Two pipes a and b can fill a tank in 1 hour 12 minutes and 1 hour 30 minutes respectively. Pipe c can empty the tank in 1 hour. Initially pipes a and b are opened and after 14 minutes c is also opened. In how much time will the tank be full? (in min)
Answers
Answer:
Total time taken by the tank to fill will be 92 minutes.
Step-by-step explanation:
Time taken by a to fill the tank = 72 minutes
=> in one minute a can fill = 1/72 of the tank
Time taken by b to fill the tank = 90 minutes
=> in one minute a can fill = 1/90 of the tank
Hence in one minute both can fill,
1/72 + 1/90
= 1/40 of the tank
=> in initial 14 minute both can fill = 14/40 of the tank
=> tank remaining to be filled = 1 - 14/40 = 26/40 of the tank
Time taken by c to empty the tank = 60 minutes
=> in one minute c can empty = 1/60 of the tank
In one minute with all three pipes opened, the amount of tank filled
= 1/72 + 1/90 - 1/60
= 1/40 - 1/60
= 1/120
Hence time taken by whole tank to be filled by all 3 pipe = 120 minutes
=> time taken by 26/40 of the tank tank to be filled by all 3 pipes
= 26/40 x 120
=78 minutes
=> total time taken by the tank to fill = 14 + 78 = 92 minutes.