Bank Math Master

Question: A and B can make a dam in 3 day's. B alone can make the dam in 6 day's. In how many days A alone can make the dam?

Solution:
A's 1 day's work = ( 1/3 - 1/6 ) = 1/6
∴ A alone can make the dam in 6 day's.

Question: A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

Solution:
(B+C) 2 day's work:
2 × ( 1/20 + 1/30 )
= 2 × (3+2)/60
= 1/6 part

Remaining work
= 1−1/6
= 5/6 part

A's one day's work
= 1/18 part

Time taken to complete the work
= (5/6) / (1/18) days

Hence,
Time taken to complete the work
= 5/6×18
=15 days

Question: There is a provision of food in fort for 800 soldiers for 40 days. After 10 days, 200 soldiers leave the fort. Remaining food will last for how many days? 

Solution:
After 10 days 200 soldiers leave the fort.
So, remainig days (40-10)= 30 days
& remaing soldiers (800-200)= 600 soldiers

Now,  800 soldiers can have the food for 30 days
             1  soldier can have the food for 800×30 days
           600 soldiers can have the food for (800×30)/600 days = 40 days
Hence the remaining food will last for 40 days.

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is- 

Solution:
Let, A alone takes x days and B alone takes 3x days to complete the work.

According to the question,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A takes 20 days and B takes ( 3 × 20) = 60 days 

Now, ( A+B )'s 1 days work = (1/20) + (1/60)
= 4/60
= 1/15 

∴ A & B together can do the work in 15 days.

Question: A can do a piece of work in 8 days working 12 hours per day. If B is two-thirds as efficient as A, then in how many days B alone do the same piece of work, working 4 hours per day?

Solution:
Time taken by A alone to do the work = 8×12 = 96 hrs.
 Since B is 2/3 efficient as A, so time taken by B is 3/2 times of A = ( 96×3/2 ) hrs = 144 hrs.
∴ Required days = ( 144/4 ) = 36 days.

Question: Rajib can do a work in 5 days while Farez can do the same work in 3 days. Both of them finish the work together and get Tk. 240. What is Rajib's share?

Solution:
Rajib's wages : Farez's wages = Rajib's 1 day's work : Farez's 1 day's work 
= 1/5 : 1/3
= 3 : 5

Sum of the ratio = 3 + 5 = 8

So, Rajib's share = (3/8) × 240 = Tk. 90

Question: 30 women can do a work in 15 days. 18 men can complete the same work in 10 days. What is the ratio between the capacity of a man and a woman?

Solution:
( 30 × 15 ) women can complete the work in 1 day
1 woman's 1 day's work = 1/450

( 18 × 10 ) men can complete the work in 1 day
1 man's 1 day's work = 1/180

 So, required ratio = 1/180 : 1/450
 = 1/2 : 1/5 
= 5 : 2

Question: A building contractor undertook to finish a certain work in 162 days and employed 150 men. After 72 days, he found that he already done 2/3 of the work. How many men can be discharged now, so that the work finish in time?

Solution:
2/3 of the work done in 72 days by 150 men
∴ Day remaining = 162 - 72 = 90 days

Work remaining = 1- (2/3) = 1/3

In 72 days 2/3 of the work can be done by 150 men
In 1 day 1 of the work can be done by (150 × 3 × 72)/2 men
In 90 days 1/3 of the work can be done by = (150 × 3 × 72)/(2 × 3 × 90) men
= 60 men

∴ The number of men can be discharged = 150 - 60 = 90 men

Question: Two pipes A and B can fill a tank in 10 and 15 minutes respectively. If both the pipes are used together, how long will it take to fill the tank? 

Solution:
Part filled by A in 1 min = 1/10
Part filled by B in 1 min = 1/15 
Part filled by ( A + B ) in 1 min = ( 1/10 + 1/15 ) = 5/30 = 1/6 
∴ Both the pipes can fill the tank in 6 minutes.

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to to fill the tank. The leak can drain all the water of the tank in?

Solution: 
Work done by the leak in 1 hour
 = ( 1/2 − 3/7 ) = 1/14

∴ Leak will empty the tank in 14 hours

Question: A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time to fill the cistern completely?

Solution:
Time is taken to fill half of the tank = 1/2 ×16 = 8 hrs
In 1 hour pipe can fill = 1/16 part filled by 4 pipes in1 hour = 4 × 1/16 = 1/4 part
So, remaining half part = 4 × 1/2 = 2 hours
∴ Total time = 8 +  2 = 10 hours

Question: A leak in the bottom of a tank can empty the whole tank in 6 hours. An inlet pipe fills water are the rate of 5 liters a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 10 hours. How many liters does the tank hold? 

Solution:
Work done by the inlet pipe in 1 hour = ( 1/6 - 1/10 ) = 2/30 = 1/15
Work done by the inlet pipe in 1 minute = ( 1/15 × 1/60 ) = 1/900
 Volume of 1/900 part = 5 liters
 Volume of the whole tank = ( 900 × 5 ) = 4500 liters

Question: Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off, so that the cistern be fill in 24 minutes?

Solution:
P can fill the cistern in 36 minutes
So in 1 min P can fill the cistern = 1/36 th part
In 24 min, P can fill the cistern = 24/36 = 2/3 rd
Remaining part = 1- 2/3 = 1/3 rd
As Q can fill full cistern in 48 minutes
So it will fill 1/3 rd part in = ( 1/3 × 48) = 16 minutes.

Question: A cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time the cistern will get filled?

Solution:
The cistern fill in 1 hour = ( 1/6 ) - ( 1/9 ) part = 1/18 part
The cistern fill 1/18 part = 1 hour 
The cistern fill full = ( 1 × 18 ) /1 hour = 18 hours

Question: A outlet pipe can empty a cistern in 8 hours. In what time will it empty 1/2 part of the cistern?

Solution:
The outlet pipe empties one complete cistern in 8 hours.
Time taken to empty (1/2) × 8 = 4 hours

Question: Two pipes A and B can fill a pool in 3 hours and 6 hours respectively. If both pipes work together, how long it will take to fill the pool?

Solution:
A can fill in 1 hour = 1/3 part
B can fill in 1 hour = 1/6 part 
Both pipe in 1 hour can fill = ( 1/3 + 1/6 ) = 3/6 = 1/2 part  
Again, 1/2 part can be filled in 1 hour 
∴ 1 part ( full ) can be filled in 2 hour

Question: A pipe can fill up an empty tank in 12 minutes, Another pipe flows out 8 liters of water per minute. If the two pipes are opened together and the empty tank is filled up in 84 minutes. How much water does the tank contain? 

Solution:
Let the tank empty in x minute

According to the question, 
 (1/12) - (1/x) = 1/84
⇒ (1/12) - (1/84) = 1/x
⇒ 6/84  = 1/x
⇒ x = 84/6 
⇒ x = 14 

The tank emptied by the other pipe in 14 minute

∴ The tank contain = 14 × 8 = 112 liter