Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 1
Shahjalal Islami Bank Ltd.
Management Trainee Officer 2016 [Exam Taker: BIBM]
1. Babu, Arif & Salam started a business investing Tk. 28000 where Arif invested Tk. 4500 more
what Babu invested and Babu invested Tk. 7000 less than what Salam invested. Their business
earned Tk. 5600. What is Babu's share in that profit? Abyev`t
evey, Avwid I mvjvg †gvU 28000 UvKv wb‡q GKwU e¨emv ïiæ K‡i| evey hZ UvKv †`q Avwid Zvi †P‡q 4500 UvKv †ewk †`q
Ges mvjvg hZ UvKv †`q evey Zvi †P‡q 7000 UvKv Kg †`q| hw` Zv‡`i †Kv¤úvwbi 5600 UvKv jvf nq Zvn‡j evey KZ UvKv
jf¨vsk cv‡e?
Solution:
Let, the amount of Babu = Tk. x
Then, the amount of Arif = Tk. (x+4500)
And the amount of Salam = Tk. (x+7000)
According to the question,
x + x +4500 + x + 7000 = 28000
Or, 3x + 11500 = 28000
Or, 3x = 16500
x = 5500
So, the amount of Babu = Tk. 5500
The amount of Arif = Tk. (5500 + 7000) = Tk.12500
And the amount of Salam = Tk. (5500 + 4500) = Tk.10000
We get,
Babu: Arif: Salam = 5500 : 12500 : 10000
= 11:25:20
Babu’s profit =Tk. (
×5600) = Tk. 1100 (Ans.)
2. Rahim can do a piece of work in 80 days. After working 10 days he left and rest of the work is
done by Karim in 42 days. If they worked together how many days they need to complete the
work? Abyev`t
iwng GKwU KvR 80 w`‡b Ki‡Z cv‡i| †m 10 w`b KvR Kivi ci Kwig GKvB evwK KvR 42 w`‡b †kl K‡i| Zviv `yÕR‡b
GKmv‡_ KvR Ki‡j m¤ú~b© KvRwU Ki‡Z Zv‡`i KZw`b mgq jvM‡e?
Solution:
Let, the whole work be 1 portion
In 80 days, Rahim can do 1 portion
In 1 day,…………
portion
In 10 days………
portion
=
portion
Rest of the work = (1–
)=
portion
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 2
Now,
In 42 days, Karim can do
portion
In 1 day, Karim can do
portion
=
portion
In 1 day, Rahim and Karim together can do = (
+
) portion
=
portion
=
portion
So, they can do
part works in 1 day
They can do 1 part works in 30 days. (Ans.)
3. Length of a rectangular field is 1.5 times as large as its width. The field cost Tk. 10260 for
planting grass at Tk. 1.9 per sq. meter. What will be the total cost of providing fence around the
field that costs Tk. 2.5 per meter? Abyev`t
GKwU AvqZKvi gv‡Vi •`N¨© Gi cÖ‡¯’i †`o ¸Y| cÖwZ eM©wgUv‡i 1.9 UvKv wnmv‡e m¤ú~Y© gvVwU‡Z Nvm jvMv‡Z 10,260 UvKv
cÖ‡qvRb| cÖwZ wgUvi 2.5 UvKv wnmv‡e gvVwUi Pvicv‡k †eov w`‡Z KZ UvKv LiP n‡e?
Solution:
Let, the width of the rectangular field be x meters and length = 1.5x meters.
Total area = 1.5x×x = 1.5x2
Total cost = 1.9×1.5x2
According to the question,
1.9×1.5x2 = 10260
Or, 2.85x2 = 10260
Or, x2 = 3600
x = 60
Width = 60m and length = 1.5×60 = 90m
Perimeter = 2(90 + 60) = 300m
Cost = Tk. (300×2.5) = Tk. 750 (Ans.)
4.
+
=
Solution:
+
=
Or,
+
=
Or,
+
=
+
Or,
-
=
-
Or, ( ) ( )
( )( ) = ( ) ( )
( )( )
Or,
( ) =
( ) [Multiplying both sides by (3x-5)]
Or,
( ) =
( )
Or,
( ) =
( ) [Dividing both sides by 5]
Or, 4(2x-5) = 5(x+5)
Or, 8x – 20 = 5x + 25
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 3
Or, 8x – 5x = 25+20
Or, 3x = 45
x = 15.
Trainee Senior Officer 2016 [Exam Taker: BIBM]
1. A man’s running speed is 3 times of his walking speed. The man runs a distance and comes
back walking. Total time taken by him 2 hours. What is the distance in miles if he runs 9 miles
per hour?
Solution: Running speed = 9 miles per hour.
So, walking speed = 9/3 = 3 miles per hour.
Let, the distance be x km.
According to the question,
+
= 2 [Time =
]
Or,
= 2
Or, 4x = 18
x = 4.5
The distance = 4.5 miles. (Ans.)
2. A borrower pays 8.5% interest per year on the first Tk. 600 he borrows and 7.25% per year
on the part of the loan in excess of Tk. 600. How much interest will the borrower pay on a loan
of Tk. 6500 for one year? Abyev`t
†Kvb FYMÖnxZv F‡Yi 1g 600 UvKvi Rb¨ 8.5% Ges 600 UvKvi AwZwi³ UvKvi 7.25% my` †`q| Zvi F‡Yi cwigvb 6,500
UvKv n‡j wZwb eQ‡i KZ UvKv my` w`‡eb?
Solution: Out of Tk. 6500, the first 600 is charged with 8.5% interest and the rest amount Tk. (6500 – 600) =
Tk.5900 is charged with 7.25% interest.
So, 8.5% interest for first Tk. 600 = 8.5% of 600 = Tk. 51
7.25% interest for rest Tk.5900 is = 7.25% of 5900 = Tk. 427.75
So, total interest for 6500 Tk. for 1 year =Tk. (51 + 427.75)
=Tk. 478.75 (Ans.)
