Question 1

Three pipes A, B and C can fill a cistern in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill it in 7 hours. The time taken by C alone to fill the cistern is?

Accepted Answer

Part filled in 2 hours = 2 x 1/6 = 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 = (2/3 x 1/7) = 2/21 (A + B + C)'s 1 hour's work = 1/6 C's 1 hours work = (1/6 - 2/21) = 1/14 Hence, C alone can fill the cistern in 14 hours.

Question 2

If two 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 the faster pipe take to fill the reservoir?

Accepted Answer

Suppose that one pipe takes N hours to fill the reservoir. Then another pipe takes (N - 10) hours. ∴ 1/N + 1/(N - 10) = 1/12 ⇒ 12(N - 10 + N) = N(N - 10) or N2 - 34N + 120 = 0 or (N - 30)(N - 4) = 0 ∴ N = 30 or N = 4 So, the faster pipe takes 30 hours to fill the reservoir.

Question 3

Two pipes A and B can fill a tank in 15 hours and 20 hours respectively while a third pipe C can empty the full tank in 25 hours. All the three pipes are opened in the beginning. After 10 hours, C is closed. The time taken to fill the tank is?

Accepted Answer

Part filled in 10 hours = 10 x (1/15 + 1/20 - 1/25) = 23/30 Remaining part = (1 - 23/30) = 7/30 Now, (1/15 + 1/20) part is filled by A and B in 1 hr. 7/30 part be filled them in (60/7) x (7/30) = 2 hrs. ∴ Total time taken to fill the tank = (10 + 2) hrs. = 12 hrs.

Question 4

A cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full, in what time will the leak empty it?

Accepted Answer

Let the leak empty the full cistern in N hours Now, applying the given rule (9 x N) / (N - 9) = 9 + 1 or N = 90 hours.

Question 5

A cistern has 3 pipes A, B and C, A and B can fill it in 2 and 3 hours respectively. C is a waste pipe. If all the 3 pipes be opened at once, 7/24 of the cistern will be filled up in 30 minutes. In what time can C empty the full cistern?

Accepted Answer

∵ 7/24 of the cistern will be filled up in 1/2 hr. ∴ The whole of the cistern will be filled up in (1/2) x (24/7) = 12/7 hrs. Let the pipe C be empty the whole cistern in h hours Now, applying the given rule we have, (2 x 3 x h) / (3 x h + 2 x h - 2 x 3) = 12/7 or 42h = 60h - 72 ∴ h = 4 hours.

Question 6

Two pipes, P ans Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?

Accepted Answer

12(1 - t/25) = 3 ∴ t = 45/4 = 111/4 minutes ∴ Required answer = 111/4 - 3 = 81/4 minutes

Question 7

Three pipes A, B and C can fill a cistern in 10 hours, 12 hours and 15 hours respectively. First A was opened. After 1 hour, B was opened and after 2 hours from the start of A, C also opened . Find the time in which the cistern is just full?

Accepted Answer

[(A's 1 hour work) + (A + B)'s 1 hour work] = (1/10) + [(1/10) + (1/12)] = 17/60 Remaining part = 1 - (17/60) = 43/60 Now, (A + B + C)'s 1 hour work = (1/10) + (1/12) + (1/15) = 1/4 1/4 part is filled by 3 pipes in 1 hour. 43/60 part will be filled by them in 4 x (43/60) hrs. = 2 hours 52 min. ∴ Total time taken to fill the cistern = 4 hours 52 min.

Question 8

A pipe can fill a cistern in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 minutes in the beginning and then third pipe is also opened. In what time is the …

Accepted Answer

Part filled in 5 min. = 5 x (1/12 + 1/15) = 5 x 9/60 = 3/4 Part emptied in 1 min. (when all the pipes are opened) = 1/6 - (1/12 + 1/15) = (1/6 - 3/20) = 1/60 Now, 1/60 part is emptied in 1 min. 3/4 part will be emptied in (60 x 3/4) = 45 min.

Question 9

A leak in the bottom of a tank can empty the full tank in 6 hours. An Inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the Inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank is?

Accepted Answer

Part filled by inlet in 1 hour = (1/6 - 1/8) = 1/24 So, the inlet can fill the tank in 24 hours ∴ Capacity of the tank = Water that flows in 24 hours = (4 x 24 x 60) liters = 5760 liters

Question 10

Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?

Accepted Answer

Let Y be closed after T min Then, T x (1/ 24 + 1/32) + (18 - T) x 1/24 = 1 ⇒ (7 x T)/96 + (18 - T)/24 = 1 or 7T + 72 - 4T = 96. ∴ 3T = 24 or T = 8 min.

