Career Aid for Bank & BCS Math

Mensuration
1) The perimeter of a square field is equal to the perimeter of a rectangle field. Length of the
rectangle fields is 3 times of its width and the area is 768 square meter. How many square sized
tiles of 80 centimeter wide will be required to cover the square field? [AIBL-PO-2017] [SIBL-PO-
2017][National PO-17] [Modhumoti PO-2018] [NRBC MTO-18]
Solution: Let, The width of the rectangle be x meter
So, The length of the rectangle be 3x meter
According to the question,
3x*x=768
0r, x =16
So, The perimeter of the rectangle =2(3 16+16)=128
So, the perimeter of the square is 128 meters.
Suppose, Each Side of square is a.
From question,
4a=128
Or, a =32
Area of the square is =(a)2=(32)2=1024 square meter=10240000 square cm
Area of the tiles =(80 80) square cm =6400 square cm
Number of tiles=10240000/6400=1600 piece
Answer:1600
2) The length of a rectangle field is 1.5 times of width. An amount of Tk 10,260 was needed to cover
the field with grass at the rate of 1.9 Tk per square meter. How much would it cost to fence the
four sides of the rectangular field at the rate of Tk 2.5 per meter? [Bank ASIA MTO -2017] [One
Bank (SCO)-2017] [Lankabangla Finance -MTO-2017]
Solution: Area of the rectangle =(10260/1.9)=5400 square meter
Let, Width of the rectangle=x meter
Length of rectangle=(3x/2) meter
We know, (3x/2)*x=5400
Or, x=60
And Length=(3*60/2)=90 meter
Perimeter of rectangle =2[90+60]= 300 meter
So total Tk needed around rectangle fence=(300*2.5)=750 Tk
Answer:750 Tk
3) The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along
the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then what
is the area of the park (in sq. m)?[City Bank MTO -2017 ][AIBL MTO-2013}
Solution: Let, Length=3x and Breadth=2x
We have, 60 minutes the man cover=12km=12000 m
So, In 8 minutes the man cover=[(12000*8)/60]=1600 meters
Perimeter of the rectangle is
2(3x+2x) = 1600
x= 160
The Area of the rectangle =(3x*2x)= (3*160)(2*160) =153600 square meter
Answer: 153600 sq.m
4) During the next tree plantation week, Mr. X is considering planting trees in one of its own
rectangular piece of land which is 90 feet long 66 feet wide. This is suspended by boundary wall
of 5 feet height. It has been decided that trees will be planted leaving 5 feet and free from the
wall in all four sides. It was been decide that the distance from one tree to another in both row
and column will be 4 feet. What is the maximum numbers of trees that can be planted in the
land? ?[City Bank MTO -2017 ] [Standard Bank MTO-2016] MTB MTO-2014]

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Career Aid for Bank & BCS Math
Solution: Given that, The length of the field=90 feet
Possible length of the rectangle = 90-(5*2)= 80 feet
Possible Width of the rectangle = 66-(5*2) = 56 feet
Possible trees in row= (56/4 )+ 1 = 15
And Possible trees in Column = (80/4) + 1 =21
Maximum tree = 21*15= 315 (Answer)
5) The length of a rectangular field is 30 feet more than its breadth. If the perimeter of rectangular
field is 380 feet. What is the area of the field in square feet? [SJIBL TO-2016]
Solution: Let, Breath = x & length = (x+30)
We know that, perimeter of Rectangular = 2( length + breath)
Or, 380 = 2( x+x+30)
Or, x = 80
Now, Breath = 80 and length = x+30 =80+30 = 110
So, Area = (length*breath) = (110*80)=8800 square feet
Answer: 8800 square feet
6) 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? [BB AD-10]
Solution: Let, Breath = x & length = (x+20)
We know that, perimeter of Rectangular = 2( length + breath)
Or, 160 = 2( x+x+20)
Or, x = 30
Now, Breath = 30 and length = x+20 =30+20= 50
So, Area = (length*breath) = (50*30)=1500 square meters
Answer: 1500 square meters
7) A garden is 60 meter long and 20 meter wide. Inside the garden there is a 5 meter wide path
around it. What is the area of the path in square meter?[Standard Bank(TAO)Cash 16]
Solution: Area of the garden with path= (60×20) sq. m. = 1200 sq. m.
Area of the garden without path= (60-5-5)×(20-5-5) sq. m. = 50×10 sq. m. = 500 sq. m.
Area of the path= (1200-500) sq. m. = 700 sq. m.
Answer: 700 sq. m.
8) On his way home from shopping, Mike must travel due south for 5 miles and then due east for
another 12 miles to reach his house. If Mike could travel in a straight line from the store to his
house, how many fewer miles would he travel? [GIB]
Solution

