ‡¶‡Îi ˆ`N©¨ 10% eov‡bv n‡jv Ges cÖ¯’ 10% Kgv‡bv n‡jv| G

Ae¯’vq AvqZ‡¶‡Îi †¶Îdj -

[¯îvóª gš¿Yvj‡qi Aaxb cvm‡cvU© I Bwg‡MÖkb Awa`ß‡ii mnKvix cwiPvjK-2007]

a) 1% evo‡e b) 2% evo‡e

c) 1% Kg‡e d) GKB _vK‡e


20-20+20(-20)

100 = -4% [(-) = n«vm cvIqv]


awi,

ˆ`N©¨ = 100 GKK Ges cÖ¯’ = 100 GKK

‡¶Îdj = 10000 eM© GKK

myZivs ‰`N¨© 10% evov‡bv n‡j, ˆ`N¨© = 110 GKK

Ges cÖ¯’ 10% Kgv‡bv n‡j, cÖ ’ =90 GKK

G †¶‡Î †¶Îdj =110×90 = 9900 eM© GKK

†¶Îdj Kg‡e = (10000 - 9900) = 100 eM© GKK

†¶Îdj n«v‡mi nvi = 100

10000 ×100=1% Ans. C

15. hw` ‡Kvb cixÿvq 200 R‡bi g‡a¨ 70% evsjvq, 60% Bs‡iRx‡Z Ges 40% Dfq

wel‡q cvm K‡i| Dfq wel‡q †dj K‡i KZ Rb?

[mÂq Awa`ß‡ii mnKvix cwiPvjK cixÿv- 2007]

a) 10 Rb b) 15 Rb

c) 25 Rb d) 20 Rb


†d‡ji nvi = 100 - (1g wel‡q cv‡ki nvi + 2q wel‡q cv‡ki nvi-Dfq

wel‡q cv‡ki nvi)

= 100 -(70 + 60 - 40) = 100 - 90 = 10%

Dfq wel‡q †dj K‡i = 10% 200 = 20%


ïay evsjvq cvm K‡i = (70% - 40%) = 30%

ïay Bs‡iRx‡Z cvm K‡i = (60% - 40%) = 20%

myZivs GK wel‡q ev Dfq wel‡q cvk K‡i = 30% + 20% + 40% = 90%

Dfq wel‡q †dj K‡i = 100% - 90% = 10%

Zvn‡j, 100 R‡bi g‡a¨ †dj K‡i = 10 Rb

200 R‡bi g‡a¨ †dj K‡i = 10 200

100 = 20 Rb Ans. D

16. hw` ‡Kvb cixÿvq 20% cixÿv_©x MwY‡Z Ges 30% cixÿv_©x Bs‡iRx‡Z †dj Ki‡jv|

Dfq wel‡q 13% cixÿv_x© †dj Ki‡j kZKiv KZ Rb cixÿv_x© cvm Ki‡jv?

[cÖv_wgK mnKvix wkÿK (Lyjbv) cixÿv- 2006]

a) 50% b) 57%

c) 63% d) 67%


cv‡ki nvi = 100 - (1g wel‡q †d‡ji nvi + 2q wel‡q †d‡ji nvi Dfq wel‡q

†d‡ji nvi) = 100 - (20 + 30 - 13) = 63%




GLv‡b, ïay MwY‡Z †dj Kij = (20 - 13)% = 7%

ïay Bs‡iRx‡Z ‡dj Kij = (30 - 13)% = 17%

Dfq wel‡q †dj Kij = 13%

cvk Kij = {100 - (7 + 17 + 13)} = 63% Ans. C

17. GKwU kvU© I GKwU c¨v‡›Ui g~j¨ 525 UvKv| hw` kv‡U©i g~j¨ 5% Ges c¨v‡›Ui

g~j¨ 10% e„w× cvq, Zvn‡j H¸‡jv wKb‡Z 568.75 UvKv jv‡M| cÖwZwU kvU© I

c¨v‡›Ui g~j¨ KZ ?

