Bangladesh bank written math 2001 2018 [www.onlinebcs.com]

1. Bangladesh Bank written maths Solved by : Md. Helal Uddin
1
Q-1: Three partners A, B & C start a business. Twice the investment of A is equal to thrice
the capital of B is 4 times the capital of C. They share the profit in the ratio of their capital.
In a particular year, the gross profit is Tk. 250000 and the administrative expenses are 20
% of the gross profit. Find the share of profit each partner. [BB Asst. Director – 2010]
Invest ratio , A : B ⇒ 3 : 2
Invest ratio , B : C ⇒ 4 : 1
So , The ratio of investment , A : B : C ⇒ 6 : 4 : 1
Sum of the terms of the ratio of investment ⇒ (6+4+1) = 11
Profit excluding adst. Expenses ⇒ 250000×
4
5
= 200000
A’s share of profit ⇒ 200000×
6
11
= 109090.909 ≈ Tk. 109090
B’s share of profit ⇒ 200000×
4
11
= 27727.2728 ≈ Tk.27727
C’s share of profit ⇒ 200000×
1
11
= 18181.8182 ≈ Tk. 18181
Q-2 : A boy purchased some chocolates from a shop for Tk 120. In the next shop he found
that the price of per piece chocolate is Tk 3 less than that charged at the previous shop, as
such he could have purchased 2 more chocolates. How many chocolates did he buy from the
first shop? [BB Asst. Director – 2010]
Let , A boy purchased ‘N’ chocolates from a shop for Tk. 120.
So , The price of per piece chocolate ⇒
120
N
In the next shop , price of each chocolate ⇒
120
N+2
ATQ ,
120
N
−
120
N+2
= 3
⇒ 120(N+2) – 120N = 3(N² + 2N)
⇒ 120N+240– 120N = 3N² + 6N
⇒ N² + 2N – 80 = 0
⇒ N² + 10N – 8N – 80 = 0
⇒ N(N+10) – 8(N+10) = 0
⇒ (N+10)(N-8) = 0
Here , N = 8 and N ≠ - 10
Therefore , he purchased 8 chocolates from the shop. [Ans.]

2. Bangladesh Bank written maths Solved by : Md. Helal Uddin
2
Q-3 : Tanim bought some oranges. He gave
𝟏
𝟐
of them to his sister,
𝟏
𝟒
of the remainder to his
neighbour,
𝟑
𝟓
of those left to his children and had 6 left in the end. How many oranges did
Tanim buy? [BB Asst. Director – 2010]
Let , Tanim bought ‘T’ oranges .
ATQ , T ×
1
2
×
3
4
×
2
5
= 6
⇒ 3T = 6×20
⇒ T = 40
Therefore , Tanim bought 40 oranges [Ans.]
Q-4 : A person sold two articles. Each for the same price of Tk. 1040. He incurs 20% loss on
the first and 10% loss on the second. Find his overall percentage of loss.
[BB Officer- 2015]
CP₁ : SP₁ ⇒ 5 : 4 = 45 : 36
CP₂ : SP₂ ⇒ 10 : 9 = 40 : 36
Total CP ⇒ (45+40) = 85 units ; Total SP ⇒ (36+36) = 72 units
Loss ⇒ (85 – 72) = 13
So , % Loss ⇒ (
13
85
)×100 = 15.29% [Ans.]
Q-5 : The annual incomes and expenditures of a man and his wife are in the ratios 5:3 and
3:1, respectively. If they decide to save equally and find a balance of Tk. 4000 at the end of
the year, what was their income? [BB Officer- 2015]
Income ratio , Man : Wife ⇒ 5 : 3
Expenditure ratio , Man : Wife ⇒ 3 : 1
Now , (5 – 3) i.e. 2 units ≡ Tk. 2000
Then , 5 units ≡
2000×5
2
= Tk. 5000
Similarly , 3 units is equivalent to Tk. 4000
Another approach :
Let , The income of a man and his wife be 5a , 3a respectively.
ATQ ,
5a−2000
3a−2000
=
3
1
⇒ 9a – 6000 = 5a – 2000 ⇒ 4a = 4000 ⇒ a = 1000
So, The income of a man ⇒ 5×1000 = Tk. 5000

