Bank Math Master

Question: A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left is-

Solution:
Man’s 1 day’s work = 1/20
Woman’s 1 day’s work = 1/15

(Man + woman)’s 1 day’s work = (1/20 + 1/15)  = 7/60
(Man + woman)’s 5 day’s work = (7/60 × 5) = 7/12

Thus, Remaining work = 1 - 7/12 = 5/12

Question: Two pipes A and B can fill a tank separately in 12 and 16 hours respectively. If both of them are opened together when the tank is initially empty, how much time will it take to completely fill the tank?

Solution:
Part of tank filled by pipe A in one hour working alone = 1/12
Part of tank filled by pipe B in one hour working alone = 1/16

∴ Part of tank filled by pipe A and pipe B in one hour working together = (1/12) + (1/16) = 7/48
Therefore, time taken to completely fill the tank if both A and B work together = 48/7 hours  

Question: Compute the total surface area of the cylinder, with a radius of 5cm and height of 10cm?

Solution:
Since, we know, 
Total surface area of a cylinder, A = 2πr(r + h) square units

Therefore, A = 2π × 5(5 + 10) = 2π × 5(15) 
= 2π × 75 = 150 × 3.14 
= 471 cm²

Question: If 30 oranges cost Tk. 210, how much does 10 oranges cost?

Solution:
The cost of 30 oranges 210
Unit value (cost of 1 orange) = 210/30 = 7

The cost of 10 oranges = (7 × 10) = 70

Question: L can finish a work in  16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.

Solution:
(L + M + N)’s 1 day’s work =1/4
L’s 1 day’s work = 1/16
M’s 1 day’s work = 1/12

Therefore, N’s 1 day’s work 
= 1/4 - (1/16 + 1/12)
= 1/4 - 7/48 = 5/48

 So, N alone can do the work in 48/5 days.

Question: Three pipes A, B, and C are connected to a tank. Out of the three, A is the inlet pipe and B and C are the outlet pipes. If opened separately, A fills the tank in 10 hours, B empties the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?

Solution:
Part of tank filled by pipe A in one hour working alone = 1/10
Part of tank emptied by pipe B in one hour working alone = 1/12
Part of tank emptied by pipe C in one hour working alone = 1/30

∴ Part of tank filled by pipes A, B and C in one hour working together = (1/10) - (1/12) - (1/30) =  - (1/60)
Therefore, time taken to completely empty the tank if all pipes are opened simultaneously = 1/60 hours = 60 hours

Question: What is the volume of a cylindrical shape water container, that has a height of 7cm and diameter of 10cm?

Solution: 
Given,
Diameter of the container = 10cm
Thus, radius of the container = 10/2 = 5cm
Height of container = 7cm

As we know, from the formula,
Volume of a cylinder = πr²h cubic units.

Therefore, volume of given container, V = π × 5² × 7
V = π × 25 × 7 = (22/7) × 25 × 7 = 22 × 25
V = 550 cm³

Question: A recipe requires 2 cups of flour for 8 cupcakes. How many cups of flour are needed for 12 cupcakes?

Solution:
We know the amount of flour required for 8 cupcakes (2 cups).
Flour per cupcake = Total flour/Number of cupcakes = 2 cups/8 cupcakes = 0.25 cups per cupcake.

We need to find the flour for 12 cupcakes.
Flour Required = Unit value(flour per cupcake) × Number of cupcakes
Flour Required = 0.25 cups/cupcake × 12 cupcakes = 3 cups.

Question: P, Q and R can do a job in 20, 30 and 60 days respectively. In how many days can P do the job if he is assisted by Q and R every third day?

Solution:
P’s 2 day’s work = 2/20 = 1/10
(P + Q + R)’s 1 day’s work  = (1/20 + 1/30 + 1/60) = 6/60   = 1/10
Job done in 3 days = (1/10 + 1/10) = 1/5

Now, 1/5 jobs is done in 3 days
Whole job  will be done in (3 × 5) = 15 days.

Question: A cistern has two pipes. Both working together can fill the cistern in 12 minutes. First pipe is 10 minutes faster than the second pipe. How much time would it take to fill the cistern if only second pipe is used?

Solution:
Let the time taken by first pipe working alone be ‘t’ minutes.
Time taken by second pipe working alone = t + 10 minutes.

Part of tank filled by pipe A in one hour working alone = 1/t
Part of tank filled by pipe B in one hour working alone = 1/(t + 10)

∴ Part of tank filled by pipe A and B in one hour working together = (1/t) + (1/t+10) = (2t + 10)/[t × (t + 10)]
But we are given that it takes 12 minutes to completely fill the cistern if both pipes are working together.
∴ (2t + 10)/[t × (t + 10)] = 1/12
⇒ t × (t + 10)/(2t + 10) = 12
⇒ t² + 10t = 24t + 120
⇒ t² - 14t - 120 = 0
⇒ (t - 20) (t + 6) = 0
∴ t = 20 minutes (Time cannot be negative)

Therefore, time taken by second pipe working alone = 20 + 10 = 30 minutes  

Question: Parimal wants to purchase a cylindrical can with a radius equivalent to 5 inches. The can contains 1 gallon of oil. Find the height of the cylinder. 

Solution:
Volume V is given by= 1 gallon
1 gallon= 231 cubic inches
Radius r = 5 inches

Volume of the cylinder is given by, 
V = πr²h
⇒ 231 = (22/7) × (5)² × h
⇒ (231 × 7)/(22 × 25) = h
∴ h = 2.94 inches.

Therefore, the height is equivalent to 2.94 inches.

