Pipes and cisterns

1. Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank ?

A. 12 minutes

B. 6 minutes

C. 8 minutes

D. 10 minutes

Ans: A

Explanation:

$\text{Part&space;filled&space;by&space;A&space;in&space;1&space;minute&space;}&space;=&space;\frac{1}{20}$

$\text{Part&space;filled&space;by&space;B&space;in&space;1&space;minute&space;}&space;=&space;\frac{1}{30}$

$\text{Part&space;filled&space;by&space;(A&space;+&space;B)&space;in&space;1&space;minute&space;}&space;=&space;\left&space;(\frac{1}{20}&space;+&space;\frac{1}{30}\right&space;)&space;=&space;\frac{1}{2}$

$\therefore&space;\,&space;\text{Both&space;the&space;pipes&space;can&space;fill&space;the&space;tank&space;in&space;12&space;minutes.}$

2. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank ?

A. 15 hours

B. 18 hours

C. 20 hours

D. 22 hours

Ans: C

Explanation:

$\text{Part&space;filled&space;by&space;A&space;in&space;one&space;hour&space;}&space;=&space;\frac{1}{36}$

$\text{Part&space;filled&space;by&space;B&space;in&space;one&space;hour&space;}&space;=&space;\frac{1}{45}$

$\text{Part&space;filled&space;by&space;(A&space;+&space;B)&space;in&space;one&space;hour&space;}&space;=&space;\left&space;(&space;\frac{1}{36}&space;+&space;\frac{1}{45}&space;\right&space;)&space;=&space;\frac{9}{180}&space;=&space;\frac{1}{20}$

$\text{Hence,&space;both&space;the&space;pipes&space;together&space;will&space;fill&space;the&space;tank&space;in&space;20&space;hours.}$

3. Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled ?

A. 2

B. 2.5

C. 3

D. 3.5

Ans: C

Explanation:

$\text{Part&space;filled&space;by&space;A&space;in&space;one&space;hour&space;}&space;=&space;\frac{1}{5}$

$\text{Part&space;filled&space;by&space;B&space;in&space;one&space;hour&space;}&space;=&space;\frac{1}{10}$

$\text{Part&space;filled&space;by&space;C&space;in&space;one&space;hour&space;}&space;=&space;\frac{1}{30}$

$\text{Part&space;filled&space;by&space;(A&space;+&space;B&space;+&space;C)&space;in&space;1&space;hour&space;}&space;=&space;\left&space;(&space;\frac{1}{5}&space;+&space;\frac{1}{10}&space;+&space;\frac{1}{30}\right&space;)&space;=&space;\frac{1}{3}$

$\text{All&space;the&space;three&space;pipes&space;together&space;will&space;fill&space;the&space;tank&space;in&space;3&space;hours.}$

4. A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled ?

A. 4.5 hours

B. 5 hours

C. 6.5 hours

D. 7.2 hours

Ans: D

Explanation:

$\text{Net&space;part&space;filled&space;in&space;1&space;hour}&space;=&space;\left&space;(&space;\frac{1}{4}&space;-&space;\frac{1}{9}\right&space;)&space;=&space;\frac{5}{36}$

$\therefore&space;\,\,&space;\text{The&space;cistern&space;will&space;be&space;filled&space;in&space;}&space;\frac{36}{5}&space;\,\,&space;\text{hours&space;i.e.,&space;7.2&space;hours.}$

5. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely ?

A. 3 hours 15 minutes

B. 3 hours 45 minutes

C. 4 hours

D. 4 hours 15 minutes

Ans: B

Explanation:

$\text{Time&space;taken&space;by&space;one&space;tap&space;to&space;fill&space;half&space;the&space;tank}&space;=&space;\text{3&space;hours.}$

$\text{Part&space;filled&space;by&space;the&space;four&space;taps&space;in&space;1&space;hour&space;}&space;=&space;\left&space;(&space;4&space;\times&space;\frac{1}{6}&space;\right&space;)&space;=&space;\frac{2}{3}$

$\text{Remaining&space;part}&space;=&space;\left&space;(&space;1&space;-&space;\frac{1}{2}&space;\right&space;)&space;=&space;\frac{1}{2}$

$\frac{2}{3}&space;:&space;\frac{1}{2}&space;:&space;\,:&space;1&space;:&space;x$

$x&space;=&space;\left&space;(&space;\frac{1}{2}&space;\times&space;1&space;\times&space;\frac{3}{2}\right&space;)&space;=&space;\frac{3}{4}&space;\,\,&space;\text{hrs&space;i.e.,&space;45&space;minutes}$

$\text{So,&space;total&space;time&space;taken&space;}&space;=&space;\text{3&space;hours&space;45&space;minutes.}$

6. Two pipes can fill a tank in 10 hours and 12 hours respectively while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time will the tank be filled ?

