Question

Two taps T₁ and T₂ can fill a tank in 2 hours and 3 hours respectively. If an outlet tap T₃ is opened, then all three can together fill the tank in 6 hours. How much time will tap T₃ take to empty the completely filled tank?
1. 3 hours
2. 3/2 hours
3. 4 hours
4. 2 hours

Answer 1

Correct Answer - Option 2 : 3/2 hours

Given:

T₁ fill the tank = 2 hours 

T2 fill the tank = 3 hours 

T₃ is outlet tap

All together fill tank = 6 hours

Concept used:

The efficiency of outlet pipe negative 

Calculation:

Let the tap T₃ empty the tank in x hours

The tank fill in an hour by T1 = 1/2 

The tank fill in an hour by T₂ = 1/3

The tank empty in an hour by T₃ = - (1/x)

All together fill the tank in an hour = 1/6

⇒ (1/2) + (1/3) - (1/x) = (1/6)

⇒ (5/6) - (1/x) = (1/6)

⇒ 1/x = 2/3

⇒ x = 3/2

∴ The tap T3 empty the completely filled tank in 3/2 hours