[gva¨wgK mnKvix cÖavb wk¶K I †Rjv mnKvix wk¶v Awdmvi wb‡qvM cix¶v-2003]

a) kv‡U©i g~j¨ 150 UvKv I c¨v‡›Ui g~j¨ 375 UvKv

b) kv‡U©i g~j¨ 165 UvKv I c¨v‡›Ui g~j¨ 360 UvKv

c) kv‡U©i g~j¨ 170 UvKv I c¨v‡›Ui g~j¨ 355 UvKv

d) kv‡U©i g~j¨ 175 UvKv I c¨v‡›Ui g~j¨ 350 UvKv

g‡bKwi, me UvKv c¨v›U µq Ki‡Z e¨q nq|

525+ 52510% = 577.50 UvKv|

Difference = 577.50 - 568.75 = 8.75

% Gi Difference = 10% - 5% = 5%

Ab¨ wRwb‡mi `vg = ‡gvU cv_©K¨

% cv_©K¨ 100

kv‡U©i g~j¨ = 8.75

5 100 =

8.75100

5100 = 175

c¨v‡›Ui g~j¨ = (525-175) = 350


g‡bKwi,

kv‡U©i g~j¨ = x UvKv

c¨v‡›Ui g~j¨ = (525 - x) UvKv

GLb, 5% e„w×‡Z kv‡U©i g~j¨ = (100+5) = 105 UvKv

Ges 10% e„w×‡Z c¨v‡›Ui g~j¨ = (100+10) = 110 UvKv

kv‡U©i †¶‡Î, µqg~j¨ 100 UvKv n‡j weµq g~j¨ = 105 UvKv

µqg~j¨ x UvKv n‡j weµq g~j¨ = 105×x

100 UvKv =

21x

20 UvKv

c¨v‡›Ui †¶‡Î, µqg~j¨ 100 UvKv n‡j weµq g~j¨ 110 UvKv

µqg~j¨ (525-x) UvKv n‡j weµq g~j¨ = 110(525-x)

100 UvKv

= 11(525-x)

10 UvKv

kZ©g‡Z, 21x

20 +

11(525-x)

10 = 568.75

21x+11550-22x

20 = 568.75

x =175

c¨v‡›Uig~j¨ = (525-175) UvKv = 350 UvKv Ans. D

18. GKwU ¯‹zj cixÿvq 70% MwY‡Z Ges 80% cixÿv_x© evsjvq cvk K‡i| wKš‘

10% Dfq wel‡q †dj K‡i| hw` 360 Rb cixÿv_x© Dfq wel‡q cvm K‡i, Zvn‡j

KZ Rb cixÿv_x© cixÿvq AskMÖnb K‡iwQj? [32Zg wewmGm]


ïay MwY‡Z †dj K‡i‡Q = (100 - 70 - 10)% = 20%

Ges ïay evsjv‡Z †dj K‡i‡Q = (100 - 80 - 10) = 10%

myZivs ‡gvU †dj K‡i = (20 + 10 + 10) % = 40 %

Dfq wel‡q cvm K‡i = (100 - 40) = 60%

GLb, 60 Rb cvm K‡i 100 R‡bi g‡a¨

360 Rb cvm K‡i 100 360

60 Rb

= 600 Rb



19. GKwU cixÿvq 90% cixÿv_©x Bs‡iRx‡Z Ges 85 % cixÿv_© MwY‡Z K…ZKvh© nq|

Dfq wel‡q †KD hw` †dj bv K‡i Ges Dfq wel‡q 225 Rb QvÎ K…ZKvh© n‡q

_vK‡j H cixÿvq AskMÖnYKvix Qv‡Îi msL¨v KZ? [28Zg wewmGm]