Question: If 7 meters of cloth cost Tk. 140, what is the cost of 3 meters of cloth?

Solution:
We know the cost of 7 meters of cloth Tk. 140
Cost per meter = Total cost / Number of meters = 140/7 meters = Tk. 20 per meter.

Cost of 3 meters = Unit value (cost per meter) × Number of meters
= 20 × 3
= 60

Question: M’s efficiency is three times N’s efficiency. M can finish a job in 60 days less than N. If they work together, then in how many days the job will be done.

Solution:
Let the number of days N takes to finish the job be x days. Since M is three times as efficient as N, M will take x/3 days to finish the same job.
It is also given that M can finish the job in 60 days less than N, so-
x/3 = x - 60
⇒ x = 3(x - 60)
⇒ x = 3x - 180
⇒ 0 = 2x - 180
⇒ 2x = 180
∴ x = 90

So, N takes 90 days to do the job.
And N takes (90 ÷ 3) = 30 days to do the job.
M’s 1 day’s work = 1/30
N’s 1 day’s work = 1/90

(M + N)’s 1 day’s work =( 1/30 + 1/90) = 2/45
M and N together can do the job in 45/2 days = 22.5 days.

Question: Three pipes A, B and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours and B fills the tank in 30 hours. If all three are opened simultaneously, it takes 30 minutes extra than if only A and B are opened. How much time does it take to empty the tank if only C is opened?

Solution:
Let the capacity of tank be LCM (10, 30) = 30 units
⇒ Efficiency of pipe A = 30/10 = 3 units/hour
⇒ Efficiency of pipe B = 30/30 = 1 units/hour
∴ Combined efficiency of pipes A and B = 4 units/hour

Therefore, time taken to completely fill the tank if only A and B are opened = 30/4 = 7 hours 30 minutes
∴ Time taken to completely fill the tank if all pipes are opened = 7 hours 30 minutes + 30 minutes = 8 hours
∴ Combined efficiency of all pipes = 30/8 = 3.75 units/hour
Now,
efficiency of pipe C = Combined efficiency of all three pipes - Combined efficiency of pipes A and B
Therefore, efficiency of pipe C = 4 - 3.75 = 0.25 units/hour

Thus, time taken to empty the tank if only C is opened = 30/0.25 = 120 hours.

Question: A water tank has a radius of 40 inches and a height of 150 inches. Find the area.

Solution:
Water tank is cylindrical in nature. 
Total Surface Area of a cylinder is given by,  2πr(h + r)
TSA = 2 × 22/7 × 40(150 + 40)
TSA = 2 × 22/7 × 40 × 190
TSA = 44/7 × 7600
TSA = 334400/7

∴ Area = 47771.4 sq. inches.

Question: A painter needs 5 liters of paint to cover 20 square meters of wall. How much paint is needed to cover 10 square meters?

Solution:
We know the paint needed for 20 square meters (5 liters).
Paint per square meter = Total paint / Area covered = 5 liters / 20 square meters = 0.25 liters per square meter.
Paint needed for 10 square meters = Unit value (paint per square meter) × Area to be covered
= 0.25 liters/square meter × 10 square meters
= 2.5 liters.

Question: Anik alone can do a piece of work in 6 days and Bishal alone in 8 days. Anik and Bishal undertook to do it for Tk. 4800. With the help of Dinesh, they completed the work in 3 days. How much is to be paid to Dinesh?

Solution:
Anik’s 1day work = 1/6
Bishal’s 1 day work = 1/8
(Anik + Bishal + Dinesh)’s 1 day work =1/3

Dinesh’s 1 day work = 1/3 - (1/6 + 1/8) = 1/24
So, Dinesh’s 3 day work = 3 × 1/24 = 1/8

If Dinesh contributed 8th part of work then he will receive 8th part of total payment
∴ 4800 × 1/8 = 600

Question: Time required by two pipes A and B working separately to fill a tank is 36 seconds and 45 seconds respectively. Another pipe C can empty the tank in 30 seconds. Initially, A and B are opened and after 7 seconds, C is also opened. In how much more time the tank would be completely filled?

Solution:
Let the capacity of the tank be LCM (36, 45, 30) = 180 units
∴ Efficiency of pipe A = 180/36 = 5 units/second
Efficiency of pipe B = 180/45 = 4 units/second
Efficiency of pipe C = - 180 / 30 = - 6 units/second

Now,
for the first 7 seconds, A and B were open. 
Combined efficiency of A and B = 5 + 4 = 9 units/second 
∴ Part of the tank filled in 7 seconds = 7 × 9 = 63 units

Part of tank empty = 180 - 63 = 117 units

Now, all pipes are opened.
Combined efficiency of all pipes = 5 + 4 - 6 = 3 units/second
Therefore, more time required = 117/3 = 39 seconds.

Question: Find the volume of the cylinder having a radius of 5 units and a height of 8 units?

Solution:
We have, 
Radius,r = 5 units
Height,h = 8 units

Volume of the cylinder, V = πr²h cubic units.
V = (22/7) × 5² × 8
V = 22/7 × 25 × 8
V = 628.57 Cubic units.

Hence, the volume of the cylinder is 628.57 cubic units.

Question: If 45 students can consume a stock of food in 2 months, then for how many days the same stock of food will last for 27 students?

Solution:
According to the first condition, students consume food in 2 months, i.e. in 60 days.
So this ratio would be 45 : 60

According to the second condition, the same amount of food is consumed by 27 students in x days.
So that ratio would be 27 : x.

By Inverse Proportion,
45 × 60 = 27 × x
⇒ x = (45 × 60) / 27
∴ x = 100