Correct Answer - Option 2 : 20
Given:
Pipe A fills in 10 hours
Pipe C empties in 24 hours
Pipes A, B, and C together fill in 40 hours
Concept Used:
Capacity of a tank is LCM of time taken by all pipes to fill and empty the tank.
Efficiency of Pipe = Capacity of a tank/ Time taken to fill the tank
Calculation:
Capacity of a tank is the LCM of 10, 24, and 40
⇒ Capacity of a tank = 120 liters.
Efficiency of Pipe A = 120/10
⇒ Efficiency of Pipe A = 12 liters/hour
Efficiency of Pipe C = 120/24
⇒ Efficiency of Pipe C = 5 liters/hour
Efficiency of Pipe A – B – C(– because B and C empties the tank) = 120/40
⇒ Efficiency of Pipe A – B – C = 30 liters/hour
Putting the values of result (I) and (II), in above equation
⇒ 12 – B – 5 = 3
⇒ 7 – B = 30
⇒ – B = 3 – 7 = – 4
⇒ B = 4 liters/hour
Now B needs to empty 2/3rd of a tank,
⇒ 2/3 × 120
⇒ 80
Time taken by Pipe B,
⇒ 80/4 = 20
∴ Time taken by Pipe B to empty the 2/3rd tank is 20 hours.