Bank Math Master

Question: A rectangular water tank is 8 m high, 6 m long and 2.5m wide. How many liters of water can it hold?

Solution:
Volume = length × width × height 
= (6 × 2.5 × 8) m³
= 120 m³ 

1 m³ = 1000 litre
120 m³ = 120 × 1000 litre
= 1,20,000 litre

Question: An outlet pipe can empty a cistern in 5 hours. In what time will it empty 3/5 part of the cistern?

Solution:
The outlet pipe empties one complete cistern in 5 hours
Time taken to empty 3/5 Part of the cistern = (3/5) × 5 = 3 hours.

Question: The cost of the paint is 36.50 Tk. per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint the outside of a cube having 8 feet on each side?

Solution:
Total surface area = 6 × 8² square ft.
∴ total paint needed = (6 × 8²)/16 kg
= 24 kg

Total cost = (24 × 36.5) taka
= 876 Taka

Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

ATQ,
∴1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
∴ x = 35 hours

Question: 66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Solution:
Let, the length of the wire be h
Radius = 1/2 mm = 1/20 cm

ATQ,
πr²h = 66
⇒ (22/7) × (1/20)² × h = 66
⇒ h = (66 × 7 × 20 × 20)/22
⇒ h = 8400 cm
⇒ h = 8400/100 m
∴ h = 84 m

Question: In 1 minute 3/7 of a bucket is filled. The rest of the bucket can be filled in -

Solution:
Filled of the bucket 3/7 part.
Remaining = 1 - (3/7) = 4/7 part.

3/7 part is filled in = 1 min
∴ 1 part is filled in = 7/3 min
So, 4/7 part is filled in = (7/3) × (4/7) min
= 4/3 minutes

Question: A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days since 9 people were absent throughout. How many people were supposed to be working originally?

Solution:
Let,
the total number of people were working originally = x
When 9 people were absent,
Total present workers were = x - 9

x workers can complete it = 24 days.
∴ 1 workers can complete it = 24x days.
∴ (x - 9) workers can complete it = 24x/(x - 9) days.

ATQ,
24x/(x - 9) = 32
⇒ 3x/(x - 9) = 4
⇒ 4x - 36 = 3x
∴ x = 36

The total number of people were working originally 36.

Question: A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is.

Solution: 
The upper part of the calf is open. Here the area of ​​the wetted part is asked.
Therefore, the upper opening has to be excluded from the total area.
Here,
Length = 6 m
Width = 4 m
Height = 1 m 25 cm = 1.25 m

So, the area of total wet surface = 2{(6 × 4) + (4 × 1.25) + (6 × 1.25)} - (6 × 4)
= (2 × 36.5) - 24 
= 73 - 24
= 49 m²

Question: 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?

Solution:
According to the question,
3 men = 5 women
As they complete the same work in the same time
6 men + 5 women
= 6 men + 3 men
= 9 men

If, 3 men do work in 12 days
1 man does a work in 12 × 3
∴ 9 men do work in (12 × 3)/9
  = 4 days

Question: Three men, four women, and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?

Solution:
Let, women's 1 day's work = x
1 man's 1 day's work = x/2
1 child's 1 day's work = x/4

ATQ,
3x/2 + 4x + 6x/4 = 1/7
⇒ (6x + 16x + 6x)/4 = 1/7
⇒ 28x/4 = 1/7
⇒ 7x = 1/7
∴ x = 1/49

1 woman alone can complete 1/49 of the work in 1 day.
So, 1 woman alone can complete the work in 49 days.
To complete the work in 7 days, the number of women required = 49/7 = 7 days.

Question: An aluminum sheet 27 cm long, 8 cm broad, and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be

Solution: 
Volume of cube = Volume of sheet = (27 × 8 × 1) cm³
= (27 × 8) cm³

Length of the cube = a
∴ a³ = (27 × 8)
⇒ a³ = 3³ × 2³
⇒ a = (3 × 2)
∴ a = 6

Surface area of sheet =2(lb + bh + lh)
= 2(27 × 8 + 8 × 1 + 27 × 1) cm²
= 2(216 + 8 + 27) cm²
= 502 cm²

Surface area of cube = 6a² =(6 × 6²) cm²
= 216 cm²

∴ Required difference = (502 - 216) cm²
= 286 cm²

Question: If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

Solution:
Here,
10 men = 20 boys
1 men = 2 boys
8 men = (2 × 8) boys
= 16 boys

If 20 boys can make 260 mats in 20 days,
8 men and 4 boys or, (16 + 4) = 20 boys can make in 20 days = 260 mats.

