# Pipes and Cistern Questions

FACTS  AND  FORMULAE  FOR  PIPES  AND  CISTERN  QUESTIONS

1. Inlet : A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

2. Outlet : A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

(i) If a pipe can fill a tank in x hours, then:

part filled in 1 hour = 1/x

(ii) If a pipe can empty a tank in y hours, then:

part emptied in 1 hour = 1/y

(iii) If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = $\inline \fn_cm \frac{1}{x}-\frac{1}{y}$

(iv) If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes,  the net part emptied in 1 hour = $\inline \fn_cm \frac{1}{y}-\frac{1}{x}$

Q:

Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?

 A) 10 min. 20 sec. B) 11 min. 45 sec. C) 12 min. 30 sec. D) 14 min. 40 sec.

Explanation:

Part filled in 4 minutes =${\color{Black}&space;4\left&space;(&space;\frac{1}{15}+\frac{1}{20}&space;\right&space;)=\frac{7}{15}}$

Remaining part =${\color{Black}&space;\left&space;(&space;1-\frac{7}{15}&space;\right&space;)=\frac{8}{15}}$

Part filled by B in 1 minute =${\color{Black}&space;\frac{1}{20}}$

${\color{Black}\therefore&space;\frac{1}{20}:\frac{8}{15}::1:x}$

${\color{Black}x=\left&space;(&space;\frac{8}{15}&space;\times&space;1\times&space;20\right&space;)=10\frac{2}{3}min=10min.40sec.}$

${\color{Black}&space;\therefore&space;}$The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

28 18379
Q:

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:

 A) 10 B) 12 C) 14 D) 16

Explanation:

Part filled in 2 hours =${\color{Black}&space;\frac{2}{6}=\frac{1}{3}}$

Remaining part =${\color{Black}&space;\left&space;(&space;1-\frac{1}{3}&space;\right&space;)=\frac{2}{3}}$

${\color{Black}&space;\therefore&space;}$ (A + B)'s 7 hour's work =${\color{Black}&space;\frac{2}{3}}$

(A + B)'s 1 hour's work =${\color{Black}&space;\frac{2}{21}}$

${\color{Black}&space;}$${\color{Black}\therefore&space;}$C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=${\color{Black}&space;\left&space;(&space;\frac{1}{6}-\frac{2}{21}&space;\right&space;)=\frac{1}{14}}$

${\color{Black}&space;\therefore&space;}$C alone can fill the tank in 14 hours.

16 9945
Q:

A pump can fill a tank with water in 2 hours. Because of a leak, it took $\inline \fn_jvn 2\frac{1}{3}$ hours to fill the tank. The leak can drain all the water of the tank in:

 A) 7 hours B) 8 hours C) 12 hours D) 14 hours

Explanation:

Work done by the leak in 1 hour =${\color{Black}&space;\left&space;(&space;\frac{1}{2}-\frac{3}{7}&space;\right&space;)=\frac{1}{14}}$

${\color{Black}&space;\therefore&space;}$ Leak will empty the tank in 14 hrs

17 6339
Q:

A booster pump can be used for filling as well as for emptying a tank. The capacity of the tank is 2400 ${\color{Blue} m^{3}}$. The emptying capacity of the tank is 10 $\inline {\color{Blue} m^{3}}$ per minute heigher than its filling capacity and the pump needs 8 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

 A) 50 m^3/min B) 60 m^3/min C) 72 m^3/min D) None of these

Explanation:

Let the filling capacity of the pump be x $\inline {\color{Black} m^{3}}$/min.

Then, emptying capacity of the pump=(x+10) $\inline {\color{Black} m^{3}}$/min.

so,$\inline {\color{Black} \frac{2400}{x}-\frac{2400}{x+10}=8\; \; \Leftrightarrow x^{2}+10x-3000=0}$

$\inline {\color{Black} \Leftrightarrow \left ( x-50 \right )+\left ( x+60 \right )=0\; \; \Leftrightarrow x=50}$

15 5420
Q:

Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

 A) 60 gallons B) 100 gallons C) 120 gallons D) 180 gallons

Work done by the waste pipe in 1 minute =${\color{Black}&space;\frac{1}{15}-\left&space;(&space;\frac{1}{20}+\frac{1}{24}&space;\right&space;)=\left&space;(&space;\frac{1}{15}-\frac{11}{120}&space;\right&space;)=-\frac{1}{40}}$ [-ve sign means emptying]
Volume of ${\color{Black}&space;\frac{1}{40}}$ part = 3 gallons