Pipe A can fill the tank in 45 min and pipe B can empty the tank in 1 hour 30 min. If pipe B is opened after 30 min of start of pipe A, what is the total time required to fill the tank?
1). 1 hour
2). 1 hour 10 min
3). 1 hour 20 min
4). 1 hour 30 min
Time require to fill the tank by pipe A = 45 min
Time require to empty the tank by pipe B = 1 hour 30 min = 60 + 30 = 90 min
Amount of tank filled in 30 min by pipe A,
⇒ Amount of tank filled = (1/45) × 30 = 2/3
⇒ Remaining part of tank = 1 - 2/3 = 1/3
For time require to fill the tank,
⇒ (1/45 - 1/90) × t = 1/3
⇒ [(2 - 1)/90] × t = 1/3
⇒ (1/90) × t = 1/3
⇒ t = (1/3) × (90)
⇒ t = 30 min
∴ Total time taken = 30 min + 30 min = 1 hour