3. The length of a rectangular field is 30 feet long than its width and the perimeter is 380 feet.
How much would it cost to cover the field with grass at the rate of Tk. 20 per square? Abyev`t
GKwU AvqZKvi gv‡Vi •`N¨© Gi cÖ‡ ’i †P‡q 30 dzU j¤^v Ges AvqZ‡¶ÎwUi cwimxgv 380 dzU| cÖwZ eM©wgUv‡i 20 UvKv LiP n‡j
m¤ú~Y© gv‡V Nvm jvMv‡Z KZ UvKv LiP n‡e?
Solution:
Let, width be x feet and length be (x+30) feet.
We know,
Perimeter =2(width+ length)
=2(x+x+30)
= 2(2x+30)
= 4x+ 60
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 4
According to the question,
4x+ 60 = 380
Or, 4x = 380-60
Or, 4x = 320
x = 80
Width = 80 feet and length = (80+ 30) feet = 110 feet
Area of the field = (length× width)
= (110×80) sq. feet
= 8800 sq. feet (Ans.)
Total cost to cover the field with grass at rate of Tk. 20 per square feet
= Tk. (8800×20)
= Tk. 176,000 (Ans.)
4. If √x+
√ = a, then x
2+
=?
Solution:
Given that,
√x+
√ = a
Or, (√x+
√ )2 = a
2 [Squaring both sides]
Or, x +
+ 2. √x.
√ = a
2
Or, x +
+ 2 = a
2
Or, x +
= a
2-2
Or, (x +
)2 = (a
2-2)
2
Or, x2 +
+ 2.x.
= a
4 – 4.a
2+ 4
Or, x2 +
+ 2 = a
4 – 4.a
2+ 4
Or, x2 +
= a
4 – 4.a
2+ 4 -2
x2 +
= a
4 – 4.a
2+ 2 (Ans.)
Trainee Officer (Cash) 2013 [Exam Taker: BIBM]
1. Age of three persons is now in the proportion 2: 3: 4 and in 5 years from now, the proportion
will be 5: 7: 9. What is the present age of the youngest person?
Solution:
Let, the age of the persons be 2x, 3x and 4x respectively.
After 5 years, ratio of 1st two persons
(2x+5) : (3x+5) = 5: 7
Or, 5(3x+5) = 7(2x+5)
Or, 15x + 25 = 14x + 35
Or, 15x – 14x = 35- 25
x = 10
The present age of the youngest person = 2×10 = 20 years. (Ans.)
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 5
2. Mr. X can finish a work in 6 days and Mr. Y can finish the same work in 8 days. How many
days will it take to finish the work it they work together? Abyev`t
X GKwU KvR 6 w`‡b Ges Y GKB KvR 8 w`‡b Ki‡Z cv‡i| Zviv GK‡Î H KvR KZ w`‡b †kl Ki‡Z cvi‡e?
Solution:
In 6 days X can do 1 part of the work
” 1 ” X ” ” 1/6 ” ” ”
In 8 days Y can do 1 part of the work
” 1 ” Y ” ” 1/8 ” ” ”
In 1 day (X+Y) can do = (
+
) part of the work
= (
) ” ” ”
=
” ” ”
part of the work can do in 1 day
1 ” ” ” ” ” ”
days
Ans:
days.
3. A shirt was sold for Tk. 171 and the gain was as much percent as it costs in Taka amount.
What was the purchase price of the shirt?
Solution: Let, the purchase price be Tk. x and profit be x%.
According to the question,
x + x% of x = 171
Or, x +
= 171
Or, 100x + x2 = 17100
Or, x2 + 100x – 17100 = 0
Or, x2 + 190x -90x – 17100 = 0
Or, x(x+190) -90(x+190) = 0
Or, (x+190) (x-90) = 0
x = 90
The purchase price = Tk. 90. (Ans.)
4. If
= 2, then the value of
.
Solution: Given that,
= 2
Or,
= 2
Or, x2 +1 = 2x
Or, x2 – 2x +1 = 0
Or, (x-1)2 = 0
Or, x-1 = 0
x = 1
=
= 1 (Ans.)
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 6
Management Trainee Officer 2013 [Exam Taker: BIBM]
1. The percentage profit earned by selling an article for Tk. 1920 is equal to the percentage loss
incurred by selling the same article for Tk 1280. At what price should the article be sold to make
25% profit? (South East Bank MTO 13, BB AD(ff) 15, Shahjalal Islami Bank MTO 13) Abyev`t
GKwU cY¨ 1,920 UvKvq weµq Ki‡j kZKiv hZ jvf nq, cY¨wU 1,280 UvKvq weµq Ki‡j kZKiv ZZ UvKv ¶wZ nq| 25%
jvf Ki‡Z n‡j cY¨wU‡K KZ `v‡g weµq Ki‡Z n‡e?
Solution: Let, cost price be Tk. x
According to the question,
SP1-CP = CP-SP2
1920-x = x-1280
Or, 1920+1280 = x+ x
Or, 2x = 3200
Or, x = 3200/2
x = 1600
Cost price is Tk. 1600
At 25% profit,
New selling price = Tk. (1600+25% of 1600) = Tk. 2000
Ans: Tk. 2000.
Alternative Method:
Let, profit and loss both be Tk. x
According to the question,
SP1-Profit = SP2+ Loss
1920-x = 1280+x
Or, 2x = 640
x = 320
Cost price = Selling price – profit
= Tk. (1920-320)
= Tk. 1600
At 25% profit,
New selling price = Tk. (1600+25% of 1600) = Tk. 2000
Ans: Tk. 2000
Alternative Method:
Let, amount of cost price be Tk. x
Profit percentage =
×100% =
×100%
Loss percentage =
×100% =
×100%
According to the question,
×100% =
×100%
Or, 1920-x = x-1280
Or, 2x = 3200
Or, x = 3200/2
x = 1600
At 25% profit,
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 7
New selling price = Tk. (1600+25% of 1600) = Tk. 2000
Ans: Tk. 2000
Alternative Method:
Let, profit and loss both be x %.
( ) =
( )
Or, 128,000+1280x = 192,000-1920x
Or, 1280x+1920x = 192,000-128,000
Or, 3200x = 64,000
x = 20
Cost price = Tk.