3. Bangladesh Bank written maths Solved by : Md. Helal Uddin
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The income of his wife ⇒ 4×1000 = Tk. 4000 [Ans.]
Q-6 : A shop stocks four types of caps, there are
𝟏
𝟑
as many red caps as blue caps and
𝟏
𝟐
as
many green caps as red caps. There are equal number of green caps and yellow caps. If there
are 42 blue caps, then what percent of the total caps in the shop are blue?
[BB Officer- 2015]
Here , Blue caps 42 . So , Red caps ⇒ 42×
1
3
= 14
Green caps ⇒ 14×
1
2
= 7 ; Therefore , Yellow caps = 7
Now , Total caps ⇒ (42+14+7+7) = 70
Hence , Blue% = (
42
70
) × 100 = 60% [Ans. ]
Q-7 : If the sum of five consecutive integers is S, what is the largest of those integers in terms
of S? [BB Asst. Director-04]
ATQ , N + (N+1) + (N+2) + (N+3) + (N+4) = S
⇒ 5N + 10 = S
⇒ N =
S−10
5
So ,The largest integers ⇒
S−10
5
+ 4 =
S+10
5
[Ans. ]
Q-8 : The difference between two numbers is five and the difference of their squares is 65.
What is the larger number?
Let ,The smaller number be ‘N’ . So ,The largest number ⇒ (N+5)
Now , (N+5)² - N² = 65
⇒ N² + 10N + 25 – N² = 65
⇒ 10N = 40
⇒ N = 4
Therefore , the largest number ⇒ ( 4+5) = 9 [Ans.]
Q-9 : Robi drove 100 miles to visit a friend. If he had driven 8 miles per hour faster than he
did, he would have arrived in
𝟓
𝟔
of the time, he actually took. How many minutes did the trip
take?
Time ratio ⇒ 6 : 5
Speed ratio ⇒ 5 : 6 [Time and speed are inversely proportional]
Now , (6 – 5) i.e. 1 unit ≡ 8 kmph ; Then , 5 units ≡ 40 kmph

4. Bangladesh Bank written maths Solved by : Md. Helal Uddin
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So , Actual time ⇒
100
40
= 150 min. [Ans. ]
Q-10 : Of the three numbers, second is twice the first and is also thrice the third. If the
average of the three numbers is 44, then what will be the largest number?
First : Second ⇒ 1 : 2 = (1 : 2)×3 = 3 : 6
Second : Third ⇒ 3 : 1 = (3 : 1)×2 = 6 : 2
So , The ratio of numbers , F : S : T ⇒ 3 : 6 : 2
Now , (3+6+2) i.e. 11 units ≡ 3×44 ; Then , 6 [largest] units ≡ 72 [Ans.]
Q-11 : a, b, c, d, e are 5 consecutive numbers in increasing order, deleting one of them from
the set decreased the sum of the remaining numbers by 20% of the sum of 5. Which one of
the number is deleted from the set [BB Asst. Director -2014 , 12]
Here , 5 numbers be N , (N+1) , (N+2) , (N+3) , (N+4)
So , Sum of numbers ⇒ (5N+10)
ATQ , (5N+10) – R = (5N+10)×
4
5
⇒ 25N + 50 – 5R = 20N + 40
⇒ R = N +2
So , The deleted number N+2 [Ans.]
Q-12 : A team of 2 men and 5 women completed
𝟏
𝟒
th of a job in 3 days. After that another
man joined them and they all complete the next
𝟏
𝟒
th of the job in 2 days. How many men
can complete the whole job in 4 days? [BB Asst. Director – 2014]
Here , (2M + 5W)×4×3 = (3M + 5W)×4×2
⇒ 6M + 15W = 6M + 10W
⇒ M : W ⇒ 5 : 0 [Efficiency]
So, total work be ⇒ (2×5+5×0)×4×3 = 120 units
Therefore , Required men ⇒
120
5×4
= 6 [Ans.]
Q-13 : Rahim bought 2 varieties of rice costing Tk. 5 & 6 per kg each. Then he sold the
mixture at Tk. 7 per kg , making profit of 20%. What was the ratio of the mixture?
[BB Asst. Director – 2014]
Here , Cost price of mixture ⇒ 7×
5
6
=
35
6

