20:I[84784,["/_next/static/chunks/0h7j95za6o12g.js","/_next/static/chunks/2qgnw7sg7_z2q.js","/_next/static/chunks/2zfih7flb946a.js","/_next/static/chunks/2qs0hgoybrf5v.js"],"default"] 21:T641,

Pipe P fills the tank in 20 hours → rate = 1/20 per hour
Pipe Q fills the tank in 30 hours → rate = 1/30 per hour
Pipe P is opened alone for the first 5 hours:
Water filled = 5 × (1/20) = 5/20 = 1/4 of the tank
Remaining part of the tank = 1 - 1/4 = 3/4
Now both P and Q are opened together:
Combined rate = 1/20 + 1/30
LCM of 20 and 30 is 60
1/20 = 3/60
1/30 = 2/60
Total rate = 3/60 + 2/60 = 5/60 = 1/12 per hour
Time to fill remaining 3/4 = (3/4) ÷ (1/12) = (3/4) × 12 = 9 hours
Total time = 5 hours (initial) + 9 hours = 14 hours

22:T566,

Pipe A fills the tank in 12 hours → rate = 1/12 per hour
Pipe B fills it in 16 hours → rate = 1/16 per hour
Pipe C empties it in 8 hours → rate = -1/8 per hour
Add all three rates:
1/12 + 1/16 - 1/8
LCM of 12, 16, and 8 is 48
1/12 = 4/48
1/16 = 3/48
1/8 = 6/48
Total rate = 4/48 + 3/48 - 6/48 = 1/48
Since 1/48 of the tank is filled in one hour, the net effect is that the tank will be filled slowly, and it will take 48 hours to fill the tank completely.

23:T559,

The first inlet pipe fills the tank in 30 minutes → rate = 1/30 per minute
The second inlet pipe fills it in 40 minutes → rate = 1/40 per minute
The outlet pipe empties it in 24 minutes → rate = -1/24 per minute
Add all three rates:
1/30 + 1/40 - 1/24
LCM of 30, 40, and 24 is 120
1/30 = 4/120
1/40 = 3/120
1/24 = 5/120
Total rate = 4/120 + 3/120 - 5/120 = 2/120 = 1/60
Since 1/60 of the tank is filled in 1 minute, the full tank will be filled in: 60 Minutes

24:T622,

The pipe fills the tank in 20 hours, so its rate is 1/20 of the tank per hour.
With the leak, it takes 25 hours to fill the tank, so the combined rate is 1/25 per hour.
Let the leak’s rate be L (a negative value since it empties the tank).
So, pipe rate + leak rate = combined rate
1/20 + L = 1/25
Solve for L:
L = 1/25 - 1/20
LCM of 25 and 20 is 100
1/25 = 4/100
1/20 = 5/100
So, L = 4/100 - 5/100 = -1/100
The leak alone empties 1/100 of the tank in 1 hour.
So, it will empty the full tank in 100 hours.

25:T766,

All three pipes A, B, and C together fill the tank in 4 hours → rate = 1/4 per hour
Pipe A fills it alone in 8 hours → rate = 1/8 per hour
Pipe B fills it alone in 12 hours → rate = 1/12 per hour
Let pipe C’s rate be 1/x per hour.
So, total rate = A + B + C = 1/8 + 1/12 + 1/x = 1/4
Combine 1/8 and 1/12:
LCM of 8 and 12 is 24
1/8 = 3/24
1/12 = 2/24
So, 1/8 + 1/12 = 5/24
Now, 5/24 + 1/x = 1/4
Subtract 5/24 from both sides:
1/x = 1/4 - 5/24
LCM of 4 and 24 is 24
1/4 = 6/24
So, 1/x = 6/24 - 5/24 = 1/24
Therefore, x = 24

26:T8bb,

Pipe A fills the tank in 6 hours → rate = 1/6 per hour
Pipe B fills it in 8 hours → rate = 1/8 per hour
Pipe C empties it in 12 hours → rate = -1/12 per hour
For the first 2 hours, pipes A and C are open:
Combined rate = 1/6 - 1/12
LCM of 6 and 12 is 12
1/6 = 2/12
1/12 = 1/12
Net rate = 2/12 - 1/12 = 1/12
Water filled in 2 hours = 2 × (1/12) = 2/12 = 1/6 of the tank
Remaining tank = 1 - 1/6 = 5/6
Now pipe A is closed, and pipes B and C are open:
Combined rate = 1/8 - 1/12
LCM of 8 and 12 is 24
1/8 = 3/24
1/12 = 2/24
Net rate = 3/24 - 2/24 = 1/24
Time to fill remaining 5/6 at rate 1/24 = (5/6) ÷ (1/24) = (5/6) × 24 = 20 hours
Total time = 2 hours (initial) + 20 hours = 22 hours

