Question

Pipe A and pipe B can fill a tank alone in 6 and 8 hours respectively and pipe C can empty the same tank in 12 hours. If all three pipes are opened at the same time then in how many time the tank will be filled?
1. 4 hours 36 minutes
2. 4 hours 12 minutes
3. 4 hours 48 minutes
4. 3 hours 48 minutes

Answer 1

Correct Answer - Option 3 : 4 hours 48 minutes

Given:

Pipe A and pipe B can fill a tank alone in 6 and 8 hours respectively and pipe C can empty the same tank in 12 hours.

Concept Used:

If in x hour a tank is filled by a pipe then in 1 hour the tank will be filled by 1/x part of the tank.

Calculation:

Pipe A can fill 1/6 part of the tank in 1 hour

Pipe B can fill 1/8 part of the tank in 1 hour

Pipe C can empty 1/12 part of the tank in 1 hour

In 1 hour tank will be filled by (1/6 + 1/8 - 1/12) part

⇒ (4 + 3 - 2)/24

⇒ 5/24 part

The tank will be fill in 1/(5/24) = 24/5 hours

⇒ (24/5) × 60 minutes

⇒ 288 minutes

⇒ 4 hour 48 minutes

∴ The tank will be filled in 4 hours 48 minutes.