Two pipes A and B can fill a tank with water in 30 minutes and 45 minutes respectively. The third pipe C can empty the tank in 36 minutes. First A and B are opened. After 12 minutes C is opened. Total time (in minutes) , in which the tank will be filled up is:

Correct Answer: 24 min

 

 

A…..(+)30 minutes

 

B…..(+)45 minutes

 

c…..(−)36 minutes

 

Water filled by (A+B) in 12 mm

 

= 12×(6+4)

 

= 12×10=120 litre

 

Remaining capacity

 

= 180−120=60 litre

 

After 12 min. emptied pipe C is also opened

 

Total capacity (A+B−C)=(6+4−5)=5 l./m.

 

Time taken by (A+B−C) with capacity 5 l./m. to fill the remaining part

 

=60/l./5 l/m.=12min

 

Therefore, total time in which the tank will be filled up is

 

= 12+12=24 minutes.