Bs‡iRx‡Z †dj K‡i‡Q = (100 - 90)% = 10%

Ges MwY‡Z †dj K‡i‡Q = (100 - 85) = 15%%

myZivs Bs‡iRx Ges MwY‡Z †dj K‡i = (10 + 15) = 25%

‡gvU cvm K‡i = (100 - 25) = 75%

kZ©vbyhvqx,

75 Rb cvk K‡i 100 R‡bi g‡a¨

225 Rb cvk K‡i 100 225

75 Rb

= 300 Rb

20. hw` 15wU †cvkv‡Ki g‡a¨ kZKiv 40 fvM †cvkvK kvU© nq Z‡e 15wU †cvkv‡Ki g‡a¨

KZwU kvU© bq ? [25Zg wewmGm]

a) 6 b) 9

c) 12 d) 10


100wU †cvkv‡Ki g‡a¨ kvU© = 40wU

15wU †cvkv‡Ki g‡a¨ kvU© = 40×15

100 wU = 6wU

kvU© bq (15-6) = 9wU Ans. B

21. Pv‡ji `vg 12 1

2 % K‡g hvIqvq 14,000 UvKvq c~‡e©i `v‡g †h cwigvY †Kbv

†hZ, eZ©gvb `v‡g Zvi †P‡q GK KzB›Uvj Pvj †ewk †Kbv hvq| cÖwZ †KwR Pv‡ji

`vg Av‡M KZ wQj| [25 Zg wewmGm]


Pv‡ji c~e©g~‡j¨ 100 UvKv n‡j eZ©gvb g~j¨ = (100 - 25

2 ) UvKv

= 175

2 UvKv

Pv‡ji c~e©g~‡j¨ 14000 UvKv n‡j eZ©gvb g~j¨ = 175 14000

2 100 UvKv

= 12250 UvKv

eZ©gv‡b 1 KzB›Uvj ev 100 †KwR Pv‡ji g~‡j¨ (14000 - 12250) UvKv

= 1750 UvKv

1 †KwR Pv‡ji g~j¨ 1750

100 = 17.5 UvKv

cybivq,

eZ©gvb 175

2 g~j¨ UvKv n‡j c~e©g~j¨ = 100 UvKv

eZ©gvb 17.5 g~j¨ UvKv n‡j c~e©g~j¨ = 100 2 17.5

175 = 20 UvKv

AZGe cÖwZ †KwR Pv‡j `vg Av‡M wQj 20 UvKv|

22. GKwU †kÖYx‡Z 100 Rb QvÎ wQj| evwl©K cixÿvq 94 Rb QvÎ MwY‡Z cvm K‡i,

80 Rb QvÎ Bs‡iRx‡Z cvk K‡i‡Q I 75 Rb QvÎ Dfq wel‡q cvm K‡i‡Q| KZ

Rb QvÎ Dfq wel‡q †dj K‡i‡Q? [25Zg wewmGm]


‡Ìqv Av‡Q,

‡gvU QvÎ 100 Rb

Ges Dfq wel‡q cvm K‡i 75 Rb|

ïay MwY‡Z cvm K‡i = (94 - 75) = 19 Rb

Ges ïay Bs‡iRx‡Z cvm K‡i = (80 - 75) = 5 Rb

Dfq wel‡q cvm K‡i = (75 + 19 + 5) = 99 Rb

Dfq wel‡q ‡dj K‡i = (100 - 99) = 1 Rb



23. hw` ‡Kvb ¯‹z‡j 70% wkÿv_x© Bs‡iRx‡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 Z‡e H ¯‹z‡j KZRb wkÿv_©x cixÿv w`‡q‡Q? [23 Zg wewmGm,]