A. 5 hours 30 minutes

B. 6 hours 45 minutes

C. 7 hours

D. 7 hours 30 minutes

Ans: D

Explanation:

$\text{Net&space;part&space;filled&space;in&space;one&space;hour&space;}&space;=&space;\left&space;(&space;\frac{1}{10}&space;+&space;\frac{1}{12}&space;-&space;\frac{1}{20}\right&space;)&space;=&space;\frac{8}{60}&space;=&space;\frac{2}{15}$

$\text{The&space;tank&space;will&space;be&space;full&space;in}&space;\,\,&space;\frac{15}{2}&space;\,\,&space;\text{hours&space;=&space;7&space;hours&space;30&space;minutes}$

7. Pipe A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in

$\text{A.}&space;1\frac{13}{17}&space;\,\,&space;\text{hours}$

$\text{B.}&space;2\frac{8}{11}&space;\,\,&space;\text{hours}$

$\text{C.}&space;3\frac{9}{17}&space;\,\,&space;\text{hours}$

$\text{D.}&space;4\frac{1}{2}&space;\,\,&space;\text{hours}$

Ans: C

Explanation:

$\text{Net&space;part&space;filled&space;in&space;1&space;hour}&space;=&space;\left&space;(&space;\frac{1}{5}&space;+&space;\frac{1}{6}&space;-&space;\frac{1}{12}&space;\right&space;)&space;=&space;\frac{17}{60}$

$\therefore&space;\,\,&space;\text{The&space;tank&space;will&space;be&space;full&space;in&space;}&space;\frac{60}{17}&space;\,\,&space;\text{hours&space;i.e.,}&space;\,&space;3\frac{9}{17}&space;\,&space;\text{hrs.}$

8. A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely ?

A. 6 min. to empty

B. 6 min. to fill

C. 9 min. to fill

D. None of these

Ans: A

Explanation:

$\text{Clearly,&space;pipe&space;B&space;is&space;faster&space;than&space;pipe&space;A&space;and&space;so,&space;the&space;tank&space;will&space;be&space;emptied.}$

$\text{Part&space;to&space;be&space;emptied}&space;=&space;\frac{2}{5}$

$\text{Part&space;emptied&space;by&space;(A&space;+&space;B)&space;in&space;1&space;minute}&space;=&space;\left&space;(&space;\frac{1}{6}&space;-&space;\frac{1}{10}&space;\right&space;)&space;=&space;\frac{1}{15}$

$\frac{1}{15}&space;:&space;\frac{2}{5}&space;\,&space;:&space;\,&space;:&space;1&space;:&space;x$

$x&space;=&space;\left&space;(&space;\frac{2}{5}&space;\times&space;1&space;\times&space;15\right&space;)&space;=&space;\text{6&space;min.}$

$\text{So,&space;the&space;tank&space;will&space;be&space;emptied&space;in&space;6&space;min.}$

9. If two pipes function simultaneously, the reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours does it take the second pipe to fill the reservoir ?

A. 10 hours

B. 20 hours

C. 15 hours

D. 30 hours

Ans: D

Explanation:

$\text{Let&space;the&space;reservoir&space;be&space;filled&space;by&space;first&space;pipe&space;in&space;}\,&space;x&space;\,\,&space;\text{hours.}$

$\text{Then,&space;second&space;pipe&space;will&space;fill&space;it&space;in&space;}&space;(&space;x&space;+&space;10)&space;\,&space;\text{hours}$

$\frac{1}{x}&space;+&space;\frac{1}{\left&space;(&space;x&space;+&space;10&space;\right&space;)}&space;=&space;\frac{1}{12}$

$\frac{x&space;+&space;10&space;+&space;x}{x\left&space;(&space;x&space;+&space;10&space;\right&space;)}&space;=&space;\frac{1}{12}$

$x^2&space;-&space;14x&space;-&space;120&space;=&space;0$

$\left&space;(&space;x&space;-&space;20&space;\right&space;)&space;\left&space;(&space;x&space;+&space;6&space;\right&space;)&space;=&space;0$

$x&space;=&space;20&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\,&space;\text{Neglecting&space;the&space;-ve&space;value&space;of}&space;\right&space;x&space;\,&space;]$

$\text{So,&space;the&space;second&space;pipe&space;will&space;take&space;(20&space;+&space;10)&space;hours&space;i.e.,&space;30&space;hours&space;to&space;fill&space;the&space;reservoir.}$

10. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern ?

A. 10 minutes

B. 15 minutes

C. 12 minutes

D. 8 minutes

Ans: A

Explanation:

$\text{Work&space;done&space;by&space;the&space;waste&space;pipe&space;in&space;1&space;minute&space;}&space;=&space;\frac{1}{20}&space;-&space;\left&space;(&space;\frac{1}{12}&space;+&space;\frac{1}{15}\right&space;)&space;=&space;-&space;\frac{1}{10}$

$\therefore&space;\,\,&space;\text{Waste&space;pipe&space;will&space;empty&space;the&space;full&space;cistern&space;in&space;10&space;minutes.}$