5. Bangladesh Bank written maths Solved by : Md. Helal Uddin
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ATQ , 5V₁ + 6V₂ =
35
6
×(V₁ + V₂)
⇒ 30V₁ + 36V₂ = 35V₁ + 35V₂
⇒ V₁ : V₂ = 1 : 5 [Ans.]
Q-14: A bus is traveling with 52 passengers. When it arrives at a stop, Y passengers get off
and 4 get in at the next stop one-third of the passengers get off and 3 get on. There are 25
passengers. Find out how many passengers got off at the first stop?
[BB Asst. Director – 2013]
ATQ , [(52 – Y) + 4]×
2
3
+ 3 = 25
⇒ 104 – 2Y + 8 = 66 ⇒ Y = 23 [Ans.]
Q-15 : A,B and C do a job alone in 20, 30, and 60 days respectively. In how many days can
A do the job he is assisted by B & C?
Let , the total work be 60 units [LCM of 20 , 30 , 60)
So , Efficiency , A : B : C ⇒ 3 : 2 : 1
Sum of the terms of the ratio of efficiency ⇒ (3+2+1) = 6 units
Required time ⇒
60
6
= 10 days [Ans.]
Q-16 : Two alloys A and B are composed of two basic elements. The ratios of the
compositions of the two basic elements in the two alloys are 5:3 and 1:2. A new alloy X is
formed by mixing the two alloys A & B in the ratio 4:3. What is the ratio of the composition
of the two basic elements in alloy X? [BB Asst. Director – 2012]
Here , 5 : 3 ⇒ (5 : 3)×4×3 = 60 : 36
1 : 2 ⇒ (1 : 2)×3×8 = 24 : 48
The ratio of the composition of two elements ⇒ (60+24) : (36+48) = 1 : 1 [Ans.]
Q-17 : A series has 3 numbers a, ar, ar². In the series, the first term is twice of the second
term. What is the ratio of the sum of the first 2 terms to the sum of the last 2 terms.
[BB Asst. Director – 2012]
Here , a = 2×ar ⇒ r =
1
2
Now , (a+ar) : (ar+ar²) = a +
a
2
∶
a
2
+
a
4
= 2 ∶ 1 [Ans. ]

6. Bangladesh Bank written maths Solved by : Md. Helal Uddin
6
Q-18 :The length of a rectangle is twice its width. If the length is increased by 4 inches and
the width is decreased by 3 inches, a new rectangle is formed whose perimeter is 62 inches.
What is the length of the original rectangle? [BB Asst. Director – 2012]
Let , the width of a rectangle be ‘W’ inches .
So , The length of a rectangle is 2W inches .
ATQ , 2×[(2W+4)+(W-3)] = 62
⇒ 3W+1 = 31 ⇒ W = 10
Therefore , The length of the original rectangle ⇒ (10×2) = 20 in.
Q-19 : The length of rectangular plot is greater than its breadth by 20 meters. If the
perimeter of the plot is 160 meters, what is the area of the plot in square meters?
ATQ , 2[(B+20) + B] = 160
⇒ 2B + 20 = 80 ⇒ B = 30
So , The length of the rectangular ⇒ (30+20) = 50
Therefore ,The area of the plot ⇒ 50×30 = 1500 Sq. Meters [Ans.]
Q-21 : Two cars race around a circular track in opposite directions at constant rates. They
start at the same point and meet every 30 seconds. If they move in the same direction, they
meet every 120 seconds. If the track is 1800 meter long, what is the speed of each car?
Relative speed in opposite direction ⇒
1800
30
= 60 m/s
Relative speed in same direction ⇒
1800
120
= 15 m/s
So , Speed of the first car ⇒
60+15
2
= 37.5 m per sec.
Speed of the second car ⇒
60−15
2
= 22.5 m per sec
Q-22. Mr. Hasan has few notes of Tk. 10 and Tk. 50. A total of his 150 notes amount to
Tk.5100. What is the number of each kind of note?
ATQ , 50Q + 10(150 – Q) = 5100
⇒ 40Q + 1500 = 5100
⇒ Q = 90