a) 400 Rb b) 500 Rb

c) 560 Rb d) 760 Rb




= 300

30 + 20 + 10 100 = 500 Rb


ïay Bs‡iRx‡Z †dj K‡i (100 - 70 - 10)% - 10% = 20%

Ges ïay evsjvq †dj K‡i (100 - 80 - 10)% - 10% = 10%

`yB wel‡q †gvU †dj K‡i = (20 + 10 + 10)% = 40%

`yB wel‡q †gvU cvm K‡i = (100 - 40)% = 60%

GLb, 60 Rb cvm K‡i 100 R‡bi g‡a¨

300 Rb cvm K‡i 100 300

60 R‡bi g‡a¨ = 500 Rb

myZivs DËi n‡e 500 Rb| Ans. B

24. GKwU cixÿvq 1200 evjK cixÿv_©x wQj| hw` 50% evjK I 40% evwjKv

cixÿvq cvm K‡i, evwjKv cixÿv_©xi msL¨v wbY©q Kiæb| †hLv‡b †gvU 46%

cixÿv_©x cvm K‡i‡Q| [22Zg wewmGm]


‡Ìqv Av‡Q,

50% evjK K…ZKvh© n‡q‡Q|

100 Rb evj‡K cvk K‡i 50 Rb

1200 Rb evjK cvk K‡i 50 1200

100 = 600 Rb

awi, evwjKv cixÿv_©xi msL¨v = K Rb

40% evwjKv K…ZKvh© n‡j,

100 Rb evwjKvq cvk K‡i 40 Rb

K Rb evwjKvq cvk K‡i 40 K

100 =

2K

5 Rb

‡gvU cixÿv_©xi msL¨v = (1200 + K) Rb

100 R‡bi g‡a¨ K…ZKvh© nq = 46 Rb

(1200 + K) R‡bi g‡a¨ K…ZKvh© nq,

= 46(1200 + K)

100 =

27600 + 23 K

50 Rb

kZ©g‡Z,

600 + 2K

5 =

27600 + 23 K

50

3000 + 2 K

5 =

27600 + 23 K

50

30000 + 20 K = 27600 + 23 K

- 3 K = - 2400

K = 800 Rb

myZivs evwjKv cwiÿv_x© = 800 Rb|

25. ‡Kvb cixÿvq evsjvq 60% Ges MwY‡Z 50% cixÿv_x© K…ZKvh© n‡q‡Q| hw` Dfq

welq‡q 40% K…ZKvh© n‡q _v‡K Ges Dfq wel‡q †gvU 60 Rb †dj K‡i _v‡K

Z‡e †gvU cixÿv_©xi msL¨v KZ? [21Zg wewmGm]


ïay evsjvq cvm K‡i‡Q = (60 - 40)% = 20%

Ges ïay Mwj‡Z cvm K‡i‡Q = (50 - 40) = 10%

‡gvU cvm K‡i K‡i = (20 + 10 + 40) % = 70 %

Dfq wel‡q ‡dj K‡i = (100 - 70) = 30%

30 Rb ‡dj K‡i 100 R‡bi g‡a¨



60 Rb cvk K‡i 100 60

30 = 200 Rb

26. ‡Kvb GK dj eëmvqxi 6% dj c‡P hvq Ges AviI 4% dj cwien‡bi mgq bó

nq| evwK dj kZKiv KZ jv‡f weµq Ki‡j †gv‡Ui Dci Zvi 20% jvf n‡e?

[17 Zg wewmGm]


‡gvU dj bó nq (6 + 4) % = 10%

evKx _v‡K (100 - 10) % = 90 %

20% jv‡f weµq g~j¨ (100 + 20) = 120 UvKv

cÖkœg‡Z, (120 - 90) = 30 UvKv

90 UvKvq jvf Ki‡Z n‡e = 30 UvKv

100 UvKvq jvf Ki‡Z n‡e = 30 100

90 = 33

1

3 UvKv ev 33

1

3 %

27. hw` K Gi †eZb L Gi †eZb A‡cÿv kZKiv 35 UvKv †ewk n‡j L Gi †eZb K

A‡cÿv kZKiv KZ UvKv Kg? [11Zg wewmGm]

a) 25.5 UvKv b) 25.93 UvKv



kZKiv Kg / †ewk = 100 kZKiv Kg/‡ewk

100 +kZKiv Kg /‡ewk

= 100 35

100 + 35

= 25.93% Ans. B

Question for BBA / MBA/ EMBA / MBM:

01. What percent of 15 is 15 percent of 1 [Executive MBA (IBA)]

a) 1% b) 10%

c) 2.5% d).25% O) none of these


15 percent of 1

= 15

100 1

= 0.15

.15

15 100

= 1% Ans. A

02. The number of automobile sold by a company decreased by

15% as the price was increased by 15%. What was the net

effect on revenue of company? [Executive MBA (IBA)]


Let,

former price car = 100

formaer units sold = 100

Price units revenue

former 100 100 10000

Now 115 (+15%) 85 (- 15%) 9775

Change = -225

dddd Percentage =

change

original 100

= - 225

1000 100

= - 2.25%

Ans. 2.25% Decreased

03. If x = 4y, what percent of 2x is 2y? [Executive MBA (IBA)]


x = 4y



Let,

y = 10 when x = 40

2x = 80 and 2y = 20

2y

2x 100 =

20

80 100 = 25%

Ans. 25%

04. In a class, 34% of the students are female. Given that therea

are 16 more male than femal. How many female students are

there in the class? [IBA (MBA)-2012]

a) 17 b) 32

c) 34 d) 42 e) none of these


34% femal n‡j A_©vr 66% n‡”Q males

Difference = (66 – 34)% = 32% or ejv hvq 32% †ekx maleAv‡Q|

So, 32% equivalent to 16 students

There 1% equivalent to 1

2 students,

and 34% equvalent to 17 students. Ans. A

05. The prcie of a stock increased by 10% in june. It declined by

20% in July. The price went up by 20% in August. What is the

percentage change in stock price from the beginning of June

to the end of August? [IBA (MBA)-2012]

a) 5.6 b) 6.4

c) 7.2 d) 42 e) none of these


Applying the formula of successive change, a + b + ab

100

Change occured in June & July,

= +10 – 20 + -10.20

100 = -12%

Now combined change in June, July and August,

= - 12 + 20 - - 12. 20

100

= 5.6 Ans. A

06. Sanwar spent 20% of his salary for food, 30% apatemtn rent

and 25% for other expenses. If the remaining Tk. 3500 were

his monthly savings, how much (Taka) was his apartment

rent? [MBA(IBA)-2012 June]

a) 2400 b) 3600



Food + rent + other expense = 20% + 30% + 25% = 75%

Saving = (100 – 75)% = 25%

So, 25% = Tk. 3500

1% = Tk. 140

And rent 30% = 140 30 = Tk. 4200 Ans. C

07. A vendor sells 60 pecent of mangoes he has and disributes 15

percent of the remainder to the poor. Next day he sells 50

percent of the remainder and distributes the rest to the poor.

What percent of his mangoes did the vendor distribute to the

poor in two days? [MBA(IBA)-2012 June]

a) 15% b) 23%

c) 27% d) 34% e) none of these


awi, †gvU Av‡gi msL¨v = 100

cÖ_g w`‡b wewµ K‡i 60% = 60

Mix‡ei gv‡S †`q = 40 15% = 6



evKx _vKj = 100 - 60 - 6 = 34

wØZxq w`‡b wewµ K‡i 50% 34 = 17

Ges Mix‡ei †`q evKx 17 wU

ZvB Mixeiv †gvU cvq = 6 + 17 = 23 wU Ans. B

08. An NGO hired some volnteers. If 55% of the volunteers hired

were male, and the remaining 180 were female, how many

volunteers were hired? [MBA(IBA)-2012 June]


55 % were male. So the remaining

45% volunteers were female.