= Tk. 1600
At 25% profit,
Selling Price = Tk. (1600+25% of 1600) = Tk. 2000
Ans: Tk. 2000
2. The ratio between the perimeter and the breadth of rectangle is 5:1. If the area of the
rectangle is 216 sq. cm, what is the length of the rectangle?(Shahjalal Bank MTO 13,South East
Bank MTO 13) Abyev`t
GKwU AvqZKvi †¶‡Îi cwimxgv Ges cÖ‡¯’i AbycvZ 5 t 1| AvqZ‡¶ÎwUi †¶Îdj 216 eM© †m.wg n‡j, Gi •`N©¨ KZ?
Solution: Given that, perimeter: breadth = 5:1.
Let, the perimeter be 5x and breadth be x.
Here,
2(length +breadth) = 5x
Or, 2(length +x) = 5x
Or, 2×length+2x = 5x
Or, 2×length = 5x-2x = 3x
Length = 1.5x.
According to the question,
(1.5x)×(x) = 216 [Area = Length ×Breadth]
Or, x2 = 216/1.5 = 144
x = 12
Length = 1.5×12 = 18 cm.
Ans: 18 cm
Alternative Method:
Let, the length be x and breadth be y
So, area of the rectangle, xy = 216 …………. (1)
Now, the perimeter = 2(x + y)
According to question,
2(x+ y): y = 5:1
Or, 2x + 2y = 5y [Cross multiplication]
Or, 2x = 3y
x = 1.5y
From equation (1)=>
y×1.5y = 216
Or, y2 = 144
y = 12
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 8
x = 1.5×12 = 18
Length = 18 cm.
Ans: 18 cm
Alternative Method:
Let, Length = L and Breadth = B
According to the question,
2(L+B) : B = 5:1
Or, ( )
= 5
Or, 2(L+B) = 5B [Cross multiplication]
Or, 2L+2B = 5B
Or, 5B-2B = 2L
Or, 3B = 2L
B =
L
Again,
Length × Breadth = Area
Or, L×B = 216
Or, L×
L = 216 [ B =
L]
Or, L2 = 216 ×
Or, L2 = 324
L = 18
Length = 18 cm. (Ans.)
3. A, B and C enter into a partnership in the ratio 7/2:4/3:6/5. After 4 months, A increases his
share by 50%. If the total profit at the end of one year is Tk. 21,600, then what is B's share in the
profit? (Shahjalal Islami Bank MTO 13, South East Bank MTO 13) Abyev`t
A, B I C
t
t
Abycv‡Z GKwU Askx`vix Kvievi ïiæ K‡i| 4 gvm ci A Zvi †kqvi 50% e„w× K‡i| hw` 1 eQi c‡i
†gvU jv‡fi cwigvb 21,00 UvKv nq Zvn‡j B Gi jf¨vsk KZ n‡e?
Solution:
Given ratio,
A:B:C = (
:
:
)
= 105: 40: 36 [LCM of 2,3 and 5 = 30; so, multiplying by 30]
Let, the initial investments of A = 105x, B = 40x and C = 36x.
Total investment of
A = (105x×1) + 105x×50%×(
) [Here, 8 months =
year]
= 105x+ 35x
= 140x
B = 40x×1 = 40x and C = 36x×1 = 36x
A: B: C = 140x: 40x: 36x = 35: 10: 9
Sum of the ratio = 35+10+9 = 54
B's share = Tk. 21600×(
) = Tk. 4000
Ans: Tk. 4000
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 9
4. In a country, 60% of the male citizen and 70% of the female citizen are eligible to vote. 70%
of the male and 60% of female citizen are eligible to cast their vote. What fraction of citizens
voted during their election?( Janata Bank EO 12, South East Bank MTO 13, Shahjalal Islami
Bank MTO 13, Midland Bank MTO 15) Abyev`t
GKwU †`‡ki 60% cyiæl Ges 70% gwnjv †fvU w`‡Z cvi‡eb| G‡`i g‡a¨ 70% cyiæl Ges 60% gwnjv †fvU `vb K‡ib|
KZRb bvMwiK wbe©vP‡bi mgq †fvU cÖ`vb K‡ib?
Solution:
Let, the number of male be x and female be y.
So, male voted =60% of 70% of x
= 0.6×0.7× x = 0.42x
And female voted = 70% of 60% of y
= 0.7×0.6× y = 0.42y
Total citizen = x+y
Total citizen voted = 0.42x +0.42y = 0.42(x+y)
Fraction of the citizen voted = ( )
( ) = 0.42 =
=
Ans:
Alternative Method:
Let, the number of male be 100 and number of female be 100
Total citizen = 100+100 = 200
So, eligible Male voter = 60% of 100 = 60 and Female = 70% of 100 = 70
Male voted = 70% of 60 = 42 and female voted = 60% of 70 = 42
Total voted= 42+42= 84
Fraction of the citizen voted =
=
Ans:
Trainee Senior Officer 2013 [Exam Taker: BIBM]
1.The total income of Mr. Atiq in the years 2008, 2009 and 2010 was Tk. 36,40,000. His income
increased by 20% each year. What was his income in 2010? (Shahjalal Islami Bank TSO 13) Abyev`t
Rbve AvwZ‡Ki 2008, 2009 Ges 2010 mv‡ji †gvU Avq 36,40,000 UvKv| Zvi Avq cÖ‡Z¨K eQi 20% e„w× cvq| 2010
mv‡j Zvi Avq KZ wQj?
Solution: Let, in 2008 income was Tk. 100x
So, in 2009 income = Tk. (100x+20% of100 x) =Tk. 120x
And in 2010 income = Tk. (120x+20% of 120x) =Tk. 144x
According to the question,
100x+120x+144x = 36,40,000
Or, 364x = 36,40,000
Or, x = 36,40,000/364
Or, x = 10000
100x = 10,00,000
In 2010 income = Tk. (10,00,000×144) =Tk 14,40,000
Ans: Tk. 14,40,000.
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 10
2. In a set of three numbers, the average of first two numbers is 2, the average of the last two
numbers is 3, and the average of the first and last numbers is 4. What is the average of three
numbers? (Shahjalal Islami Bank TSO 13) Abyev`t
wZbwU msL¨vi g‡a¨ 1g msL¨v ywUi Mo 2, †kl msL¨v ywUi Mo 3 Ges 1g I †kl msL¨vi Mo 4| msL¨v wZbwUi Mo KZ?
