A tank can be filled by pipe A in 5 hours and emptied by pipe B in 8 hours respectively. How much time will it take for the tank to be half full?

Question: A tank can be filled by pipe A in 5 hours and emptied by pipe B in 8 hours respectively. How much time will it take for the tank to be half full?

Solution:
Pipe alone can fill the tank in = 5 hrs.
Pipe alone can empty the tank in = 8 hrs.
Let, the tank to be half full in x hrs,

ATQ,
x/5 - x/8 = 1/2
⇒ (8x - 5x)/40 = 1/2
⇒ 3x/40 = 1/2
⇒ 3x = (1/2) × 40
⇒ 3x = 20
∴ x = 20/3 hours