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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 C alone can empty the full tank in 24 hours. If all three pipes are opened together, the tank is completely filled in 40 hours. In how many hours can pipe B alone empty two-third part of the tank?
1. 24
2. 20
3. 18
4. 30

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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.

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