Question

Two pipes A and B can fill a cistern in 4 minute , 6 minutes, respectively. If these pipes are turn on alternately for 1 minute each how long will its the cistern to fill?

• A. 4 min 40 sec
• B. 3 min 20 sec
• C. 4 min 50 sec
• D. 3 min 30 sec

Answer 1

The correct option is A 4 min 40 sec

As the pipes are operating alternately, thus their 2 minutes job is
$\frac{1}{4}+\frac{1}{6}=\frac{5}{12}$

In the next 2 minutes the pipes can fill another 5/12 part of cistern. Therefore, in 4 minutes the two pipes which are operating alternately will fill

$\frac{5}{12}+\frac{5}{12}=\frac{10}{12}=\frac{5}{6}part$

The part of the cistern left unfilled
$=1-\frac{5}{6}=\frac{1}{6}$

Pipe A can filled 1/4 of the cistern in 1 minutes.

Pipe A can filled 1/6 of the cistern in
$4\times \frac{1}{6}=\frac{2}{3}minutes.$

Total time taken to fill the cistern
$4+\frac{2}{3}=4\frac{2}{3}min$
Or, 4 minutes 40 seconds.