7. Bangladesh Bank written maths Solved by : Md. Helal Uddin
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So , The number of notes of Tk. 50 is 90
Therefore , the number of notes of Tk. 10 is (150-90) = 60 [Ans.]
Q-23 : The area of a rectangular plot is 323 square meters. Its perimeter is 72 meters. Find
the length and breadth of the plot. [BB Asst. Director – 2011]
Let , The length and breadth of the plot be ‘L’ , ‘W’ respectively.
First case , LW = 323 (i)
Second case , 2(L+W) = 72
⇒ L+W = 36 ⇒ L = 36 – W (ii)
We get from equation ( i ) and ( ii )
Now , (36 – W)×W = 323
⇒ 36W – W² = 323
⇒ W² - 36W + 323 = 0
⇒ W² - 19W – 17W + 323 = 0
⇒ W(W – 19) – 17(W – 19) = 0
⇒ (W – 19) (W – 17) = 0
Here , W = 19 and W = 17
Therefore , The breadth of plot 17 m [Because , Length > Breadth]
So , The length of plot ⇒
323
17
= 19 m [Ans.]
Q-24 : A loss of 15% is incurred by selling a watch for Tk. 612. How much is the sum of
money by which it is sold to make a profit of 10%?
612×
20
17
×
11
10
= 792 [Ans. ]
Q-25 : 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.
Cost price ⇒
1920+1280
2
= 1600
So , Selling price ⇒ 1600×
5
4
= Tk. 2000 [Ans. ]

8. Bangladesh Bank written maths Solved by : Md. Helal Uddin
8
Q-26 : A trade while selling an item was asking for such a price that would enable him to
offer a 10% discount and still make a profit of 20%. If the cost of the product was Tk 50,
what was his asking price?
50×
6
5
×
10
9
= 66.67 [Ans. ]
Q-27 : A can do a work in 10 days, while B alone can do it in 15 days. They work together
for 5 days and rest of the work is done by C in 2 days. If they get Tk 4500 for whole work,
how should they divide money? [BB Asst. Director (FF) - 2015]
Let , the total work be 30 units [LCM of 10 , 15]
So , Efficiency , A : B ⇒ 3 : 2
In 5 days , Done by A ⇒ 3×5 = 15 units
In 5 days , Done by B ⇒ 2×5 = 10 units
Remaining work ⇒ [30 – (15+10)] i.e. 5 units , done by C
So , Work ratio , A : B : C ⇒ 15 : 10 : 5 = 3 : 2 : 1
Therefore , A : B : C ⇒ (3 : 2 : 1)×750 = 2250 : 1500 : 750 [Ans.]
Q-28 : The simple interest rate of a bank was reduced to 5% from 7%. As a consequences
Mr. B’s income was reduced by Tk. 2100 in 5 years. How much is Mr. B’s initial deposit in
the bank? [BB Asst. Director – 2001]
Here , (7% - 5%) = 2%
Now , 5×2% ≡ 2100 ; Then , 100% ≡ 21000 [Ans.]
Q-29 : A bus hired at the cost of Tk. 2400 and it was decided that every student would share
the cost equally. But 10 more students jointed and as a result the fare decreased by Tk. 8
per person. How many students were travelling in the bus?
[BB Asst. Director (FF) - 2015]
Let , The total students be ‘T’ and Increased students (T+10).
ATQ ,
2400
T
−
2400
T+10
= 8
⇒ 300(T + 10) – 300T = T² + 10T
⇒ T² + 10T – 3000 = 0
⇒ T² + 60T – 50T – 3000 = 0

