Bank Math Master

Question: A solid iron cube of 4m length is converted into a wire of 100m length. the circumference of the wire is- 

Solution: 
the volume of the cube is = 4³ m³
= 64 m³

the volume of the wire will be same as the cube.
let,
the radius of the wire is = r 
∴ πr² × l = 64
⇒ r² = 64/(3.1416 × 100)
⇒ r² = 0.2037
⇒ r = 0.4513

∴ circumference = 2πr
= 2 × 3.1416 × 0.4513
= 2.835m

Question: 15 machine can produce 30 phones in 30 seconds. How much time will 75 machines take to produce 150 phones?

Solution:
15 machine 30 phones 30 sec
1 machine 1 phone = (15 × 30)/30 sec
75 machines 150 phones = (15 × 30 × 150)/(30 × 75)
= 30 sec

Question: 125 small sphere balls are formed from a big ball with radius 25cm. What will be the surface area of a small ball?

Solution: 
converting a big sphere ball to 125 small balls,
the volume will be the same for both case.
let, 
small ball radius = r
given, big ball radius, R = 25cm

∴ (4/3)πR³ = 125 × (4/3)πr³
⇒ R³ = 125 × r³
⇒ R = 5 × r
⇒ r = 25/5
r = 5cm

∴ total surface area of a small ball is 
a = 4πr²
= 4 × 3.1416 × (5)²
= 314.16 cm²

Question: A cube of dimension a fits perfectly in a hollow spherical ball. What is the total surface area of that ball?

Solution: 
here,
the lenght of the cube is = a
∴ Diagonal of the cube is = √3a

as the diagonal of the cube is equal to the diameter of the ball,
2r = √3a
r = √3a/2

∴ the total surface area of the ball is = 4πr²
= 4π(√3a/2)²
= 3πa²

Question: If 2 tables and 3 chairs cost Tk. 4800 and 3 tables and 2 chairs cost Tk. 5700, then how much does a table cost?

Solution:
Let
The cost of a table and that of a chair be Tk. x and Tk. y respectively.

Then,
2x + 3y = 4800................(i)
and
3x + 2y = 5700................(ii)

(ii)× 3 - (i) × 2 ⇒
9x + 6y - 4x - 6y = 17100 - 9600
5x = 7500
x = 1500

The cost of a table Tk. 1500

Question: The curved surface area of a cone is 47.124m² and radius is 3m. What is the volume of that cone?

Solution: 

let,
height = h
slant height = l

we know,
curved surface area is = πrl
∴ πrl = 47.124
l = (47.124)/ (3.1416 × 3)
l = 5

l² = r² + h²
h² = l² - r²
h² = 5² - 3²
h = 4

∴ volume, V = (1/3)πr²h
= (1/3) × 3.1416 × (3)² × 4
= 37.699 m³

question: In a school, there is a meal for 150 teachers or 250 students. If 180 students have taken the meal, how many teachers will be able to do with remaining meal?

Solution:
here,
250 students  = 150 teachers.
if 180 students have taken their meal.
the ramaining meal will cover = (250 - 180) = 70 students

∴ 70 students are equal to = (70 × 150)/250 teachers
= 42 teachers

Question: A cylinder of 2m radius and 5m length can store water of - 

Solution: 
here,
r = 2m
h = 5m

volume = πr²h
= 3.1416 × (2)² × 5
= 62.832 m³

we know, 
1 m³ = 1000 liters
∴ 62.832 m³ = (62.832 × 1000) liters
= 62832 liters

Question: 24 men can complete a piece of work in 24 days. In how many days can 36 men complete the same piece of work ?

Solution: 
24 men can do in 24 days
1 man can do in = (24 × 24) days
36 men can do in = (24 × 24)/36 days
= 16 days

Question: The external and internal diameters of a hemispherical bowl are 10 cm and 8 cm respectively. What is the total surface area of the bowl?