45% = 180

100% = 400

Ans. 400

09. If 75% of x is equal to 505 fo y. Then (x + y) = ?

[MBA(IBA)-2011-12 December]

a) 1.25 y b) 1.80 y

c) 2.25x d) 2.50x e) none of these


1

2 y =

3

4 x y =

3

2 x

x + y = x + 3

2 x = 2.5 x Ans. D

10. If x is 30% greater than y, what percent of y is x?

[MBA(IBA)-2008-09 ]

a) 70 b) 77



x = y + y 30% = y + 30y

100 = y

130

100 =

13y

10

x

y 100% =

13

10 100% = 130%

x = 130% of y Ans. D

11. In a class of 400 students, 72 received A’S. If 15% of the male

students and 20% of the female students received “A” Then

the number of male students in the class-- [MBA(IBA)-2008-09]

a) 160 b) 175



Suppose, male students = x

female students = (400 – x)

According to question,

15% of x + 20% of (40 – x) = 72

15x

100 +

20(400 -x)

100 = 72

15 x – 20 x + 8000 = 7200

5x = 800

x = 160 Ans. A

Practic Work:

01. MZKvj †kqv‡ii `vg 25% †e‡owQj, wKš‘ AvR 25% K‡g‡Q| †kqv‡ii `vg †gvU

KZ †e‡o‡Q ev K‡g‡Q? [mgvRKj¨vY gš¿Yvj‡qi mgvR‡mev Awa`ß‡ii mgvR‡mev Awdmvi-2010, kªg

Awa`ß‡ii Rbkw³, Kg©ms¯’vb I cÖwk¶Y ey¨‡iv DcmnKvix cwiPvjK 2001]

a) 4

1

6 % †e‡o‡Q b) 4

1

6 % K‡g‡Q

c) 2

1

4 % K‡g‡Q d) 2

1

4% †e‡o‡Q




25 + (-25) +

100

2525

= - 6.25% Ans. B

02. 1

5 of 30% of 0.60? [Bangladesh Bank Cash Officer-2011]

a) 0.12 b) 0.18

c) 3.6 d) 0.036


1

5 of 30% of 0.60 =

1

5 ×

30

100 ×0.6

= 0.036 Ans. D

03. 75% of 0.08 = ? [Bangladesh Bank 2010]

a) 0.04 b) 0.50

c) 0.06 d) 0.060 e) 6.0


75 1

100 0.08 %

1

100

= 75 1

100

8

100 of

= 0.06


.75 .08 = 0.0600. Ans. C

04.

If 18 is 15 percent of 30 percent of a certain number, what is the

number? [Bangladesh Bank AD 2009]

a) 9 b) 26

c) 40 d) 81 e) 400

Abyev`t †Kvb msL¨vi 30% Gi 15% nq 18?


g‡bKwi,

msL¨vwU x

x Gi 30% 15% = 18

or, 30x

100

15

100 = 18

or, x = 400| Ans. E

05. 6

15 -‡K kZKivq cÖKvk Ki‡j KZ nq?

[Lv`¨ Awa`ß‡ii mnKvix Dc-Lv`¨ cwi`k©K / mnKvix Acv‡iUi / muvUgy ªv¶wiK / muvUwjwcKvi-2009]

a) 36% b) 30%

c) 40% d) ‡KvbwUB bq


6

15 =

6×100

1500

= 600

1500

= 40

100 =40% Ans. C

06. MZKvj GKwU wRwb‡mi `vg 10% †e‡owQj, AvR 10% K‡g‡Q| wRwbmwUi `vg

†gvU KZ †e‡o‡Q ev K‡g‡Q? [cÖv_wgK cÖavb wk¶K-2009 (kvcjv)]

a) 1% K‡g‡Q b) 1% †e‡o‡Q

c) 1.5% K‡g‡Q d) 1.5% †e‡o‡Q


10 + (-10) + 10(-10)