Pythagorean ratio: 5, 12, 13

How many fewer miles= (5+12)-13 = 4
Answer: 4
9) In the figure, rectangle PQRS is inscribed in the circle and PQ = 6 If the area of t rectangular region
is 48, what is the area the circular region? [RAKUB SO-14]
Solution: Here, area of PQRS = 48 and Breadth, PQ = 6
Length, PS = 48/6 = 8 Q R
Diagnal of the rectangular is =√ √
Radius = 10/2 = 5 P S
& the area of the circle is = (Answer)

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Career Aid for Bank & BCS Math
10) In the figure ABCD is a square. If the length of the square is 10ft, then what will be the area of the
triangle OCD? A B [RAKUB Officer-14]

C D
Solution: Given that, the length of a arm of a square = 10ft
So, Diagonal of the square, BC = √ √ √ ft
√
Half of the diagonal is, OC = √ ft
Here, OC = OD = √ ft
As we know, area of triangle OCD = the length of two arm's attached to the right angle.
= √ √
11) ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What
is the area of the square? [BB AD-15]

Solution: is a right angle. So, ABO is a right angled triangle and AB is the side hypotenuse of
the triangle and side of a square.
According to Phythagoras theorem,

√
So, the side of square is √
Hence, area of square= ( √ ) square unit (Answer)
12) A hall is 15m long and 12m broad. If the sum of the areas of the floor and the ceiling is equal to the
sum of the areas of the 4 walls, what is the volume of the hall? [PKB Officer cash-21]
Solution:

13) A box without lid is made of wood everything 0.5cm thick and its external dimensions are 6 cm by 5
cm by 4 cm. Find the volume of wood used to making the box. [Combined So-21]
Solution: Given that, external dimensions are 6cm, 5cm and 4cm.
So, External will be as follows, length = 6 - (0.5 x 2 ) = 6 - 1 = 5cm.
width = 5 (0.5 x 2 ) = 5 - 1 = 4cm.
and hight = 4 – (0.5 x 1 ) = 4 - 0.5 = 3.5cm.
Hence, the required volume of wood = external capacity- internal capacity
=(6 × 5 × 4)-(5 x 4 x 3.5)= 120 - 70 = 50cm3 (Answer)

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Career Aid for Bank & BCS Math
14) The hypotenuse of a right angled triangled 2x-6 & the other two sides are x+2 & x. What is the
value of x [Combined So-21]
Solution: Let, ABC is the right angle triangle. A
Here, hypothenuse AB=(2x-6) 2x-6
One arm, AC=x and other arm, BC=(x+2) x
According to Phythagoras theorem, C x+2 B

15) The area of a curved surface of a right circular cylinder is 100 sq. cm. and its volume is 150 cubic
cm. Find the height and the radius of the cylinder. [PKB officer Gen-21]
Solution: Let, the radius and height of the cylinder be r and cm respectively.
We know, surface area of cylinder is
And volume of the cylinder is =
Dividing equation (ii) by equation (1), we get

Putting, r = 3 in equation (i) we get

Required radius = 3cm and height = 5.3cm. (Answer)

16) What is the circumference of the circle if a 3 by 4 rectangle is inscribed in the circle? [PKB officer
Gen-21]
Solution: Let us depict a figure according to question.

