A tank is fitted with 2 taps , first tap can completely fill the tank
in 45 minutes and second tank can empty the full tank in 1 hour. If both the taps are opened alternatively for one minute, then in how many hours empty tank will be filled completely ?
Let the capacity of the tank = X
Time taken by tap first to fill the tank 45 minutes .
So tape first takes 45 minutes to fill tank of X litres ,
Volume of water filled in 1 minute = x / 45 L.
Tape Second takes 60 minutes to empty the tank of X litres .
Volume emptied in one Minute = x / 60
Therefore the volume of water filled in opening tap one for a minute then closing it (tap first )and opening of tap second for a minute = x/ 45 - x/ 60
Let the total time taken to fill the tank by alternatively opening and closing of tape first and second tap = t minutes ,
volume filled in t minutes = capacity of tank
t (x /45 - x/60) = x
t (60x - 45x ) / 60*45 = x
t (15 x ) = 2700 x
t = 2700 /15
t= 180 minutes .
t = 3 hours
Hope this helps you.