### PIPES AND CISTERNS QUIZ 001

- Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are used alternately for one hour each, the time taken to fill the tank is?

**(a) 4 hrs 24 min**

(b) 5 hrs

(c) 6 hrs

(d) 7 hrs

(e) 5hrs 50 min

Explanation:

A and B combine work 2 hour work=1/4+1/5=9/20

4-hour work =9/20+9/20=9/10

remaining work=1-9/10=1/10

now it’s A’s turn so =1/10*4=2/5

to convert it into minute

5/2 = 60/X

cross multiplication x=60*2/5= 24 min

So Answer is 4hr and 24min

- A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?

**(a) 3 A.m.**

(b) 3.30 A.M.

(c) 4 A.M.

(d) 5 P.M.

(e) 5.30 P.M.

Explanation:

In 1 hour A can fill the cistern in = 1/4hr.

In 1 hour B can fill the cistern in = 1/5hr.

In 1 hour C can empty the cistern in =1/2hr.

Now consider in X hrs cistern will be empty after opening C then C is working X hrs

B is working (X+1) hrs

A is working (X+2) hrs

So,

(X+2)/4 + (X+1)/5 – x/2=0

X=14hrs

So, Answer is 5 p.m

- A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?

(a) 20

(b) 45

(c) 30

**(d) 28**

(e) 29

Explanation:

1/A + 1/B + 1/C = 1/8 (Given)

Also given that A = 2B and B = 2C

=> 1/2B + 1/B + 2/B = 1/8

=> (1 + 2 + 4)/2B = 1/8

=> 2B/7 = 8

=> B = 28 hours

- One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill tank in 36 min., then the slower pipe alone will be able to fill the tank in?

(a) 81 min

**(b) 144 min**

(c) 168 min

(d) 167 min

(e) 187 min

Explanation:

Let the slower pipe alone fill the tank in x min.

Then, faster pipe will fill it in x/3 min.

1/x + 3/x = 1/36

4/x = 1/36 => x = 144 min.

- A large tanker can be filled by two pipes A and B in 60 and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

**(a) 30 min**

(b) 40 min

(c) 60 min

(d) 50 min

(e) 70 min

Explanation:

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24

Suppose the tank is filled in x minutes.

Then, x/2(1/24 + 1/40) = 1

x/2 * 1/15 = 1 => x = 30 min.

- A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank?

**(a) 144 min**

(b) 150 min

(c) 160 min

(d) 170 min

(e) 185 min

Explanation:

Let the slower pipe alone fill the tank in x minutes then faster will fill in x/3 minutes.

Part filled by slower pipe in 1 minute = 1/x

Part filled by faster pipe in 1 minute = 3/x

Part filled by both in 1 minute = 1/x+3/x=1/36

=>4/x=1/36

x =36∗4=144 min

- Three pipes A, B and C are connected to a tank. These pipes can fill the tank separately is 5 hrs, 10 hrs and 15 hrs, respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at three-fourths of their normal rates for the 1st hrs after which they supplied water at the normal rate. Pipe C supplied water at two-thirds of its normal rate for first 2 hrs, after which it supplied at its normal rate. In how much time, tank would be filled?

(a) 1.05 hrs

(b) 2.05 hrs

**(c) 3.05 hrs**

(d) 4.05 hrs

(e) 2.55 hrs

Explanation:

(c); The part of the tank filled by A and B in first two hrs

- Two pipes A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together fill the tank in 15 minutes, the capacity (in gallons) of the tank is:

(a) 180

(b) 150

**(c) 120**

(d) 60

(e) None of these

Explanation:

let the capacity of the tank be x gallons.

Quantity of water filled in the tank in 1 minute when all the

pipes A, B and C are opened simultaneously

For better understanding of the topic, please refer to our videos

and other relevant notes. Please visit our website for more information.

- There are two leakages in the bottom of a cistern. Both together empty the cistern in 12 hours. If the first leakage alone empties it in 30 hours, then in how many hours will the second leakage alone empty it?

**(a) 20 hours**

(b) 25 hours

(c) 30 hours

(d)15 hours

(e) 12 hours

Explanation:

For better understanding of the topic, please refer

to our videos and other relevant notes. Please visit

our website for more information.

- Pipe A, B and C are kept open and fill a tank in ‘t’ minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipes A and B are kept open continuously, the tank would be filled completely in ‘t’ minutes. How long will C alone take to fill the tank?

(a) 18

(b) 36

(c) 27

**(d) 24**

(e) 20

Explanation:

A is kept open for all t minutes and fills one-third the tank. Or, A should be able to

fill the entire tank in ‘3t’ minutes.

A and B together can fill the tank completely in t minutes.

A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank.

A is kept open for all 20 minutes. B is kept open for 10 minutes.

C, which is kept open for = (10-2) = 8 minutes also fills one third of the tank.

Or, c alone can fill the tank in = (8*3) = 24 minutes.

- Two taps can fill a tank in 20 mins and 30 mins respectively. There is an outlet tap at exactly half level of that rectangular tank which can pump out 50 litres of water per minute. If the outlet tap is open, then it takes 24 mins to fill an empty tank. What is the volume of the tank?

**(a) 1200 litres**

(b) 1500 litres

(c) 1800 litres

(d) 2400 litres

(e) None of these

Explanation:

12. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hrs faster than the first pipe and 4 hrs slower than the third pipe. The time required by the first pipe is-

(a) 6 hrs

(b) 10 hrs

(c) 15 hrs

(d) 30 hrs

(e) None of these

Explanation:

13. A bathtub can be filled by a cold water pipe in 20 mins and by a hot water pipe in 30 mins. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment when the bathtub should be full. Finding however, that the waste pipe has been open, he now closes it. In 3 mins more the bathtub is full. In what time would the waste pipe empty it?

(a) 38 mins

(c) 43 mins

(c) 45 mins

**(d) 48 min**

(e) None of these

Explanation:

14. Pavan builds an overhead tank in his house, which has three taps attached to it. While the first tap can fill the tank in 12 hrs, the second one takes one and a half times more than the first one to fill it completely. A third tap is attached to the tank which empties it in 36 hrs. Now, one day, in order to fill the tank. Pavan opens the first tap and after two hrs opens the second tap as well. However, at the end of the sixth hour, he realizes that the third tap has been kept open right from the beginning and promptly closes it. What will be the total time required to fill the tank?

(a) 8 hrs 48 mins

(c) 9 hrs 36 mins

**(b) 9 hrs 12 mins**

(d) 8 hrs 30 mins

(e) None of these

Explanation:

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