100 = -1% Ans. A

07. GKwU †kqv‡ii `vg MZKvj‡K 20% K‡g‡Q Ges AvR‡K Zv †e‡o‡Q 30%|

‡gvU e„w× ev n«v‡mi nvi KZ? [evsjv‡`k cjøx Dbœqb †evW© (BRDB)-Gi Dc‡Rjv cjøx Dbœqb Kg©KZ©v-



2009]

a) 10% e„w× b) 4% e„w×

c) 6% e„w× d) 4% n«vm


%C = - 20 + 30 + -20 (30)

100 = 4% Ans. B

08. What number divided by 250 gives 15%? [Bangladesh Bank AD

2008]

a) 25 b) 15

c) 37.5 d) 60 e) 80

Abyev`t †Kvb msL¨v‡K 250 w`‡q fvM Ki‡j fvMdj 15% nq?


g‡bKwi,

msL¨vwU x hv‡K 250 w`‡q fvM Ki‡j fvMdj 15% nq|

x

250 = 15%

or, x

250 =

15

100

or, x = 15 250

100

x = 37.5. Ans. C

09. Number 29 is 10 percent of what number? [Bangladesh Bank AD

2008]

a) 87 b) 270

c) 269 d) 249 e) 290

Abyev`t †Kvb msL¨vi 10% nq 29?


g‡bKwi,

msL¨vwU = x

kZ©g‡Z,

x Gi 10% = 29

x 10

100 = 29

x = 290. Ans. E

10. 66

2

3 % = KZ? [†hvMv‡hvM gš¿Yvj‡qi Aaxb evsjv‡`k †ijI‡q mnKvix Kgv‡Û›U-2007]

a)

1

3 b)

1

8

c)

8

5 d)

2

3


662

3 % =

200

3 % =

200

3 ×

1

100 =

2

3 Ans. D

11. 125% Gi mgvb fMœvsk †KvbwU? [miKvwi gva¨wgK we`¨vjq mnKvix wk¶K-2006]

a)

3

2 b)

5

4

c)

6

5 d)

3

4


125% = 125 × 1

100

= 5

4 Ans. B

12.

If 18 is 15 percent of 30 percent of a certain number, what is the

number? [Bangladesh Bank AD 2006]

a) 9 b) 36

c) 40 d) 81 e) 400

Abyev`t hw` †Kvb msL¨vi 30% Gi 15% gvb nq 18? Zvn‡j msL¨vwU KZ?




g‡bKwi,

msL¨vwU x

x Gi 30% = 30x

100

cybivq, 30x

100

15

100 = 18

or, 9x = 18 200

or, x = 18 200

9

x = 400 Ans. E

13. If 2% of X is 0.03 then X equals to [Bangladesh Bank AD 2004]

a) 150 b) 66.67

c) 15 d) 6.67 e) 1.5

Abyev`t hw` x Gi 2% nq .03 Z‡e x Gi gvb KZ?


x Gi 2% = .03

= 2x

100 = .03

or, 2x = 3

x = 3

2 = 1.5 Ans. E

14. 0.03 times 0.05 is: [Bangladesh Bank AD

2001]

a) 1.5% b) 0.15%

c) 0.015% d) 0.0015

Abyev`t .03 Gi 0.05 ¸Y KZ?


.03 .05 = .0015 ans. D

15. What is 1 percent of 0.025? [Bangladesh Bank AD

2001]

a) 0.25 b) 0.025

c) 0.0025 d) 0.00025

Abyev`t .025 Gi 1% KZ?


100 Gi g‡a¨ Av‡Q = 1

.025 Gi g‡a¨ Av‡Q = .025

100 = .00025 Ans. D

16. wPwbi g~j¨ 20% Kg‡jv, wKš‘ wPwbi eënvi 20% e„w× †c‡jv| G‡Z wPwb eve` e¨q

kZKiv KZ evo‡jv ev Kg‡jv?

