Two pipes A and B can fill a tank in 20 and 30 hours, respectively. Both pipes are opened to fill the tank, but when the tank is
one-third full, a leak develops through which one-fourth of the water supplied by both pipes goes out. Find the total time (in
hours) taken to fill the tank.

Question

Accepted Answer

Step 1: Calculate the rate of filling by each pipe.  
- Pipe A fills the tank in 20 hours, so rate of A = 1/20 tank per hour.
- Pipe B fills the tank in 30 hours, so rate of B = 1/30 tank per hour.

Step 2: Combined rate when both pipes are open without leak:   
= 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12 tank per hour.
 
Step 3: Time to fill one-third of the tank without leak:         
= (1/3) / (1/12) = (1/3) * 12 = 4 hours.

Step 4: After the tank is one-third full, a leak develops causing one-fourth of the water supplied to go out.

Effective water filling rate after leak:    
- Water supplied by pipes = 1/12 tank per hour.
- Leak causes loss of 1/4 of this water, so effective filling = 3/4 * (1/12) = 1/16 tank per hour.

Step 5: Remaining tank to fill = 1 - 1/3 = 2/3.

Time to fill remaining 2/3 with leak:    
= (2/3) / (1/16) = (2/3) * 16 = 32/3 = 10 2/3 hours.

Step 6: Total time = time before leak + time after leak  
= 4 + 10 2/3 = 14 2/3 hours.

Therefore, the total time taken to fill the tank is 14 2/3 hours.

Answer

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