Solution: Let, the numbers be a, b, c.
= 2
a+ b = 4 ….(i)
= 3
b+ c = 6 ….(ii)
and
= 4
a+ c = 8 …..(iii)
(i)+ (ii)+(iii)=>
a+ b+ b+ c+ a+ c = 4+6+8
Or, 2(a+ b+ c) = 18
Or, (a+ b+ c) = 18/2 = 9
Or, (a+ b+ c) = 9
Or,
=
= 3
Average of three numbers = 3
Ans: 3.
Alternative Method:
Let, the numbers be a, b, c.
= 2
Or, a+b = 4
b = 4-a ….(i)
= 3
Or, b+c = 6
Or, 4-a+c = 6
c = 2+a ….(ii)
and
= 4
Or, a+c = 8
Or, a+2+a = 8
Or, 2a = 8-2
Or, 2a = 6
a = 3 …..(iii)
Putting the value of ‘a’ in equation (i) and (ii)
b = 4-3 = 1
c = 2+3 = 5
Now,
=
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 11
= 3
Average of three numbers = 3
Ans: 3.
3. (√ √ )
√ √ - √
√ =? (Shahjalal Islami Bank TSO 13)
Solution: (√ √ )
√ √ - √
√
= (√ √ )(√ √ )
(√ √ )(√ √ ) – ( √ )( √ )
( √ )( √ )
= (√ √ )
(√ ) (√ ) –
( √ )
( ) (√ )
= ( √ √ )
– ( √ )
= ( √ )
– (7+4√ )
= (8+2.2√ ) - (7+4√ )
= 8+4√ – 7- 4√
= 1
4. What is the area of the equilateral triangle if the base BC = 6? (Shahjalal Islami Bank TSO
13)
Solution:
Given that,
AB = BC = CA = 6
We know,
Area of Equilateral Triangle = √
×(6)
2 = 9√
Ans: 9√
Trainee Officer 2013 [Exam Taker: BIBM]
1. In a certain Accounting class, the ratio of the number of Accounting majors to the under of
students who are not Accounting major is 2 to 5. If 2 more Accounting majors were to enter the
class, the ratio would be 1 to 2. How many students are in the class? (Shahjalal Islami Bank TO
13) Abyev`t
†Kvb GKwU A¨vKvDw›Us K¬v‡m hv‡`i A¨vKvDw›Us †gRi Ges hv‡`i A¨vKvDw›Us †gRi bq Zv‡`i AbycvZ 2 t 5| 2 Rb bZzb
A¨vKvDw›Us †gRi K¬v‡m cÖ‡ek Kivq AbycvZ nq 1 t 2| K¬v‡m KZRb wk¶v_©x Av‡Q?
Solution: Let, number of Accounting major be 2x and non Accounting major be 5x
B
A
C
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 12
According to the question,
=
Or, 5x = 4x+4
x = 4
Total students = 2×4 + 5×4 = 28
Ans: 28.
Alternative Method:
Let, total students be x
Given that,
Accounting major : Accounting non major = 2:5
Sum of the ratio = 2+5 = 7
Number of Accounting major students =
and Accounting non major students =
According to the question,
(
+2) :
= 1:2
Or, 2(
+2) =
Or,
+4 =
Or, 4 =
-
Or, 4 =
Or, 4 =
x = 28
Ans: 28.
2. A retailer buys a sewing machine at discount of 15% and sells it for Tk. 1955. Then he makes
a profit of 15%. What is the amount of discount? (Shahjalal Islami Bank TO 13) Abyev`t
†Kvb LyPiv we‡µZv GKwU †mjvB †gwkb 15% wWmKvD‡›U µq K‡ib Ges 1,955 UvKvq weµq K‡ib| G‡Z Zvi 15% jvf nq|
wWmKvD‡›Ui UvKvi cwigvb KZ wQj?
Solution: Let, marked price = Tk. 100x
At 15% discount, cost price = Tk. (100x- 15% of 100x) = Tk. 85x
According to the question,
85x+ 15% of 85x = 1955
Or, 85x+ 12.75x = 1955
Or, 97.75 x = 1955
Or, x = 1955/97.75
100x = 2000
Amount of discount = 15% of 2000 = Tk. 300
Ans: Tk. 300.
3. If x =
, then what is the value of
√ √
√ √ =? (Shahjalal Islami Bank TO 13)
Solution: Given that,
x =
Or,
=
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 13
Or,
=
Or,
= 9
Or, √
√ = √ [Square on both sides]
Or, √
√ = 3
Or, √ √
√ √ =
Or, √ √
√ √ =
√ √
√ √ = 2 (Ans.)
4. What is perimeter of ∆ABC show in the figure? (Shahjalal Islami Bank TO 13)
Solution: Given that, AC = 2
B = x = y, C = y = z
x = y = z and B = C
And A = 2z
Now,
A + B + C = 180°
Or, 2z + z+ z = 180° [ B = C = z]
Or, 4z = 180°
z = 45°
B = C = 45° and A = 2×45° = 90°
So, it is a right angled triangle.
Pythagoras theorem,
BC2 = AB
2 + AC
2
Or, BC2 = 2
2 + 2
2 [AC = AB = 2]
Or, BC2 = 8
BC = 2√
Perimeter = AB + AC + BC = 2+ 2+ 2√ = 4+ 2√ (Ans.)
2
y0
C B
y0
Z
0
2z A
x0
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 14
Trainee Officer (Cash) 2013 [Exam Taker: BIBM]
1. If a number of two digits is divided by the product of its digits, the quotient is 3. When 18 is
added to the number, the digits of the number change their places. Find the number. (Shahjalal
Islami Bank TO cash 13) Abyev`t
`yB A¼wewkó GKwU msL¨v‡K Gi A¼Øi‡qi ¸Ydj Øviv fvM Ki‡j fvMdj 3 nq| hw` msL¨vwUi mv‡_ 18 †hvM Kiv nq Zvn‡j
A¼Øq ’vb wewbgq K‡i| msL¨vwU wbY©q Kiæb|
Solution: Let, the unit digit be y and tenth digit be x
The number = (10x + y).