[evsjv‡`k miKvix Kg© Kwgkb KZ©„K wba©vwiZ 12 wU c‡` wb‡qvM cix¶v 2001]

a) 1% evo‡jv b) 2% Kg‡jv

c) 3% evo‡jv d) 4% Kg‡jv


20 + 20 +

100

2020 = - 4% Ans. D

17.

10% of 3000 is how much more than 5% of 3000?

[Bangladesh Bank AD 2001]

a) 100 b) 150

c) 175 d) None of these

Abyev`t 3000 Gi 10%, 3000 Gi 5% A‡c¶v KZ †ewk?


GLv‡b, 3000 10% = 3000 10

100 = 300

Ges 3000 5% = 3000 5

100 = 150

†ewk = 300 - 150 = 150 Ans. B

18. In a group of 60 probationary officers, 40% of them were



promoted, 12 of them were terminated and rest to them were

placed on probation for the second time. What percent of the

probationary officers were placed on probation for the second

time? [Bangladesh Bank AD 2001]

a) 60 b) 50

c) 40 d) 30


GLv‡b, cÖ‡gvkb †c‡q‡Q = 60 40

100 = 24 Rb

Ges PvKzix P‡j †M‡Q = 12 Rb|

wØZxqev‡ii gZ cÖ‡gvkb n‡q‡Q = 60 - (24 + 12) = 24 R‡bi

wØZxqev‡ii gZ cÖ‡gvkb n‡q‡Q = 24 100

60 = 40 Rb ev 40%| Ans. C

19. 133

4 % Gi mgvb - [30Zg wewmGm]

a) 11

80 b)

11

20

c) 1

9 d)

1

8


% = 1

100

133

4 % =

55

4

1

100 (KviY, 13

3

4 =

55

4 )

= 11

80 Ans. A

20. GK eëmvqx GKwU c‡Yï g~j¨ 25% evov‡jv, AZtci ewa©Z g~j¨ †_‡K 25%

Kgv‡jv| me©‡kl g~j¨ me©cÖ_g g~‡jvi Zzjbvq [27 Zg wewmGm]

a) 45% Kgv‡bv n‡q‡Q b) 6.25% Kgv‡bv n‡q‡Q

c) 5% evov‡bv n‡q‡Q d) 6.25% evov‡bv n‡q‡Q

Shortcut Solution for MCQ:- 25 + (-25) + 25 (-25)

100 = - 6.25% Ans. B

21. 1

2 Gi kZKiv KZ

3

4 n‡e? [23Zg wewmGm]

a) 120% b) 125%

c) 140% d) 150%

Shortcut Solution for MCQ:- 1

2 ×

P

100 =

3

4 P = 150% Ans. D

22. 121

2 % -Gi mgvb fMœvsk KZ n‡e? [eb I cwi‡ek gš¿Yvj‡q mnKvix cwiPvjK 1995]

a) 1

16 b)

1

8

c) 1

4 d)

1

25


121

2 % =

1

8

25% =1

4

121

2 =

1

8 Ans. B

23. 100 UvKvi

2

1

% mgvb KZ? [AvenvIqv Awa`ß‡ii Aax‡b mnKvix AvenvIqvwe` 1995]

a) 50 UvKv b) 0.50 UvKv

c) 0.05 UvKv d) 5 UvKv


100 × 2

1 × 100

1

= 0.50 Ans. B



24. If the price of a Warid SIM was Tk. 100 in 2007 and the price

increased at 10% per year for two years, then what is the price

of the Warid SIM in 2009?

a) 121 b) 125



Net % Change = 10 + 10 + 10 10

100 = 21

Final Price = 100+ 21 = 121 Ans. A

25. Successive Increase of 10% and 30% is equivalent to single

Increase of.

a) 43 b) 30



Single increase % =10 + 30 + 10 30

100 = 43 Ans. A

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