Question

An inlet pipe can fill an empty tank in 20 hours and an outlet pipe can empty the filled tank for 50 hours. If initially, both the pipes are opened then find the total time taken to fill the tank if the outlet pipe is closed when 75% of the tank is filled.  
1. 15
2. 20
3. 30
4. 50 

Answer 1

Correct Answer - Option 3 : 30

Given :

An inlet pipe can fill a tank in 20 hours and an outlet pipe can empty the filled tank 50 hours

Concept used :

Work efficiency = Total work/Total working time

Calculations :

Total work = LCM of 20 and 50 = 100 units 

Inlet pipe per hour work = 100/20 = 5 units 

Outlet pipe per hour work = 100/50 = 2 units 

Total work of both pipes = 5 - 2 = 3 units  (outlet pipe works opposite to inlet pipe)    

Time required to fill 75% filled pipe = 75/3 = 25 hours 

Now time taken by inlet pipe to fill the remaining tank = 25/5 = 5 hours    (outlet pipe ios closed after 75% pipe is filled) 

Total time = 25 + 5 = 30 hours  

∴ Option 3 will be the correct answer.