Correct Answer - Option 2 : 5 hr
Given:
Pipe S can fill the tank alone in 6 hr
Pipe T can fill the tank alone in 4 hr
Concept used:
Let, Pipe A can fill a tank in x hrs
⇒ Pipe A can fill a tank in 1 hr = 1/x
Calculation:
Pipe S fill the tank in 1 hr = 1/6
Pipe T fill the tank in 1 hr = 1/4
Pipe (S + T) fill the tank in 2hrs when opened alternatively = (1/6) + (1/4) = 5/12
Pipe (S + T) fill the tank in 4hrs when opened alternatively = 2 × (5/12) = 10/12 = 5/6
⇒ Remaining part = (1 - 5/6) = 1/6
Now, it is S’s turn 1/6 part is filled by S in 1 hr
So, total time = (4 + 1) hours = 5 hours
∴ The time to fill the tank is 5 hours.