Question: 1 -

Three pipes A, B and C can fill a cistern in 8 minutes,12 minutes and 16 minutes respectively. What is the time taken by three pipes to fill the cistern when they are opened together?

4.5 minutes

3.7 minutes

5 minutes

4 minutes

Answer:

3.7 minutes

Solution:

Part of the tank filled by A in one minute = 

Part of the tank filled by B in one minute = 

Part of the tank filled by C in one minute = 

Net part of the tank filled by A+B+C in one minute;

=  +  + 

=

 Part of the cistern is filled in one minute.

∴ The whole tank will be filled in  = 3.7 minutes

Question: 2 -

A tank can be filled in 10 hours. After a leak in its bottom, it takes 12 hours to fill the tank. Find the time taken by the leak to empty the full tank?

55 hours

50 hours

45 hours

60 hours

Answer:

60 hours

Solution:

Part of the tank filled in one hour before the leak = 

Part of the tank filled in one hour after the leak = 

Part of the tank emptied in one hour by the leak =  - 



 part of tank will be emptied in one hour by the leak

∴ The full tank will be emptied by the leak in 60 hours.

Solution 2:

Apply formula; = 

X = 10 hours

Y = 12 hours

∴  = 60 hours

Question: 3 -

Two pipes can fill a tank in 6 hours and 8 hours respectively. A third pipe can empty the same tank in 12 hours. If all the pipes start working together, how long it will take to fill the tank?

4.5 hours

4.8 hours

4 hours

5.2 hours

Answer:

4.8 hours

Solution:

Part of the tank filled by two pipes in one hour =  + 

Part of the tank emptied by the third pipe in one hour = 

∴ Net part of the tank filled in one hour =  +  - 

= 

 Part of tank can be filled in one hour

∴ The whole tank will be filled in  = 4.8 hours

Question: 4 -

A pipe can fill a tank in 6 hours and another pipe can empty the tank in 12 hours. If both the pipes are opened at the same time, the tank can be filled in

14 hours

16 hours

12 hours

10 hours

Answer:

12 hours

Solution:

Part of the tank filled in one hour =
Part of the tank emptied in one hour =

Net part of the tank filled in one hour;

= - 



 Part of the tank can be filled in one hour.

∴ The tank will be filled completely in 12 hours.

Solution 2:

Apply formula; = 

X = 6 hours and Y = 12 hours

∴  = 12 hours

Question: 5 -

Two pipes can fill a tank in 10 and 14 minutes respectively. A third pipe can empty the tank at the rate of10 liters/minute. If all the pipes working together can fill the empty tank in 8 minutes,what is the capacity of the tank?

210 liters

215.4 liters

220 liters

225.4 liters

Answer:

215.4 liters

Solution:

Let the capacity of the tank is X liters.

Part of the tank filled by two pipes in one minute = 1/10 + 1/14

10 liters is emptied in 1 minute

X liters will be emptied in X/10 minutes

In X/10 minutes the whole tank will be emptied.

In one minute 10/X part of the tank will be emptied.

As per question;