27:T8be,

Pipe X fills the cistern in 10 hours, so its rate is 1/10 per hour.
Pipe Y fills it in 15 hours, so its rate is 1/15 per hour.
Pipe Z fills it in 30 hours, so its rate is 1/30 per hour.
All three pipes are opened together for the first 2 hours.
Combined rate = 1/10 + 1/15 + 1/30
LCM of 10, 15, and 30 is 30.
Convert: 1/10 = 3/30, 1/15 = 2/30, 1/30 = 1/30
Total rate = 3/30 + 2/30 + 1/30 = 6/30 = 1/5
So, in 2 hours they fill: 2 × 1/5 = 2/5 of the cistern
After 2 hours, pipe Z is closed. Now only pipes X and Y are open.
Combined rate = 1/10 + 1/15
LCM of 10 and 15 is 30
1/10 = 3/30, 1/15 = 2/30
Total rate = 3/30 + 2/30 = 5/30 = 1/6
Remaining part of the cistern = 1 - 2/5 = 3/5
Time to fill 3/5 at rate 1/6 = (3/5) ÷ (1/6) = (3/5) × 6 = 18/5 = 3.6 hours
So, additional time needed after closing pipe Z is 3.6 hours or 3 hours 36 minutes ≈ 4 hours

28:T646,

The outlet pipes empty the tank in 4, 6, 8, 12, and 24 hours respectively.
So, their rates are:
1/4, 1/6, 1/8, 1/12, and 1/24 (all negative since they empty the tank)
Add all the rates:
Total rate = 1/4 + 1/6 + 1/8 + 1/12 + 1/24
LCM of 4, 6, 8, 12, and 24 is 24
1/4 = 6/24
1/6 = 4/24
1/8 = 3/24
1/12 = 2/24
1/24 = 1/24
Total rate = 6/24 + 4/24 + 3/24 + 2/24 + 1/24 = 16/24 = 2/3
So, 2/3 of the tank is emptied in 1 hour.
Time to empty the full tank = 1 ÷ (2/3) = 3/2 = 1.5 hours

29:T63a,

The two pipes can fill the cistern in 15 minutes and 20 minutes respectively.
So, fast pipe rate = 1/15 per minute
Slow pipe rate = 1/20 per minute
Both pipes are opened for the first 5 minutes:
Combined rate = 1/15 + 1/20
LCM of 15 and 20 is 60
1/15 = 4/60
1/20 = 3/60
Total rate = 4/60 + 3/60 = 7/60
Amount filled in 5 minutes = 5 × 7/60 = 35/60 = 7/12 of the cistern
Remaining part = 1 - 7/12 = 5/12
Now only the faster pipe (1/15 per minute) continues
Time to fill 5/12 = (5/12) ÷ (1/15) = (5/12) × 15 = 75/12 = 6.25 minutes

2a:T49d,

The first pipe fills the pool in 8 hours, so its rate is 1/8 per hour.
The second pipe fills it in 12 hours, so its rate is 1/12 per hour.
The third pipe empties it in 6 hours, so its rate is -1/6 per hour.
Add all three rates:
1/8 + 1/12 - 1/6
LCM of 8, 12, and 6 is 24
1/8 = 3/24, 1/12 = 2/24, 1/6 = 4/24
Total rate = 3/24 + 2/24 - 4/24 = 1/24
Since 1/24 of the pool is filled in 1 hour, the pool will be completely filled in 24 hours.

2b:T5ad,

Pipe P fills the tank in 16 hours → rate = 1/16 per hour
Pipe Q fills the tank in 24 hours → rate = 1/24 per hour
Both pipes run together for 4 hours:
Combined rate = 1/16 + 1/24
LCM of 16 and 24 is 48
1/16 = 3/48
1/24 = 2/48
Total rate = 5/48
Water filled in 4 hours = 4 × (5/48) = 20/48 = 5/12 of the tank
Remaining part of the tank = 1 - 5/12 = 7/12
Pipe Q alone continues at a rate of 1/24 per hour
Time to fill 7/12 = (7/12) ÷ (1/24) = (7/12) × 24 = 14 hours

2c:T6e0,

Pipe A fills the tank in 2 hours → rate = 1/2 per hour
Pipe B fills it in 3 hours → rate = 1/3 per hour
Pipe C fills it in 6 hours → rate = 1/6 per hour
Pipe D empties it in 4 hours → rate = -1/4 per hour
Add all four rates:
1/2 + 1/3 + 1/6 - 1/4
LCM of 2, 3, 6, and 4 is 12
Convert each:
1/2 = 6/12
1/3 = 4/12
1/6 = 2/12
1/4 = 3/12
Total rate = 6/12 + 4/12 + 2/12 - 3/12 = 9/12 = 3/4
Since 3/4 of the tank is filled in 1 hour, the full tank will be filled in:
1 ÷ (3/4) = 4/3 hours = 1 hour 20 minutes.