Question: A rectangular prism has dimensions 12 cm, 8 cm, and 5 cm. Calculate the volume of the prism.

Solution: 
We know 
Volume = length × width × height
= 12 × 8 × 5 cm³
= 480 cm³

Question: If 20 men can build a wall 56 meters long in 6 days, what length of a similar wall can be built by 35 men in 3 days?

Solution:
In 6 days 20 men can build 56 meters
∴ In 1 day 1 man can build 56/(6 × 20) meters.
∴ In  3 days 35 men can build (56 × 35 × 3)/(6 × 20) meters.
 = 49 meters.

Question: A man and a boy can finish a job working together for 4 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?

Solution: 
1 man and 1 boy can do in 1 day 1/4 part
2 man and 2 boy can do in 1 day 2/4 part = 1/2 part

Now 1 man = 2 boys 
(2 + 1) man can do in 1 day is 1/2 part
3 man can do in 1 day is 1/2 part
1 man can do in 1 day is 1/(2 × 3) part = 1/6 part

∴ Man alone can do the work in 6 days.

Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

Solution: 
Here, l = 10m
h = 8m

So, r = √(l² - h²)
= √(10² - 8²)
=√(100 - 64)
= √36
= 6

∴Curved surface area = πrl
= (π × 6 × 10) m² = 60π m²

Question: A leak in the bottom of a tank can empty the whole tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened, and due to the leak, the tank is empty in 12 hours. How many liters does the tank hold? 

Solution:
Work done by the inlet pipe in 1 hour = (1/8 - 1/12) = (3 - 2)/24 = 1/24
Work done by the inlet pipe in 1 minute = (1/24 × 1/60) = 1/1440

 Volume of 1/1440 part = 6 liters
 Volume of the whole tank = (1440 × 6) = 8640 liters

Question: Rajib does 20% less work than Pavel. If Rajib can complete a piece of work in 15/2 hours, then Pavel can do it in

Solution: 
Ratio of times taken by Rajib and Pavel = 100 : 80 = 5 : 4
Let
Pavel takes  x days to do the work 

Here
5 : 4 = (15/2) : x
⇒ 5/4 = (15/2)/x 
⇒ 5x = (15 × 4/2)
⇒ 5x = 30
∴ x = 6 hours

Question: Find the cost of a cylinder of radius 14 m and height 3.5 m when the cost of its metal is Tk. 50 per cubic meter-

Solution:
We know,
The volume of the cylinder = πr²h
= (22/7) × 14 × 14 × 3.5
= 2156 m³

Cost of the cylinder = 2156 × 50
= Tk. 107800

Question: If a photocopier makes 2 copies in 1/3 second, at the same rate how many copies does it make in 4 minutes?

Solution:
Here, 4 minutes = (4 × 60) seconds = 240 seconds

In 1/3 second he can make 2 copies 
In 1 second he can make (2 × 3) copies = 6 copies
∴ In 240 seconds he can make (6 × 240) copies
= 1440 copies

Question: A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 4 cm to form a cone. What is the volume of the cone so formed?

Solution:

Given that, radius, r = 3 cm and height, h = 4 cm
Therefore, volume, V = (1/3) × πr²h
= (1/3) × π × 3² × 4
= 12π cm³

Question: Mr. Mohit moved 2/3 of his lawn in 4/3 hours. Mr. Akil makes twice a fast and finishes the remaining job. How many minutes did Mr. Akil work? 

Solution: 
2/3 of work is done in 4/3 hours 
Full work is done in (4/3) × (3/2) hours = 2 hours 
∴ Work left = 1 - (2/3) = 1/3 part

Akil can complete the work in = 2/2 hours = 1 hour
Akil can do 1/3 part of the work in = 1/3 hour
= (1/3) × 60 minutes 
= 20 minutes