Question

Inlet pipe can fill 50% of tank in 2 hours and drain pipe can empty 75% of tank in 6 hours. When will the tank be filled if both pipes are opened together?
1. 4 hours
2. 12 hours
3. 6 hours
4. 10 hours
5. 8 hours

Answer 1

Correct Answer - Option 5 : 8 hours

Given:

Inlet pipe = 50% in 2 hours

Drain pipe = 75% in 6 hours

Formula used:

1/T = (1/T1) - (1/T2)

Here, T1 = Tank filled in hours,  T2 = Tank emptied in hours

Calculation:

Inlet pipe = 50% in 2 hours

⇒ In order to fill full tank inlet pipe = 2 × (100/50)

⇒ Inlet pipe fills tank in 4 hours

Drain pipe = 75% in 6 hours

⇒ Time taken to drain full tank = 6 × (100/75)

⇒ Time taken to drain full tank = 6 × (4/3)

⇒ Time taken to drain full tank= 8 hours

Now,

⇒ 1/T = (1/4) – (1/8)

⇒ 1/T = (2 – 1)/8

∴ It will take 8 hours to fill the tank if both pipes are opened