# 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 = $\left(\frac{1}{x}-\frac{1}{y}\right)$

(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 = $\left(\frac{1}{y}-\frac{1}{x}\right)$

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 =4(1/15+1/20) = 7/15

Remaining part =(1-7/15) = 8/15

Part filled by B in 1 minute =1/20 : 8/15 :: 1:x

x = (8/15*1*20) =

The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

90 51509
Q:

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 hrs 15 min B) 3 hrs 45 min C) 4 hrs 15 min D) 4 hrs 1

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the four taps in 1 hour =4*1/6 =2/3

Remaining part =$1-12=12$

$23:12::1:x$

=> x = $12*1*32=34$

So, total time taken = 3 hrs. 45 mins.

42 19034
Q:

A pump can fill a tank with water in 2 hours. Because of a leak, it took $213$ 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:

If the total area of pump=1 part

The pumop take 2 hrs to fill 1 part

The pumop take1 hour to fill 1/2 portion

Due to lickage

The pumop take 7/3 hrs to fill 1 part

The pumop take1 hour to fill 3/7 portion

Now the difference of area = (1/2-3/7)=1/14

This 1/14 part of water drains in 1 hour

Total area=1 part of water drains in (1x14/1)hours= 14 hours

So the leak can drain all the water of the tank in 14 hours.

Leak will empty the tank in 14 hrs

52 18185
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 = 2/6=1/3

Remaining part =$1-13=23$

(A + B)'s 7 hour's work = 2/3

(A + B)'s 1 hour's work = 2/21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=1/6-2/21 = 1/14

C alone can fill the tank in 14 hours.

52 17351
Q:

A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in    ?

 A) 20 hrs B) 28 hrs C) 36 hrs D) 40 hrs

Explanation:

1/8 - 1/x = 1/10

=> x = 40 hrs

41 15934
Q:

Three taps A,B and C can fill a tank in 12,15 and 20 hours respectively. If A is open all the time and B ,C are open for one hour each alternatively, the tank will be full in:

 A) 6 hrs B) 20/3 hrs C) 7 hrs D) 15/2 hrs

Explanation:

Now, it is  the turn of A and B (3/20) part is filled by A and B in 1 hour.

Therefore, Total  time taken to fill the tank =(6+1)hrs= 7 hrs

41 15778
Q:

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 empty D) 9 min.to fill

Explanation:

Clearly,pipe B is faster than pipe A and so,the tank will be emptied.

part to be emptied = 2/5

part emptied by (A+B) in 1 minute=$16-110=115$

$115:25::1:x$

$25*15=6mins$

so, the tank will be emptied in 6 min

28 15563
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

Explanation:

Work done by the waste pipe in 1 minute = [-ve sign means emptying]

Volume of $140$part = 3 gallons

Volume of whole = (3 x 40) gallons = 120 gallons.