Question

Pipes A and B can fill a cistern in 3 and 4 hours respectively. Pipe C can empty it in 9 hours. If all the three pipes are opened together, then the tank will be filled in:

1. \(2{2 \over {17}}\) hours
2. 5 hours
3. \(3{{2 \over {17}}}\) hours
4. 4 hours
5. None of these

Answer 1

Correct Answer - Option 1 : \(2{2 \over {17}}\) hours

Given:

Pipe A can fill a cistern in 3 hours

Pipe B can fill a cistern in 4 hours

Pipe C can empty a cistern in 9 hours

Formula:

(A + B + C)’s 1 hour work = 1/A + 1/B – 1/C

Calculation:

Part of the tank filled in one hour =1/3 ​+ 1/4 ​−1/9​

⇒ 7/12 – 1/9

⇒ 17/36 part​ of the tank is filled 

the tank is filled in = 36/17​ hours = \(2{\textstyle{2 \over {17}}}\) hours.

∴ The tank is filled in \(2{\textstyle{2 \over {17}}}\)​ hours.