9. Bangladesh Bank written maths Solved by : Md. Helal Uddin
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⇒ T(T + 60) – 50(T + 60) = 0
⇒ (T + 60)(T – 50) = 0
Here , T = 50 and T ≠ - 60
So , Total students is 50 .
Therefore , increased student ⇔ (50+10) i.e. 60 [Ans.]
Q-30 : The average age of students of a class is 15.8 years. The average age of boys in the
class is 16.4 years and of the girls is 15.4 years. Find the ratio of number of boys to the
number of girls in the class. [BB Asst. Director (FF) - 2015]
ATQ , 16.4×B + 15.4×G = 15.8×(B + G)
⇒ 16.4B – 15.8B = 15.8G – 15.4G
⇒ 0.6B = 0.4G
⇒ B : G = 2 : 3 [Ans.]
Q-31 : Mr. X has a investable amount of Tk 100000, he will invest the amount for two years.
He has two options. He can invest at simple interest rate of 12% per annum; alternatively
he can invest at compound rate of 10% (compounded semi annually). Calculate the earnings
at two option and advice him accordingly. [BB officer – 2001]
Here , Simple interest in 2 yrs. ⇒ 100000×12%×2 = Tk. 24000
Amount at compound ⇒ 100000×(1 +
10%
2
)
4
= 100000×
21
20
×
21
20
×
21
20
×
21
20
= 121550.6
So , The compound interest ⇒ (100000 – 121550.6) = 21550.6
Therefore , Simple interest is better than compound interest.
Q-32 : 9. Mr. X pays 10% tax on all income over Tk. 60000 but he does not pay any tax on
interest on postal saving certificate. In 2000 he paid Tk. 7500 as tax & he earned Tk. 12000
as interest on postal savings account. What is his net income in 2000?
Here , 10% ≡ Tk. 7500 ; Then , 100% ≡ Tk. 75000
So , Total income ⇒ (75000+60000+12000) = 147000
Therefore , Net income ⇒ (147000 – 7500) = Tk. 139500 [Ans.]
Q-33 : Mr. Reach sold two properties P1 & P2 for Tk 50000 each. He sold property P1 for
20% more then what he paid for it & sold P2 less than 20% what he paid for it. What was
his total gain or loss, if any, on the scale of two properties? [BB officer – 2001]

10. Bangladesh Bank written maths Solved by : Md. Helal Uddin
10
Here , 20% =
1
5
CP₁ : SP₁ ⇒ 5 : 6 ⇒ (5 : 6)×2 = 10 : 12
CP₂ : SP₂ ⇒ 5 : 4 ⇒ (5 : 4)×3 = 15 : 12
Here , Loss = (10+15) – (12+12) = 1 unit
Now , 12 units ≡ Tk. 50000 ; Then 1 unit ≡ Tk. 4166.67 [Ans.]
Q-35 : Mr. X, a sales person earns 5% commission on all sales between Tk.20000 and 40000
and 8% on all sales exceeding Tk.40000 in a month. He does not earn any commission if
sales in a month amount to less than Tk. 20000. His monthly salary is Tk. 60000 , he has to
pay tax 20% tax on his basic salary but no tax on commission ,in April 2001,the total net
income (salary +commission) of the sales person was Tk 65000. How much were the sales in
April? [BB Asst. Director – 2001]
Here , Actual income ⇒ 60000×
4
5
= Tk. 48000
So , Commission ⇒ (65000 – 48000) i.e. Tk. 17000
ATQ , 40000×5% + 8%×(Q - 40000) = 17000
⇒ 200000 + 8Q – 320000 = 1700000
⇒ Q = 227500
Therefore , the sales in April is Tk.227500 [Ans.]
Q-36 : Mr. A purchased a house for Tk. 1000000 in 1995, he spent Tk. 100000 for routine
maintenance & upkeep of the house. 1n 1999 he sold the house for 25% of more then what
he paid for it. He paid 5% of the proceeds as gain tax & he has to pay 50% of his net profit
to the broker, what is his net income? [BB Asst. Director – 2001]
Total cost of house ⇒ (1000000+100000) = Tk. 1100000
Now , 1100000×
1
4
×
19
20
×
1
2
= Tk. 130625 [Ans. ]
Q-37 : A trader sells on an average 18 pencils and 12 pens per day. The profit comes from
pencil is
𝟏
𝟑
times the profit made by selling a pen. If he makes a profit of Tk 900 in a month
by selling pencils, how much profit does he make per month by selling pens? The trader sells
30 days in a month.
In 30 days , Sum of pencils ⇒ 18×30 = 540

