Pipe A is a filling pipe, while B and C are emptying pipes. Pipe A alone can fill a tank in 10 hours and pipe B alone can empty two third part of the tank in 20 hours. If all three pipes are opened together, the tank is completely filled in 40 hours. In how many hours can pipe C alone empty two-third part of the tank?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 16.
Given:
Pipe A is a filling pipe, while B and C are emptying pipes.
Pipe A alone can fill a tank in 10 hours and pipe B alone can empty two third part of the tank in 20 hours.
If all three pipes are opened together, the tank is completely filled in 40 hours
Calculations:
B alone empty two third of the tank in 20 hours
B alone empty the whole tank = 20 × 3/2 = 30 hours
Total work (LCM of 10, 30 and 40) = 120 units
Efficiency of A (120/10) = 12 units
Efficiency of B (120/30) = 4 units (negative)
Efficiency of (A - B - C) (120/40) = 3
Efficiency of C (12 - 4 - 3) = 5 units
Two-third part of the tank = 120 × 2/3
⇒ 80 units
Required time = 80/5 = 16 hours