Arithmatical  Pipes and Cisterns
DIRECTIONS : Problems based on Pipes&Cisterns.
1. 
Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ? 

A. 2 

B. 2.5 

C. 3 

D. 3.5 
Solution 
part filled by (A+B+C) in 1 hour  = (1/5 + 1/6 + 1/30) 
‹=› 1/3. 
All the three pipes together will fill the tank in 3 hours. 

2. 
A pump can fill a tank with water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in 

A. 5 hours 

B. 7 hours 

C. 8 hours 

D. 14 hours 
Solution 
Work done by the leak in 1 hour  =(1/2  3/7) 
‹=›1/14. 
Leak will empty the tank in 14 hours. 

3. 
Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is 

A. 60 gallons 

B. 80 gallons 

C. 120 gallons 

D. 160 gallons 
Solution 
Work done by the waste pipe in 1 minute 
=1/15(1/20+1/24) 
= (1/1511/20) 
=  1/40  [  ve sigh means emptying] 
Volume of 1/40 part  = 3 gallons. 
Volume of Whole  = (3×40) 
=120 gallons. 

4. 
Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours.If all the three pipes operate simultaneously, in how much time will the tank be filled? 

A. 7 hrs 30 min 

B. 7 hrs 45 min 

C. 8 hrs 30 min 

D. 8 hrs 45 min 
Solution 
Net aprt filled in 1 hour  = (1/10+1/121/20) 
= 8/60 
= 2/15. 
Therefore the tank will be full in 15/2 hours  ‹=› 7 hrs 30 min.


5. 
A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres 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 litres does the cistern hold? 

A. 7580 

B. 7960 

C. 8290 

D. 8640 
Solution 
Work done by the inlet in 1 hour  = (1/8  1/12) 
= 1/24. 
Work done by the inlet in 1 min.  = (1/24 × 1/60) 
= 1/1440. 
Volume of 1/1440 part = 6 litres. 
Therefore, Volume of whole  = (1440×6) 
‹=› 8640 litres. 
