Question 1

A, B and C are three pipes connected to a tank. A and B together fill the tank in 6 h, B and C together fill the tank in 10 h and A and C together fill the tank in 12 h. in how much time A, B and C fill up the tank together?

Accepted Answer

Part filled by ( A + B ) in 1 h = 1/6 Part filled by ( B + C ) in 1 h = 1/10 Part filled by ( A + C ) in 1 h = 1/12 ∴ Part filled by 2 ( A + B + C ) in 1 h = 1/6 +1/10 + 1/12 = (10 + 6 + 5)/60 = 21/60 = 7/20 ∴ Part filled by ( A + B + C ) in 1 h = 7/(2 x 20) = 7/40 ∴ Required time 40/7 = 55/7 h

Question 2

Two pipes P and Q can fill a cistern in 12 and 15 min, respectively. If both are opened together and at the end of 3 min, the first is closed. How much longer will the cistern take to fill?

Accepted Answer

Part filled by pipe P in 1 min = 1/12 Part filled by pipe Q in 1 min = 1/15 Part filled by both pipes in 1 min = 1/12 + 1/15 + = (5 + 4)/60 = 9/60 Now, Part filled by both pipes in 3 min = (3 x 9)/60 = 27/60 = 9/20 ∴ Remaining part = 1 - 9/20 = 11/20 Let the remaining part is filled by pipe Q in T min. Then, T/15 = 11/20 T = (15 x 11)/20 = (3 x 11)/4 = 33/4 = 84/4 min

Question 3

Two pipes A and B are opened together to fill a tank. Both pipes fill the tank in a certain time. If A separately takes 16 min more than the time taken by ( A + B ) and B takes 9 min more than the time taken by ( A + B ). Find the time taken by A an…

Accepted Answer

Here, a = 16 and = 9 Required time = √ab √16 x 9 = 4 x 3 = 12 min

Question 4

There are three pipes connected with a tank. The first pipe can fill 1/2 part of the tank in 1 h, second pipe can fill 1/3 part of the tank in 1 h. Third pipe is connected to empty the tank. After opening all the three pipes, 7/12 part of the tank c…

Accepted Answer

1st pipe takes 1 h to fill 1/2 part of the tank. So, time taken to fill the whole tank (m) = 2 h 2nd pipe takes 1 h to 1/3 part of the tank So, time taken to fill the whole tank (n) = 3 h Let 3rd pipe takes P h to empty the tank = x ∴ 1/m + 1/n - 1/x = 7/12 ⇒ 1/2 + 1/3 - 1/x = 7/12 ⇒ 1/x = (6 + 4 - 7)/12 = 3/12 = 1/4 ∴ x = 4 h

Question 5

Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.

Accepted Answer

Part filled by 1st pipe in 1 min = 1/20 Part filled by 2nd pipe in 1 min = 1/24 Part filled by all the pipes in 1 min = 1/15 Work done by the waste pipe 1 min = 1/15 - (1/20 + 1/24 ) = 1/15 - 11/120 = (8 - 11)/120 = ( - 3/120 ) = ( -1/40 ) [-ve sign indicates emptying] Now, volume of 1/40 part = 6 gallon ∴ Volume of whole tank = 40 x 6 = 240 gallon

Question 6

A tank can be filled by a tap in 20 min and by another tap in 60 min. Both the taps are kept open for 5 min and then the 1st tap is shut off. After this, how much time the tank will be completely filled?

Accepted Answer

Part of the tank filled by both taps in 5 min = 5 x (1/20 + 1/60) = 5 x (6 +2 )/120 = 8/24 = 1/3 ∴ Remaining part = (1 - 1/3) = 2/3 ∵ 1/60 Part is now filled in 1 min. ∴ 2/3 Part is now filled in 60 x 2/3 = 40 min.

Question 7

A cistern has three pipes A, B and C. Pipes A and B can fill it in 3 and 4 h, respectively, while pipe C can empty the completely filled cistern in 1 h. If the pipes are opened in order at 3:00 pm, 4:00 pm and 5:00 pm, respectively , at what time wi…

Accepted Answer

Let the cistern gets emptied in m h after 3:pm Work done by A in m h, by B in (m - 1) h and by c in (m - 2) h= 0 ⇒ m/3 + (m - 1)/4 - (m - 2) = 0 ⇒ 4m + 3(m - 1) - 12(m - 2) = 0 ⇒ 5m = 21 ⇒ m = 21/5 = 4.2 ∴ m = 4 h 12 min ∵ Required time = 7 : 12 pm.