Here, ABCD is a 3 by 4 rectangle which is inscribed in a circle.

So, Diagonal of the rectangle area,
√ √ √
Radius of the circle unit
Circumference of the circle

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Career Aid for Bank & BCS Math
17) Find A and B, if both A and B are acute angles and cot (A + B) = 1 , cot (A - B) = √3. [PKB officer
Gen-21]
Solution: Given, cot (A + B) = 1
=> cot(A + B) = cot 450 [As, cot 450 =1]
A + B = 450 … … … (1)
Again, cot (A - B) = √3
=> cot(A - B) = cot 300 [As, cot 300 =√3]
A - B = 300 … … … (2)
Eq (1)+(2)
2A=750
A=37.50
Again Eq (1)-(2)
2B=150
B=7.50
Hence, Required A = 37.50 and B = 7.50 (Answer)
18) There are two crosswise roads just in the middle of a field of length 50m and breadth 40m. The
breadth of each road is 1.5m. Find the area covered by two roads. [Combined SO-22]
Solution: Let us depict a picture according to question.
D C
50
1.5
40
A B
Here, the area covered by the two roads = (DC 1.5 + BC 1.5 - 1.5 1.5) m2
= (50 1.5 + 40 1.5 - 2.25) m2= (75 + 60 - 2.25) m2= 132.75 m2 Answer
19) The angle of elevation of a watch tower at a point on the ground is 60 0. If moved back 18m, the
angle of elevation becomes 450. What is the height of the watch tower?
Solution: Let us draw the required picture:

Here, AB is the height of the watch tower AB = h

For

√
For

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Career Aid for Bank & BCS Math

( )
√
(√ ) √
√
√

20) In a square field of side 30 meters, 4 cows are grazing the field as they are tied at each of the four
corners with a 14 meter long rope for each cow. What is the ungrazed area in the field?
[Combined Officer gen-22]
Solution:

Given, One side of the square = 30 m

Area of the square (30)2 m² = 900 m²
Area covered by the 4 cows in the field m²
Ungrazed area = 900-616=284 m² (Answer)
21) A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of
the smaller cubes have paint on exactly 2 sides? [GIB PO-22]
Solution: A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2.
This means , we get a 3 x 3 x 3 cube
To get the the sides with just 2 faces painted, picture the edges of the each of the sides of the cube.
Apart from the corners (which have 3 faces painted), all other small cubes have 2 faces painted.
In total, we have 12 cubes of side 2 with exactly 2 sides painted
Answer: 12
22) If the length of the two sides of a trapezoid are 4cm and 7cm and height of the trapezoid is 7cm,
calculate the area of the trapezoid. [Combined Officer cash-22]
Solution:
We know, area of the trapezoid = distance of the two parallel line x Sum of the both sides
Here, assuming, distance of the two parallelline = 7cm
Required area = x7x (4+7)= 38.5cm² (Answer)
23) If the area of a certain square (expressed in square meters) is added to its perimeter (expressed
in meters), then the sum is 77. What is the length of a side of the square? [ Combined Officer gen-
22]
Solution: Let, one side of the square is x meter
Perimeter of the square is 4x meters
According to question
x2 + 4x = 77
x2 + 4x - 77 = 0
x2+11x-7x-77=0
x(x+11)-7(x+11) = 0
(x + 11)(x - 7) =0
Here, x = -11 which is not acceptable.
So, x-7=0, x=7
A side of the square 7 meters (Answer).
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Career Aid for Bank & BCS Math
24) Faiyaz and Ehan are standing 90 yards apart on a north-south axis. Faiyaz walks 70 yards to west,
Ehan walks 50 yards to the east, and then both stop. What is the straight-line distance in yards
between them now? [Combined Officer cash-22]
Solution: Let, us depict the image according to question:

Now, Faiyaz stands at point A and Ehan stands at point C.