17:[["$","$L20","pipes-and-cisterns",{"subTopicName":"pipes-and-cisterns","initialQuestions":[{"question":{"_id":"689620e6a399ed435f0ee96c","question":"

Two pipes P and Q can fill a tank in 20 and 30 hours respectively. If pipe P is opened for 5 hours first, then both pipes are opened together, what is the total time to fill the tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"14 hours","explanation":"$21","createdAt":"2025-08-08T16:08:06.345Z","updatedAt":"2025-08-08T16:08:06.345Z","__v":0},"options":[{"_id":"689620e6a399ed435f0ee96e","question_id":"689620e6a399ed435f0ee96c","option_type":"text","option_text":"15 hours","path_url":null,"__v":0},{"_id":"689620e6a399ed435f0ee970","question_id":"689620e6a399ed435f0ee96c","option_type":"text","option_text":"14 hours","path_url":null,"__v":0},{"_id":"689620e6a399ed435f0ee972","question_id":"689620e6a399ed435f0ee96c","option_type":"text","option_text":"19 hours","path_url":null,"__v":0},{"_id":"689620e6a399ed435f0ee974","question_id":"689620e6a399ed435f0ee96c","option_type":"text","option_text":"21 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961f73a399ed435f0ee926","question":"

Three pipes A, B, and C are connected to a tank. A and B are inlet pipes that can fill the tank in 12 and 16 hours respectively, while C is an outlet pipe that can empty the tank in 8 hours. If all pipes are opened simultaneously, what will be the net effect?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"Tank empties in 48 hours","explanation":"$22","createdAt":"2025-08-08T16:01:55.000Z","updatedAt":"2025-08-08T16:01:55.000Z","__v":0},"options":[{"_id":"68961f73a399ed435f0ee928","question_id":"68961f73a399ed435f0ee926","option_type":"text","option_text":"Tank fills in 48 hours","path_url":null,"__v":0},{"_id":"68961f73a399ed435f0ee92a","question_id":"68961f73a399ed435f0ee926","option_type":"text","option_text":"Tank empties in 48 hours","path_url":null,"__v":0},{"_id":"68961f73a399ed435f0ee92c","question_id":"68961f73a399ed435f0ee926","option_type":"text","option_text":"Tank never changes level","path_url":null,"__v":0},{"_id":"68961f73a399ed435f0ee92e","question_id":"68961f73a399ed435f0ee926","option_type":"text","option_text":"Tank fills in 24 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961ec8a399ed435f0ee908","question":"

Pipe P can fill a tank in 16 hours and pipe Q can fill it in 24 hours. Both pipes are opened together for 4 hours, then pipe P is closed. How much more time will pipe Q alone take to fill the remaining tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"14 hours","explanation":"

Pipe P fills the tank in 16 hours → rate = 1/16 per hour

Pipe Q fills the tank in 24 hours → rate = 1/24 per hour

Both pipes run together for 4 hours:

Combined rate = 1/16 + 1/24

LCM of 16 and 24 is 48

1/16 = 3/48

1/24 = 2/48

Total rate = 3/48 + 2/48 = 5/48

Amount filled in 4 hours = 4 × (5/48) = 20/48 = 5/12 of the tank

Remaining part of the tank = 1 - 5/12 = 7/12

Pipe Q alone now fills the remaining tank at rate 1/24 per hour

Time = (7/12) ÷ (1/24) = (7/12) × 24 = 14 hours

","createdAt":"2025-08-08T15:59:04.845Z","updatedAt":"2025-08-09T09:10:11.402Z","__v":0},"options":[{"_id":"6897107303d64d20543b04ba","question_id":"68961ec8a399ed435f0ee908","option_type":"text","option_text":"12 hours","path_url":null,"__v":0},{"_id":"6897107303d64d20543b04bc","question_id":"68961ec8a399ed435f0ee908","option_type":"text","option_text":"14 hours","path_url":null,"__v":0},{"_id":"6897107303d64d20543b04be","question_id":"68961ec8a399ed435f0ee908","option_type":"text","option_text":"16 hours","path_url":null,"__v":0},{"_id":"6897107303d64d20543b04c0","question_id":"68961ec8a399ed435f0ee908","option_type":"text","option_text":"18 hours","path_url":null,"__v":0}]},{"question":{"_id":"68962040a399ed435f0ee94e","question":"