1st condition,
3
10x+y = 3xy …..(i)
2nd condition,
(10x + y) +18 = 10y + x
Or, 10x-x +18 = 10y-y
Or, 9x+18 = 9y
Or, 9y-9x = 18
Or, y-x = 2
y = x+2 ……(ii)
Putting the value of y in equation (i)
10x + (x+2) = 3x (x+2)
Or, 10x+x+2 = 3x2 +6x
Or, 3x2 +6x-10x-x-2 =0
Or, 3x2 -5x-2 = 0
Or, 3x2 -6x+x-2 = 0
Or, 3x(x-2) +1(x-2) = 0
Or, (x-2)(3x+1) = 0
x = 2 [x = - 1/3, not acceptable]
Putting the value of x in equation (ii)
y = x+2 = 2+2 = 4
The number = 10×2+4 = 24
Ans: 24.
2. An old man distributed all the gold coins he had to his two sons into two different numbers
such that the difference between the squares of the two numbers is 36 times the difference
between the two numbers. How many coins did the old man have? (Shahjalal Islami Bank TO
cash 13) Abyev`t
GKRb e„× †jvK Zvi mg Í ¯^Y©gy`ªv Zvi `yB cy‡Îi g‡a¨ Ggb msL¨vq fvM K‡i †`b †hb msL¨v ywUi e‡M©i AšÍi, msL¨v `ywUi
AšÍ‡ii †P†q 36 ¸Y eo nq| e„× ‡jvKwUi Kv‡Q KZwU ¯^Y©gy`ªv wQj?
Solution: Let, the two numbers be x and y.
So, total number of coins = x+ y
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 15
According to the question,
x2-y
2 = 36(x-y)
Or, (x+y)(x-y) = 36(x-y)
(x+y) = 36
Total number of gold coins is 36.
Ans: 36.
3. Two equal amount of money are deposited in two banks, each at 15% per annum, for 3.5
years and 5 years. If difference between their profits is Tk. 144, what is the each amount of
money deposited? (Shahjalal Islami Bank TO cash 13) Abyev`t
15% my‡` mgcwigvb UvKv 3.5 eQi Ges 5 eQ‡ii Rb¨ 2wU Avjv`v e¨vs‡K ivLv n‡jv| hw` G‡`i gybvdvi cv_©K¨ 144 UvKv nq
Zvn‡j cÖ‡Z¨K e¨vs‡K KZ UvKv Rgv ivLv n‡qwQj?
Solution: Let, initial deposit be Tk. 100x
According to the question,
(100x×15%×5)-(100x×15%×3.5) = 144 [Here, Interest (I) = Prn]
Or, 75x- 52.5x = 144
Or, 22.5x = 144
Or, 100x =
100x = 640
Ans: Tk. 640.
4. In the following diagram, if BC = CD = BD = 1 and angle ADC is a right angle, what is the
perimeter of triangle ABD? (Shahjalal Islami Bank TO cash 13)
Solution: Given that,
BC = CD = BD = 1
So, BCD is an equilateral triangle.
BCD = CDB = CBD = 60°
BDA = 90°-60° = 30° and ABD = 180°-60° = 120°
So, BAD = 180°-120°-30° = 30°
BAD is an Isosceles triangle.
Therefore, AB = BD = 1 and AC = AB + BC = 1+1 = 2
Pythagoras theorem,
AC2 = CD
2 + AD
2
Or, 22 = 1
2 + AD
2
Or, AD2 = 4-1 = 3
AD = √
Perimeter of ABD = 1+1+√ = 2+√ (Ans.)
A
B
D C
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 16
Management Trainee Officer 2011 [Exam Taker: BIBM]
1. A train travelling at 48 km/h completely crosses another train having half its length and
travelling in opposite direction at 42 km/h, in 12 second. It also passes a railway platform in 45
second. What is the length of the platform? (Shahjalal Islami Bank MTO 11) Abyev`t
48 wK.wg/N›Uv †e‡Mi GKwU †Uªb wecixZ w`K †_‡K 42 wK.wg/N›Uv †e‡M Avmv Gi A‡a©K •`‡N©¨i GKwU †Uªb‡K 12 †m‡K‡Û m¤ú~Y©
iƒ‡c AwZµg K‡i| GwU †ijI‡q cøvUdg©wU‡K 45 †m‡K‡Û AwZµg K‡i| cøvUd‡g©i •`N©¨ KZ?
Solution: Let, length of the smaller train = x meters
So, length of the longer train = 2x meters
Total length of two trains = x+2x = 3x meters
Actual speed of two trains = (48+42) km/hr = 90 km/hr
= 90×(
) m/s
= 25 m/s [Here, 1km/h =
m/s]
We know,
Distance = Speed ×Time
3x = 25×12
x = 100
So, length of the longer train = 2×100 = 200 meters
Let, length of the platform be y meters.
According to the question,
200 + y = 45 × (48×
) [Distance = Time ×Speed]
Or, 200 + y = 600
y = 400
So, the length of the platform = 400 meters.
Ans: 400 meters.
2. The cost price of two watches taken together is Tk. 840. If by selling one at a profit of 16%
and the other at a loss of 12%, there is no loss or gain in the whole transaction, find the cost
price of the two watches. (Shahjalal Bank MTO 11, Social Islami Bank PO 17) Abyev`t
GKm‡½ †Kbv 2wU Nwoi µqg~j¨ GK‡Î 840 UvKv| hw` GwU‡K 16% jv‡f Ges Ab¨wU‡K 12% ¶wZ‡Z weµq Ki‡j †gv‡Ui Dci
†Kvb jvf ev ¶wZ nq bv Zvn‡j Nwo 2wUi cÖwZwUi µqg~j¨ wbY©q Ki|
Solution: Let, 1st cost price = Tk. x and 2nd cost price = Tk. (840-x)
According to the question,
16% of x = 12% of (840-x)
Or, 0.16x = 0.12(840-x)
Or, 0.16x = 100.8-0.12x
Or, 0.16x+0.12x = 100.8
Or, 0.28x = 100.8
Or, x = 100.8/0.28
x = 360.