11. Bangladesh Bank written maths Solved by : Md. Helal Uddin
11
In 30 days , Sum of pens ⇒ 12×30 = 360
Profit made by selling a pencils ⇒
900
540
=
5
3
So , Profit made by selling a pen ⇒
5
3
× 3 = 5
Therefore , profit in a month by selling pens ⇒ 360× 5 = 1800
Q-38: A total of 50 employees work in a bank branch of these 22 have taken the accounting
course, 15 have taken finance, 14 marketing, 9 of them taken exactly 2 of the courses, 1 of
them has taken all. How many of the 50 employees have taken none of the course?
[BB Asst. Director-2001]
Total = A + B + C – (Exactly-2 group overlaps) – 2×All + None
⇒ 50 = 22 + 15 + 14 – 9 – 2×1 + None
⇒ None = 10
Therefore , None of the course is 10 [Ans.]
Q-39 : A square is inscribed inside a circle. What is the area of the square if the radius of
the circle is 10 cm.? [BB Asst. Director – 2018]
Here , Diagonal of the square ⇒ (10+10) = 20
ATQ , √2a = 20 ⇒ a =
20
√2
Therefore , area of the square ⇒ (
20
√2
)
2
= 200 cm [Ans. ]
Q-40 : At 8:00 A.M a car stared from Dhaka towards Cox’s Bazar at a speed of 50 km/hr.
After one hour, another car started from Dhaka towards Cox’s Bazar at a speed of 60 km/hr.
After how much time and at what distance from Dhaka the second car will overtake the first
car? [BB Asst. Director -2004]
In 1 hour , Distance is covered by first car ⇒ (50×1) = 50 km
Here , Relative speed in same direction ⇒ (60 – 50) = 10 kmph
The second car will overtake the first car after ⇒
50
10
= 5 hours
Hence , the 2ⁿᵈ car will overtake 1ˢᵗ car at ⇒ (9 A.M + 5) = 2 P.M.

12. Bangladesh Bank written maths Solved by : Md. Helal Uddin
12
So , Distance from Dhaka ⇒ 60×5 = 300 km [Ans.]
Q-41 : Karim and Rahim have equal amount of money. Radha has half of Rahim’s money
and Amena has half of Radha’s money. If you add one taka with all the money they have, it
will be Tk.100.How much Rahim has? [BB Asst. Director -2004]
Radha : Rahim ⇒ 1 : 2 = (1 : 2)×2 = 2 : 4
Amena : Radha ⇒ 1 : 2 = (1 : 2)×1 = 1 : 2
So , Radha : Rahim : Amena : Karim ⇒ 2 : 4 : 1 : 4
Let , Radha , Rahim , Amena and Karim have be 2T , 4T , T , 4T
ATQ , (2T+4T+T+4T) + 1 = 100
⇒ 11T = 99 ⇒ T = 9
Therefore , Rahim has TK. (9×4) = 36 [Ans.]
Q-42 : A Group of students has hired a bus for Taka 3000 for going to a picnic. They had an
understanding that each participant would share the charge in equal amounts. But because
of 10 students not turning up, the charged per student increased by Taka 10 over the initial
estimates. What was the number of students who originally registered for the picnic?
[BB Asst. Director -2006]
Let , The number of students who originally registered be ‘T’
ATQ ,
3000
T−10
−
3000
T
= 10
⇒T² - 10T = 300T – 300(T – 10)
⇒ T² - 10T – 3000 = 0
⇒ T² - 60T + 50T – 3000 = 0
⇒ T(T – 60) + 50(T – 60) = 0
⇒ (T – 60)(T + 50) = 0
Here , T = 60 ; [T = - 50 , But it is not acceptable -Ve sign]
Therefore , The number of students is 60 [Ans.]
Q-43 : Abir can do a piece of work in 80 days. He works for 10 days and then Basher alone
finishes the rest of the work in 42 days. How much time would it take for the two of them
together to complete the whole work? [BB Asst. Director -2006]
Here , 80×Abir = 10×Abir + 42×Basher
⇒ Abir : Basher = 3 : 5 [Efficiency]