Question 8

There are three taps of diameter 1 cm, 4/3 cm and 2 cm, respectively. The ratio of the water flowing through them is equal to the ratio of the square of their diameters. The biggest tap can fill the tank alone in 61 min. If all the taps are opened s…

Accepted Answer

Time taken to fill the tank by the tap having 2 cm diameter = 61 min ∴ Time taken to fill the tank by the tap having 1 cm diameter = 61 x (2/1)2 = 244 min Similarly, time taken to fill the tank by the tap having 4/3 cm diameter = 61 x [(2 x 3)/4]2 = 61 x 9/4 = 549/4 min. ∴ Part of the tank filled by all the three pipes in 1 min = 1/61 + 1/244 + 1/(549/4) = (36 + 9 + 16)/2196 = 61/2196 = 1/36 Hence, required time taken = 36 min

Question 9

Two pipes can fill a cistern in 14 and 16 h, respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, it took 92 min more to fill the cistern. When the cistern is full, in what time will the leak empty it?

Accepted Answer

Part filled by 1st pipe in 1 h = 1/14 Part filled by 2nd pipe in 1 h = 1/16 Part filled by the two pipes in 1 h = ( 1/14 + 1/16 ) = (8 + 7)/112 = 15/112 ∴ Time taken by these two pipes to fill the cistern = 112/15 h = 7 h 28 min Due to leakage, the time taken 7 h 28 min + 92 min = 9 h &thee4; Work done by ( two pipes + leak ) in 1 h = 1/9 Work done by the leak in 1 h = 1/9 - 15/112 = (112 - 135)/1008 = - 23/1008 ∴ Time taken by leak to empty the full cistern = 1008/23 = 4319/23 h

Question 10

Three taps A,B and C can fill a cistern in 10, 15 and 20 minutes respectively. They are all turned on at once, but after 3 minutes C is turned off. How many minutes longer will A and B take to fill the cistern?

Accepted Answer

T = (10 x 15 x 20) / (10 x 15 + 10 x 20 + 15 x 20) = 60/13 minutes Now, applying the given rule, we have [60/13 x y]/ [y - 60/13 + 3] = 20 or y = 21/10 = 2 min. 6 seconds.

Question 11

A cistern can be filled by one of two pipes in 30 minutes and by the other in 36 minutes. Both pipes are opened together for a certain time but being particularly clogged only 5 / 6 of the full quantity of water flows through the former and only 9 /…

Accepted Answer

Net filling in last 151/2 minutes = 31/2 (1/30 + 1/36) = 341/360 Now, suppose they remained clogged for x minutes. Net filling in these x minutes = (x/30 x 5/6 + x/36 x 9/10) = 19 x/360 Remaining part = (1 - 19x/360) = (360 - 19x/360) 360 - 19x/360 = 341/360 or x = 1. Hence, the pipes remained clogged for 1 minutes.

Question 12

Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes, 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack t…

Accepted Answer

Let the leak empties it in T hours From the given rule, we have (T x 30) / (T - 30) = 40 ∴ T = 120 minutes = 2 hours. Now, from the question, applying the rule, we have time taken by B to fill the tank when crack in the bottom develops = (120 x 40) / (120 - 40) = 60 minutes = 1 hour

Question 13

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?

Accepted Answer

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) = 10 2 3 m i n = 10 m i n 40 s e c The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec

Question 14

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:

Accepted Answer

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

Question 15

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?

Accepted Answer

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 - 1 2 = 1 2 2 3 : 1 2 : : 1 : x => x = 1 2 * 1 * 3 2 = 3 4 So, total time taken = 3 hrs. 45 mins.

Question 16

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:

Accepted Answer

Part filled in 2 hours = 2/6=1/3 Remaining part = 1 - 1 3 = 2 3 (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.

Question 17

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:

Accepted Answer

A + B ' s 1 h o u r w o r k = 1 12 + 1 15 = 9 60 = 3 20 A + C ' s 1 h o u r w o r k = 1 12 + 1 20 = 8 60 = 2 15 p a r t f i l l e d i n 2 h r s = 3 20 + 2 15 = 17 60 p a r t f i l l e d i n 6 h r s = 3 * 17 60 = 17 20 r e m a i n i n g p a r t = 1 - 17 20 = 3 20 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

Question 18

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 ?

Accepted Answer

1/8 - 1/x = 1/10 => x = 40 hrs

Question 19

A and B can fill the tank in 60 min and 90 min. There is a leak at 3/4th of the height. If leak is opened alone, it takes 36 min to empty till 3/4th the height. Find the time taken to fill the tank if all of the taps and the leak are opened simultan…

Accepted Answer

39

Question 20

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?

Accepted Answer

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= 1 6 - 1 10 = 1 15 1 15 : 2 5 : : 1 : x 2 5 * 15 = 6 m i n s so, the tank will be emptied in 6 min

Pipes and Cistern Questions