So, 1st cost price = Tk. 360 and 2nd cost price = Tk. (840-360) = Tk. 480.
Ans: Tk. 360 and Tk. 480.
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 17
3. A, B and C can do a piece of work in 16, 32 and 48 days respectively. They started working
together but C left after working 4 days and B left 2 days before the completion of work. How
many days it took to complete the work? (Shahjalal Islami Bank MTO 11, Social Islami Bank
PO 17) Abyev`t
A, B I C GKwU KvR h_vµ‡g 16, 32 Ges 48 w`‡b Ki‡Z cv‡i| Zviv GKmv‡_ KvR Ki‡Z ïiæ K‡i wKš‘ KvR ïiæ nIqvi 4
w`‡b ci C KvR †Q‡o †`q Ges KvR †kl nIqvi 2 w`b Av‡M B KvR †Q‡o †`q| m¤ú~Y© KvRwU †kl n‡Z KZw`b mgq jv‡M?
Solution: Let, the total work will be completed in x days.
In x days A’s work =
parts
Since left 2 days before the completion of work,
B work in (x-2) days =
parts
And C works in 4 days = 4×
=
parts
According to the question,
+
+
= 1
Or,
= 1 -
Or,
=
Or, 3x-2 = (
)×32
Or, 3x =
+ 2 =
x = 94/9 = 10
So, the total work will be completed in 10
days
Ans: 10
days.
4. Two Cans have the same height equal to 21 m. One Can is cylindrical; the diameter of whose
base is 10 cm. The other can has square base of side 10 cm. What is the difference in their
capacities? (Shahjalal Islami Bank MTO 11) Abyev`t
`ywU cv‡Îi cÖwZwUi D”PZv 21 wgUvi| GKwU cvÎ wmwjÛvi AvK…wZi hvi f~wgi e¨vm 10 †m.wg| Ab¨wU eM©vK…wZi hvi GK av‡ii
•`N¨© 10 †m.wg| cvÎ ywUi avib¶gZvi cv_©K¨ KZ?
Solution: Height, h = 21m = 2100cm [1 meter = 100 cm]
Radius, r = 10/2cm = 5cm [Radius =
×Diameter]
We know,
Volume of cylindrical Can = πr2h = 3.1416×5
2×2100 =164934 cm
3
Volume of square box Can = side2×height = 10
2×2100 = 2,10,000 cm
3
Difference = (210,000-164934) cm3 = 45066 cm
3
Ans: 45066 cm3
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 18
Trainee Senior Officer 2011 [Exam Taker: BIBM]
1. If
=
, then
= ? (Shahjalal Islami Bank TSO 11)
Solution:
=
Or,
=
[Multiplying both sides by
]
Or,
=
Or,
=
= -3 (Ans.)
2. The base of a rectangle exceeds three times the height by 8. Find the dimensions of the
rectangle if- (a) the semi-perimeter is 32 (b) the perimeter is 100. (Shahjalal Islami Bank TSO
11)
Solution: Let, the base be x.
So, height = 3x+8
a) Semi- perimeter = Base +Height = x+ 3x+8 = 4x +8
According to the question,
4x +8 = 32
Or, 4x = 32-8
Or, 4x = 24
x = 6
Base = 6 and height = 3×6+8 = 26 (Ans.)
b) Perimeter = 2(Base+ Height) = 2(x+3x+8) = 8x+16
According to the question,
8x +16 = 100
Or, 8x = 100-16
Or, 8x = 84
x = 10.5
Base = 10.5 and height = 3×10.5+8 = 39.5 (Ans.)
3. A club has 20 members. They are electing a principal and a vice president. How many
different outcome of the election are possible? (Assume the president and the vice president
must be different members of the club.) (Shahjalal Islami Bank TSO 11)
Solution: A President can be elected from 20 members by 20C1 = 20 ways.
A vice President can be elected from 19 members by 19C1 = 19 ways.
Possible outcome of the election = 20×19 = 380.
Ans: 380.
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 19
4. Tk. 1500 is invested at a rate of 10% simple interest and interest is added to the principal
after every 5 years .in how many years will it amount to Tk. 2500? (Shahjalal Islami Bank TSO
11) Abyev`t
hw` 10% mij gybvdvq 1,500 UvKv wewb‡qvM Kiv nq Ges cÖ‡Z¨K 5 eQi ci hw` gybvdv Avm‡ji mv‡_ †hvM Kiv nq Zvn‡j KZ
eQ‡i UvKvi cwigvb 2,500 n‡e?
Solution: At 10 % simple interest,
Interest of 5 years = 1500×5×10% = Tk. 750
After 5 years Total amount = Tk. (1500+750) = Tk. 2250.
Interest = Tk. (2500-2250) = Tk. 250
We know,
Interest = principal× Time× Rate of Interest
Or, 250 = 2250× Time× 10%
Or, 250 = 225× Time
Time = 250/225=1.11
Total time = 5+1.11 = 6.11 years.
Ans: 6.11years.
Trainee Officer 2011 [Exam Taker: BIBM]
1. The average income of A for 15 days is Tk. 70. The average for first five days is Tk. 60 and
that for the last nine days is Tk. 80. What is the income for the sixth day? (Shahjalal Bank
Trainee Officer 11)
Solution: Total income of 15 days = Tk. (70×15) = Tk. 1050
Income of 1st 5 days = Tk. (60×5) = Tk. 300
Income of last 9 days = Tk. (80×9) = Tk. 720
Income of sixth day = Tk. (1050-300-720) = Tk. 30
Ans: Tk. 30.
2. Nipu, Nila and Dipa formed a partnership with investments of Tk. 75000, Tk. 60000 and Tk.
40000 respectively. After 3 years of operation, the partnership had a net profit of Tk. 26250.
What was the share of Dipa in the profit? (Shahjalal Bank Trainee Officer 11)
Solution: Ratio of the capitals of Nipu, Nila and Dipa
Nipu: Nila: Dipa = 75000 : 60000 : 40000
= 75 : 60 : 40
= 15 : 12 : 8.