13. Bangladesh Bank written maths Solved by : Md. Helal Uddin
13
So, Total work be (80×3) = 240 Units.
Required time ⇒
240
3+5
= 30 days [Ans.]
Q-44 : The sum of the pay of two officers is Taka 24,000 per month. If the pay of one officer
is decreased by 9% and the pay of the second is increased by 17%, their pays become equal.
Find the pay of each officer. [BB Asst. Director -2006]
ATQ , T×91% = (2400 – T)×117%
⇒ 208T = 2400×117 ⇒ T = 1350
The pay of another officer = (2400 – 1350) = Tk. 1050 [Ans.]
Q-45 : A trader, while selling an item, was asking for such a price that would enable him to
offer a 20% discounts and still make a profit of 30% on cost. If the cost of the item was Tk.50
what was his asking price? [BB Asst. Director -2008]
Here , 20% =
1
5
and 30% =
3
10
Now , 50×
13
10
×
5
4
= 81.25 [Ans. ]
Q-46 : A square office, 1000 feet by 1000 feet, is to be partitioned into two offices by a single
interior wall. The difference between the perimeters of the resulting two officers is be 400
feet. What are their dimensions?
[BB Asst. Director -2006]
ATQ , 2×(P+ 1000) – 2×[1000 + (1000 – P)] = 400
⇒ 2P + 2000 – 4000 + 2P = 400
⇒ 4P = 2400 ⇒ P = 600
Therefore , the other partition ⇒ (1000 – 600) = 400 Feet
Hence , Their dimension are (1000×600) i.e. 600000 Sq. Feet
And (1000×400) i.e. 400000 Square feet [Ans.]
Q-47 : Mr. Zaman won an election where the ratio of his votes and those of his opponent,
Mr. Yunus, was 4:3.The total number of voters was 581, of which 91 did not vote. Calculate
the margin of votes by which Mr. Yunus was defeated? [BB Asst. Director -2006]
The ratio of Vote of Mr. Zaman and Mr. Yunus ⇒ 4 : 3
Sum of the terms of the ratio of votes ⇔ (4+3) = 7 units

