
Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed. The total time taken to fill the tank (in hours) is _____.

 13.50
 16.50
 14.50
 15.50
Correct Option: C
Here,
In 1 hr, part of tank filled by P alone is =  
6 
In 1 hr, part of tank filled by Q alone is =  
9 
In 1 hr, part of tank emptied by R is =  
12 
Initially, P and R opened for 4 hr,
So part of tank filled = 4  1    1  = (4 / 12) = (1 / 3)  
6  12 
After 4 hr, P is closed and for 6 more hr Q and R are opened.
So part of tank filled = 6  1    1  = (1 / 6)  
9  12 
So, total tank filled in 10 hr =  +  =  =  
6  3  12  2 
So, remaining 1/2 part of the tank is filled by Q alone
Now, Q will take 9/2 = 4.5 hr to fill remaining half of the tank.
Hence, total time taken = 4 + 6 + 4.5 = 14.5 hr