Sum of the ratio = 15+12+8 = 35
Nipu’s share = Tk. (26250 ×
) = Tk.11,250
Nila's share = Tk. (26250×
) = Tk. 9000
Dipa's share = Tk. (26250×
) = Tk. 6000.
Ans: Tk. 11,250, Tk. 9000 and Tk. 6000
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 20
3. A man sells articles at 5% profit. If had bought it at 5% less and sold it for Tk. 1 less, he
would have gained 10%. What is the cost price of the article? (Shahjalal Bank Trainee Officer
11) Abyev`t
†Kvb e¨w³ 5% jvf cY¨ weµq K‡ib| hw` wZwb 5% Kg `v‡g wK‡b 1 UvKv K‡g weµq Ki‡Zb Zvn‡j Zvi 10% jvf n‡Zv|
cY¨wUi µqg~j¨ KZ?
Solution:
Let, cost Price = Tk. 100x.
At 5% profit, selling price = (100x+5% of 100x) = Tk. 105x
When cost price 5% reduced,
New cost = (100x- 5% of 100x) = Tk. 95x,
New selling price = (95x+10% of 95x) = Tk. 104.5x
According to the question,
105x-104.5x = 1 [Difference of two selling price]
Or, 0.5x = 1
Or, x =
Or, 100x =
x = 200
Cost price = Tk. 200 (Ans.)
4. The length of each side of a triangle is 12 cm. Find the height of the triangle. (Shahjalal Bank
Trainee Officer 11)
Solution:
Let, height of triangle be h cm.
Given that,
AB = BC = AC = 12 cm
We know,
Area of triangle =
×BC×AD =
×12×h = 6h
Again,
Area of Equilateral Triangle = √
×(12)
2 = 36√
According to the question,
6h = 36√
h = 6√
Height of the triangle = 6√ cm. (Ans.)
A
B C D
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 21
Management Trainee Officer 2010 [Exam Taker: BIBM]
1. A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the
bridge in 20 seconds but him in 8 seconds. Find the length of the train. (Sonali Officer IT-16,
Shahjalal Islami Bank MTO 10) Abyev`t
†Kvb e¨w³ 180 wg. j¤^v GKwU †ijI‡q eªx‡Ri Dci `vwo‡q Av‡Q| wZwb †`L‡jb †h GKwU †Uªb 20 †m‡K‡Û eªxRwU AwZµg K‡i
wKš‘ Zv‡K 8 †m‡K‡Û AwZµg K‡i hvq| †Uª‡bi ‣`N © wbY©q Ki|
Solution:
Let, length of the train be x m
According to the question,
=
[Speed=
]
Or, 20x = 8(x+180)
Or, 20x = 8x + 1440
Or, 20x-8x = 1440
Or, 12x = 1440
x = 120
Length of the train = 120 m
Ans: 120 m.
2. A trader bought some mangoes for Tk. 150 per dozen and equal number of apples for Tk. 100
per dozen. If he sells all the fruits Tk. 140 per dozen, what will be his profit/loss in percentage?
(BASIC Bank Officer 1999, RAKUB SO 14, Shahjalal Islami Bank MTO 10) Abyev`t
GKRb e¨emvqx c ÖwZ WRb 150 UvKv `‡i wKQz Avg Ges cÖwZ WRb 100 UvKv `‡i mgvb msL¨K Av‡cj µq K‡ib| hw` †m
me¸‡jv dj 140 UvKv WRb wn‡m‡e weµq K‡i Zvn‡j Zvi kZKiv KZ jvf ev ¶wZ n‡e?
Solution:
Let, he bought x dozen mangoes and x dozen apples.
So, buying price = 150x + 100x = Tk. 250x
Selling price = Tk. (140×2x) = Tk. 280x
Profit = Tk. (280x-250x) = Tk. 30x
So, percentage of profit =
% = 12 %
Ans: Profit 12%
Alternative Method:
Given, cost price of per dozen mango = Tk. 150
and cost price of per dozen apple = Tk. 100
So, cost price (per dozen mango + per dozen apple) =Tk. (150+100)
= Tk. 250
Selling price (per dozen mango+ per dozen apple) = Tk. (140×2)
=Tk. 280
Profit = Tk. (280–250) = Tk. 30
Percentage of profit =
% = 12% (Ans.)
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 22
3. In a school, there are equal number of boys and girls. Among the students, 1/8 of the girls and
5/6th of the boys are residing in the hostel. What percent of the Students consists of boys who do
not reside in the hostel among all students? (Modhumoti Bank MTO 16, Shahjalal Islami Bank
MTO 10) Abyev`t
GKwU we`¨vj‡q †Q‡j Ges †g‡qi msL¨v mgvb| wk¶v_©x‡`i g‡a¨ 1/8 Ask †g‡q Ges 5/6 Ask †Q‡j †nv‡÷‡j evm K‡i| †gvU
wk¶v_©xi g‡a¨ kZKiv KZRb †Q‡j †nv‡÷‡j evm K‡i bv?
Solution:
Let, the number of boys be ‘x’ and girls be ‘x’.
Total students = 2x students.
Non-residing boys = x-
of x = x-
=
Required percentage =
× 100% =
% = 8.33% (Ans.)
Alternative Method:
L.C.M. of 8 and 6 = 48
Let, total student be 48x
So, boys = 24x and girls = 24x
Boys residing in the hostel = 24x×(
) = 20x
Boys do not reside in the hostel = 24x-20x = 4x
Required percentage = (
×100) % = 8.33 % (Ans.)
4. Two partners A and B have 70% and 30% shares respectively in a business. After sometimes,
a third partner C joined the business by investing Tk. 10 lakh and thus having 20% share in the
business. What percentage is the A’s share now in the business? (Shahjalal Islami Bank MTO
10, RAKUB SO 14)
Solution:
Given that,
A: B = 70%: 30% = 7:3
Sum of the ratios = 7+3 = 10
According to the question,
20% share = 10 lakh,
100% share =
lakh
= 50 lakh
Share of A and B = (50–10) lakh = 40 lakh
A’s share = (
×40) lakh = 28 lakh
Now A’s share percentage =
×100 % = 56% (Ans.)