14. Bangladesh Bank written maths Solved by : Md. Helal Uddin
14
Now , 7 units ≡ (581 - 91) i.e. 490 ; Then , (4 – 3) i.e. 1 units ≡ 70 vote [Ans.]
Q-48 : A man deposits Tk. 1000 in a bank at 8% interest rate compounded annually. At the
end of the 3rd
year, what will be the total amount including interest?[BB Asst. Director -2008]
The total amount including interest ⇒ 1000×(1+8%)³ = 1000×
27
25
×
27
25
×
27
25
= Tk. 1259.712 [Ans.]
Q-49 : Recently Kamal's hourly wage has been increased by 10%. Before this increase,
Kamal's total weekly wage was Tk. 137. If his weekly working hours were to decrease by
10% from last week's total working hours, what would be the change, if any, in Kamal's
total weekly wage? [BB Asst. Director -2009]
Here , Previous wages : Increased wages ⇒ 10 : 11
Previous time : Decreased time ⇒ 10 : 9
Now , Previous total weekly wage = (10×10) = Tk. 100
Present total weekly wage = (11×9) = Tk. 99
Here , Decreased wages / change ⇒ (100 – 99) = 1
Therefore , Change% ⇒ 1%
So , weekly decrease wage = 137×1% = Tk. 1.37 [Ans.]
Q-50 : Find the value of ‘a’ if (a - 3) =
𝟏𝟎
𝐚
Here , (a – 3) =
10
a
⇒ a² - 3a – 10 = 0
⇒ a² - 5a + 2a – 10 = 0
⇒ a(a – 5) + 2(a – 5) = 0
⇒ (a – 5)(a + 2) = 0
Therefore , a = -2 and a = 5 [Ans.]
Q-51 : Find the value of ‘x’ if (2x² - 1) = (3x² - 2x)

15. Bangladesh Bank written maths Solved by : Md. Helal Uddin
15
Here , 2x² - 1 = 3x² - 2x
⇒ x² - 2x + 1 = 0
⇒ (x – 1)² = 0
⇒ (x – 1) = 0
Therefore , x = 1 [Ans.]
Q-52 : After travelling 108 km, a cyclist observed that he would have required 3 hrs less if
he could have travelled at a speed 3 km/hr more. At what speed did he travel?
[BB Asst. Director-2018]
ATQ ,
108
S
−
108
S+3
= 3
⇒ S(S + 3) = 36(S+3) – 36S
⇒ S² + 3S – 108 = 0
⇒ S² + 12S – 9S – 108 = 0
⇒ S(S + 12) – 9(S + 12) = 0
⇒ (S + 12)(S – 9) = 0
Here , [S = - 12 it is not acceptable] and S = 9
Therefore , required speed 9 km/hr.
Q-53 : 50 daily workers can complete a dam project in 40 days. If 30 of them work daily and
the rest work in every alternative day, How many more days will be required to complete
the project? [BB Asst. Director – 2018]
Here , 30×T + (50 – 30)×
T
2
= 50×40
⇒ 40T = 50×40 ⇒ T = 50 days
Required more days ⇒ (50 – 40) i.e. 10 days [Ans.]
Q-54 : 3 coins are tossed at random. Construct the sample space and find the probability of
getting [BB Asst. Director – 2018]
(i) One head two tails.
(ii) One tail.
(iii) One tail and two heads.
Number of possible outcomes after tossed 3 coins randomly.

16. Bangladesh Bank written maths Solved by : Md. Helal Uddin
16
Here , 2³ = 8 ;
Such as ⇒ (HHH, HHT, HTH, THH, HTT, THT, TTH, TTT)
(i) Number of possible outcomes ⇒ (2)³ = 8
Here , Favourable outcome ⇒ (THT , HTT , TTH ) i.e. 3
So , The probability of getting one head and two tails ⇒
3
8
[Ans. ]
(ii) Number of possible outcomes ⇒ 8
Here , Favourable outcomes ⇒ (HHT, HTH, THH) i.e. 3
Therefore , probability of getting one tail ⇒
3
8
[Ans. ]
(iii) Number of possible outcomes = 8
Here , Favourable outcomes ⇒ (HHT, HTH, THH) i.e. 3
So , The probability of getting one tail and two heads ⇒
3
8
[Ans. ]
Q-55 : A senior Citizen invests Tk.50 lac in a fixed deposit scheme at 11.5% annual interest
for six months. In every six months he withdraws Tk. 2 lac from his principal plus interest
earned. What will be his principal amount to invest after two years?
[BB Asst. Director – 2018]
Here , 2 years ⇒ (2×12) = 24 months
So, the withdrawn amount after two years ⇒
2×24
6
Lac = 8 Lac
Therefore, his principle amount after 2 years ⇒ (50 – 8) Lac = 42 Lac [Ans.]