Here, direct distance between them is AC
ABC is a right angle triangle where AC = Hypotenuse
So, Applying Phthagorean theorem, we get
AC2 = AB2 + BC2=(50+70)2+902=14400+8100 =22500 =1502
AC=150
Hence, The straight distance between Faiyaz and Ehan is 150 yards. (Answer)
25) A hall, whose length is 16 meters and breadth twice its height, takes 168 meters of paper, which
is 2 meters wide, for its four walls. Find the area of the hall.
Solution:
length = 16 meter
Let height = h meter
breadth = 2h meter
Area of the four walls = 2(l + b)h = 168 × 2
=> (l + b)h = 168
=> (16 + 2h)h = 168
=> 2h2 + 16h - 168 = 0
=> h2 + 8h - 84 = 0
=> (h + 14)(h - 6) = 0
=> h = 6 meter
breadth = 2h = 2 × 6 = 12 meter
Area of the hall = lb = 16 × 12 = 192 square meter
Answer 192 square meter
26) In the figure below, AB is perpendicular to BC and BD = DC . If √ cm and AC = 4 cm, then
what is the value of BC?[Bangladesh Krishi Bank-2011] [SIBL MTO-2010][BB AD-2022]

Solution: Given, AB is perpendicular to BC

Applying Phthagorean theorem, we get

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Career Aid for Bank & BCS Math

√
Now,
√
27) The area of rectangle 24 is divided with three non-overlapping squares. What is the
longest side of rectangle? [AIBL PO-22]
Solution
Let, each side of the square = x unit
According to the question
3×x² = 24
Or, x² = 8
Or, x = √8 = 2√2
Now, longest side of the rectangle
= 3×2√2 = 6√2 unit
Answer 6√2 unit
28) If the perimeter of an isosceles right triangle is (6+3√2) meter, then what is the area of
the triangle? [Combined SO -23]
Solution
As right angle isosceles triangle
So base=height,
Say, base=height=x
By Pythagorean theorem
6+3√2
Hypotenuse =√(x2+x2)=√2x
Now perimeter= x+x+√2x=6+3√2 a
=>2x+√2x=6+3√2
=>x(2+√2)=3(2+√2)
So x=3
Hence, Area= = 4.5 m2 a
Answer 4.5 m2
29) The figure shows a circular flowerbed, with its center at O having radius of 8 feet. The flowerbed
is surrounded by a circular path, which is 3 feet wide. What is the area of the path in square feet?
[BB Engineers-23]
Solution

The radius of the bigger circle is 8 + 3 = 11 feet,

thus its area is = πr2 = π×112 = 121π sq feet
The radius of smaller circle is 8 feet.
The area of the smaller circle is = πr2 = π×8 2 = 64π sq feet
The difference is = (121-64)π =57π sq feet
Answer 57π sq feet
30) The length and width of a garden is 60 meter and 20 meter respectively. Inside the garden,
there is a 5 meter-wide path around it. What is the area of the path in square meter? [BB
Officer-22]
Solution

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Career Aid for Bank & BCS Math

Area including path = 60 × 20 = 1200 sq. m.

Length without path = 60 ‒ (5×2) = 50 m
Width without path = 20 ‒ (5×2) = 10 m
Area without path = 50 × 10 = 500 sq. m.
Area of the path = 1200 - 500 = 700 sq. m.
Answer 700 sq. m
31) The diagonal and the area of a rectangle are 25 meters and 168 square meters respectively.
Calculate the length and width of the rectangle? [Combined Officer gen-22]
(answer: 24 m & 7 m)
32) The angels of a triangle are in the ratio of 2 : 3 : 4. What is the value of the largest angle (in
degrees ) in the triangle? [Premier TJO-22]
(answer: 800)
33) A square is inscribed inside a circle. What is the area of the square, if the radius of the circle is 10 cm?
[Answer:200 CM]
34) ABCD is a square and one of its sides AB is also a chord of the circle as shown in the figure. What is the
area of the square?[Answer: 18 Square Unit]
35) ABC is triangle in which AB = 3cm , BC = 5 cm and AC = 4 cm. AD is a perpendicular from A to BC. Find the
lenght of AD. [Modhumti PO-16] [Ans: 2.4cm]