5. Taxi fare is described by the following relationship:
Total taxi Fare = Fixed Charge: Tk. A up to 2 km + Tk. B per km run exceeding 2 km + Tk. 60
for per hours waiting
A person paid Tk. 432 for running 52 km and 2 hours of waiting charge. The same person paid
Tk. 732 for running 102 km and 2 hours of waiting charge. Find the value of A and B. (Shahjalal
Islami Bank MTO 10)
Solution:
Given that,
Rate of 1st 2 km = Tk. A, per km after exceeding 2 km = Tk. B and per hour waiting charge = Tk. 60
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 23
1st Condition,
A + (52-2)×B +60×2 = 432
Or, A + 50B = 432- 120
A + 50B = 312 ....(i)
2nd Condition,
A + (102-2)×B +60×2 = 732
Or, A + 100B = 732- 120
A + 100B = 612 ....(ii)
Now, (ii) – (i) =>
100B – 50B = 612 – 312
Or, 50B = 300
B = 6
Putting the value of B in equation (i)
A + 50×6 = 312
Or, A = 312 -300
A = 12
Ans: A = 12 and B = 6.
6. In the figure below, AB is perpendicular to BC and BD = DC. If AD = √10 cm and AC = 4 cm,
then what is the value of BC? (Shahjalal Islami Bank MTO 10)
A
B D C
Solution:
Given that, AC = 4 cm and AD = √10
Let, BD = DC = x and AB = h
Now, according to the Pythagoras theorem
AD2 = AB
2 + BD
2
Or, (√10)2 = h
2 + x
2
Or, 10 = h2 + x
2
h2 = 10 – x
2 ......(i)
Again,
AC2 = AB
2 + BC
2 [BC = BD+DC = x+ x = 2x]
Or, (4)2 = h
2 + (2x)
2
Or, 16 = 10 – x2 + 4x
2 [From equation (i)]
Or, 16-10 = 3x2
Or, 3x2 = 6
Or, x2 = 2
Or, x = √2
2x = 2√2
The value of BC = 2√2 cm.
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 24
Trainee Senior Officer 2007 [Exam Taker: BIBM]
1. The sum of square of two numbers is 80 and the square of their difference is 16. Determine
the product of the two numbers.
Solution:
Let, the numbers be x and y.
1st Condition,
x2 + y
2 = 80 ....(i)
2nd Condition,
(x-y)2 = 16
Or, x2 + y
2 - 2xy = 16
Or, 80 - 2xy = 16
Or, 80-16 = 2xy
Or, 2xy = 64
xy = 32
The product of the two numbers = 32 (Ans.)
2. A and B are two stations 195 km. apart. A train starts from A at 8 a.m. and travels towards B
at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what
time do they meet? Abyev`t
2wU †÷kb A I B Gi `~iZ¡ 195 wK.wg | GKwU †Uªb †ejv 8 Uvi mgq A †_‡K hvÎv ïiæ K‡i Ges B Gi w`‡K 60 wK.wg / N›Uv
†e‡M hvq| Aci GKwU †Uªb B †_‡K †ejv 9 Uvi mgq hvÎv ïiæ K‡i A Gi w`‡K 75 wK.wg / N›Uv †e‡M †h‡Z _v‡K| KLb Zviv
gy‡LvgyLx wgwjZ n‡e?
Solution:
Let, they meet x hours after 8 a.m.
So, first train travelled = x hr and second train travelled = (x-1) hr
According to the question,
60x + 75(x-1) = 195 [Distance = Speed× Time]
Or, 60x + 75x – 75 = 195
Or, 135x = 195 + 75
Or, 135x = 270
x =
= 2 hrs.
So, they meet = (8 a.m. + 2 hrs) = 10 a.m.
Ans: 10 a.m.
3. If 2a + 3
b = 17 and 2
a+2 – 3
b+1 = 5, then determine the values of a and b.
Solution: Given that,
2a + 3
b = 17
2a = 17- 3
b .... (i)
2a+2
– 3b+1
= 5
Or, 2a.2
2 – 3
b.3
1 = 5
Or, 4.2a. – 3.3
b = 5
Or, 4(17- 3b) – 3.3
b = 5
Or, 68-4.3b -3.3
b = 5
Or, -7.3b = 5-68 = -63
Or, 3b =
= 9
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 25
Or, 3b = 3
2
b = 2
Putting the value of b in equation (i)
2a = 17- 3
2 = 17-9 = 8
Or, 2a = 2
3
a = 3
Ans: a = 3 and b = 2.
4. A number consists of two digits. The sum of the digits is 15. If 27 is subtracted from the
number, its digits are interchanged. Find the number. Abyev`t
GKwU msL¨v `ywU A¼ wb‡q MwVZ| A¼Ø‡qi †hvMdj 15| hw` msL¨vwU †_‡K 27 we‡qvM †`qv nq Zvn‡j A¼Øq ¯’vb wewbgq K‡i|
msL¨vwU wbY©q Kiæb|
Solution: Let, the ten's digit be x.
So, unit's digit = (15 - x).
Number = l0x + (15 - x) = 9x + 15.
Number obtained by reversing the digits = 10 (15 - x) + x = 150 - 9x.
According to the question,
(9x + 15) - 27 = 150 - 9x
Or, 9x +15 -27 = 150-9x
Or, 9x+9x = 150-15+27
Or, 18x = 162
x = 9
The ten's digit = 9 and unit's digit = (15 - 9) = 6.
Number = 9×9+15 = 96. (Ans.)
5. Masum has twice as much money as Selim and Selim has 50% more money than what Badal
has. The average money with them is Tk. 110, then determine the amount of Masum’s money?
Solution: Let, Badal has Tk. 2x.
So, Selim has 150% of Tk.2x = Tk. 3x and Masum has Tk. 3x×2 = Tk. 6x
According to the question,
= 110
Or, 11x = 330
Or, 6x =
6x = 180
Masum has Tk. 180. (Ans.)
Exam Aid Bank Written Math
Jafar Iqbal Ansary Page 26
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