Solution: 

here,
R = 5cm
r = 4cm

total surface area:
S = 2πR² + 2πr² + π(R² - r²)
= 2πR² + 2πr² + πR² - πr²
= 3πR² + πr²
= π {3 × (5)² + (4)²}
= (22/7) (75 + 16)
= (22/7) × 91
= 286 cm²

Question: If 8 persons working 10 hours a day earn Tk. 12000 per week, then 6 persons working 14 hours a day will earn per week ?

Solution: 
8 persons working 10 hours = 80 working hours
6 persons working 14 hours = 84 working hours

80 working hours = 12000 Tk
∴ 84 working hours = (84 × 12000)/80 Tk
= 12600 Tk.

Question: If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?

Solution: 
12 carpenters, working 6 hours for 24 days makes (12 × 6 × 24) or, 1728 working hours.
18 carpenters working 8 hours for 36 days makes (18 × 8 × 36) or, 5184 working hours.

1728 working hours = 460 chairs
∴ 5184 working hours = ( 460 × 5184 ) / 1728 chairs
= 1380 chairs

Question: A tank with a length of 3m and width of 2m can store 9000 liters. The height of the tank is?

Solution: 
Let,
 the height of the tank is h
here,
length, l = 3m
width, b = 2m 

volume, V = l × b × h
= 3 × 2 × h 
= 6h m³
as, 1m³ is equal 1000 liters
∴ (6h × 1000) = 9000
6h = 9
h = 1.5m

Question: A wall of 100 meters can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 meters ?

Solution: 
7 men in 10 days can do 100m
1 man in 1 day can do (100/70)m 
14 men in 1 days can do (100 × 14)/70 m
= 20m 

10 women in 10 days can do 100m
1 women in 1 days can do (100/100)m
20 women in 1 days can do (100 × 20)/100m
= 20m

14 men and 20 women in one day can do = 20 + 20 m
= 40m

40m can be done in 1 days
1m can be done = (1/40) days
600m can be done = (600/40) days
= 15 days

Question: If the total length of diagonals of a cube is 12 cm, then what is the total surface area of the cube ?

Solution: 
a cube has 4 diagonals
∴ Length of a diagonal
= (12/4)cm
= 3cm
Let the length of each edge of the cube is = a cm
Then,
a√3 = 3
⇒ a = 3/√3
⇒ a = √3

∴ Total surface area of the cube
= 6a²
= 6(√3)²
= 18cm²

Question: If 5 workers can collect 60 kg wheat in 3 days, how many kilograms of wheat will 8 workers collect in 5 days ?

Solution: 
5 workers 3 days collection = 60 kg
1 worker 1 day collection = (60/15) kg
8 workers 5 days collection = ( 60 × 40 ) / 15 kg
= 160 kg

Question: 9 men bind 1800 books in 20 days. Find how many binders will be required to bind 1200 books in 24 days?

Solution: 
To bind 1800 books in 20 days binders needed 9 men 
To bind 1 books in 1 days binders needed 180/1800 men 
To bind 1200 books in 24 days binders needed (180 × 1200)/(1800 × 24) men
= 5 men

Question: The ratio of total surface area to curved surface area of a cone whose radius is 7cm and height 24 cm, is - 

Solution: 
the slant height of the cone is l = √(r² + h²)
l = √(7² + 24²)
l = 25
Total surface area : curved surface area
= (πrl + πr²) : πrl
= (l + r) : l
= (25 + 7) : 25
= 32 : 25

Question: What is the wet surface area of a cistern of 8m in length, 4.5m in width, and 3.5m in height?

Solution: 
here,
l = 8m
b = 4.5m
h = 3.5m 
total surface area is = 2 ( lb + bh + lh )
= 2 {(8 × 4.5) + (4.5 × 3.5) + (8 × 3.5)}
= 2 (36 + 15.75 + 28)
= 159.5 m²

one of the surface is unwet, 
unwet area = 8 × 4.5 = 36m²

∴ Wet surface area = 159.5 - 36
= 123.5 m²