Question 11

A water tank is 2/5th full pipe A can fill the tank in 10 minutes and the 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

Time taken to fill or empty the whole tank = (6 x 10) /(6 - 10) = - 15 minutes - ve sign shows that the tank will be emptied. ∴ 2/5th full of the tank will be emptied in 15 x 2/5 = 6 minutes

Question 12

Top A can fill a water tank in 25 minutes, tap B can fill the same tank in 40 minutes and tap C can empty the tank in 30 minutes. If all the three taps are opened together, in how many minutes will the tank be completely filled up or emptied?

Accepted Answer

Required answer = (25 x 40 x 30) / (40 x 30 + 25 x 30 - 25 x 40) = 600 / 19 = 3111/19 minutes

Question 13

A cistern can be filled by two pipes. A and B in 12 minutes and 14 minutes respectively and can be emptied by a third pipe C in 8 minutes. If all the taps be turned on at the same moment, what part of cistern will remain unfilled at the end of 7 min…

Accepted Answer

Time taken to fill the whole tank = (12 x 14 x 8) / (14 x 8 + 12 x 8 - 12 x 14) = 168/5 minutes ∴ In 7 minutes 5/168 x 7 = 5/24 part of the tank will be filled ∴ Requied answer = 1 - 5/24 = 19/24 part

Question 14

A cistern can be filled by two pipes in 30 and 40 minutes respectively. Both the pipes were opened at once, but after some time the first was shut up and the cistern was filled in 10 minutes more. How long after the pipes had opened was the first pi…

Accepted Answer

Let the first pipe be shut up after x minutes Now, applying the given rule, we have 30{1 - (x + 10)/40 } = x [Here t = (x + 10) minutes] or x = 90/7 minutes

Question 15

A cistern has a leak which would empty it in 15 hours. A tap is turned on which admits 2 litres per hour into the cistern and it is now emptied in 10 hours. How many litres does the cistern hold?

Accepted Answer

Here w = 2 litres per hour ∴ Required answer = {(15 x 10) / (15 - 10)} x 2 = 60 litres.

Question 16

There are two tank A and B to fill up a water tank. The tank can be filled in 40 min, if both taps are on. The same tank can be filled in 60 min, if tap A alone is on. How much time will tap B alone take, to fill up the same tank?

Accepted Answer

Part filled by tap A in 1 min = 1/60 Let tap B fills the tank in x min Then, Part filled by tap, B in 1 min = 1/x According to the question, 1/60 + 1/x = 1/40 ⇒ 1/x = 1/40 - 1/60 &rArr ; 1/x = (3 - 2)/120 &rArr ; 1/x = 1/120 ∴ Tap B can fill the tank in 120 min.

Question 17

Three taps are fitted in a cistern. The empty cistern is filled by the first and the second taps in 3 and 4 h, respectively. The full cistern is emptied by the third tap in 5 h. If all three taps are opened simultaneously, the empty cistern will be …

Accepted Answer

Part of tank filled by first tap in 1 h = 1/3 Part of tank filled by second tap in 1 h = 1/4 Part of tank emptied by third tap in 1 h = 1/5 Part of the tank filled by all pipes opened simultaneously in 1 h = 1/3 + 1/4 - 1/5 = (20 + 15 - 12)/60 = 23/60 Time taken by all the taps to fill the tank when it is empty = 23/60 h = 214/23 h

Question 18

Pipe A can fill a Tank in 30 min, while pipe B can fill the same tank in 10 min and pipe C can empty the full tank in 40 min. If all the pipes are opened together, how much time will be needed to make the tank full?

Accepted Answer

Part filled by A in 1 min = 1/30 Part filled by B in 1 min = 1/10 Part emptied by C in 1 min = - 1/40 Net part filled in 1 h by ( A + B + C ) = ( 1/30 + 1/10 - 1/40 ) = (4 + 12 - 3)/120 = 13/120 ∴ Required time to fill the tank = 120/13 = 93/13 h

Question 19

Through an inlet, a tank takes 8 h to get filled up. Due to a leak in the bottom, it takes 2 h more to get it filled completely. If the tank is full, how much time will the leak take to empty it?

Accepted Answer

Let the leak takes x h to empty the tank. Now, part filled by inlet in 1 h = 1/8 part filled in 1 h when both tap and leak works together = 1/(8+2) = 1/10 According to the question. 1/x = 1/8 - 1/10 = (5 - 4) / 40 = 1/40 ∴ x = 40 h

Question 20

Two pipes A and B can fill a tank in 1 h and 75 min, respectively. There is also an outlet C . If all the three pipes are opened together. The tank is full 50 min. How much time will be taken by C to empty the full tank?

Accepted Answer

Work done by C in 1 min = (1/60 + 1/75 - 1/50 ) = (5 + 4 - 6)/300 = 3/300 = 1/100 Hence, C can empty the full tank in 100 min.

Pipes and Cistern Questions