A tank has two inlet pipes X and Y, and one outlet pipe Z. X can fill the tank in 10 hours, Y in 15 hours, and Z can empty it in 12 hours. If only X and Z are opened together, what happens?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"Tank empties in 60 hours","explanation":"

Rate of X = 1/10 (filling)

Rate of Z = 1/12 (emptying)

Net rate = 1/10 - 1/12 = 6/60 - 5/60 = 1/60

Time = 60 hours

","createdAt":"2025-08-08T16:05:20.631Z","updatedAt":"2025-08-08T16:05:20.631Z","__v":0},"options":[{"_id":"68962040a399ed435f0ee950","question_id":"68962040a399ed435f0ee94e","option_type":"text","option_text":"Tank fills in 60 hours","path_url":null,"__v":0},{"_id":"68962040a399ed435f0ee952","question_id":"68962040a399ed435f0ee94e","option_type":"text","option_text":"Tank empties in 60 hours","path_url":null,"__v":0},{"_id":"68962040a399ed435f0ee954","question_id":"68962040a399ed435f0ee94e","option_type":"text","option_text":"Tank fills in 30 hours","path_url":null,"__v":0},{"_id":"68962040a399ed435f0ee956","question_id":"68962040a399ed435f0ee94e","option_type":"text","option_text":"No net change","path_url":null,"__v":0}]},{"question":{"_id":"68961fdea399ed435f0ee93a","question":"

Two pipes can fill a tank in 30 and 40 minutes respectively. There is also an outlet pipe that can empty the tank in 24 minutes. If all three pipes are opened together, how long will it take to fill the empty tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"60 minutes","explanation":"$23","createdAt":"2025-08-08T16:03:42.016Z","updatedAt":"2025-08-08T16:03:42.016Z","__v":0},"options":[{"_id":"68961fdea399ed435f0ee93c","question_id":"68961fdea399ed435f0ee93a","option_type":"text","option_text":"60 minutes","path_url":null,"__v":0},{"_id":"68961fdea399ed435f0ee93e","question_id":"68961fdea399ed435f0ee93a","option_type":"text","option_text":"120 minutes","path_url":null,"__v":0},{"_id":"68961fdea399ed435f0ee940","question_id":"68961fdea399ed435f0ee93a","option_type":"text","option_text":"180 minutes","path_url":null,"__v":0},{"_id":"68961fdea399ed435f0ee942","question_id":"68961fdea399ed435f0ee93a","option_type":"text","option_text":"Never fills","path_url":null,"__v":0}]},{"question":{"_id":"68961e13a399ed435f0ee8ea","question":"

A pipe can fill a tank in 20 hours. Due to a leak at the bottom, it takes 25 hours to fill the tank. If the tank is full, how long will the leak alone take to empty it?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"100 hours","explanation":"$24","createdAt":"2025-08-08T15:56:03.172Z","updatedAt":"2025-08-08T15:56:03.172Z","__v":0},"options":[{"_id":"68961e13a399ed435f0ee8ec","question_id":"68961e13a399ed435f0ee8ea","option_type":"text","option_text":"80 hours","path_url":null,"__v":0},{"_id":"68961e13a399ed435f0ee8ee","question_id":"68961e13a399ed435f0ee8ea","option_type":"text","option_text":"100 hours","path_url":null,"__v":0},{"_id":"68961e13a399ed435f0ee8f0","question_id":"68961e13a399ed435f0ee8ea","option_type":"text","option_text":"120 hours","path_url":null,"__v":0},{"_id":"68961e13a399ed435f0ee8f2","question_id":"68961e13a399ed435f0ee8ea","option_type":"text","option_text":"150 hours","path_url":null,"__v":0}]},{"question":{"_id":"68962072a399ed435f0ee958","question":"

Three pipes A, B, and C together can fill a tank in 4 hours. Pipe A alone takes 8 hours and pipe B alone takes 12 hours to fill the tank. How long will pipe C alone take to fill the tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"24 hours","explanation":"$25","createdAt":"2025-08-08T16:06:10.370Z","updatedAt":"2025-08-08T16:06:10.370Z","__v":0},"options":[{"_id":"68962072a399ed435f0ee95a","question_id":"68962072a399ed435f0ee958","option_type":"text","option_text":"18 hours","path_url":null,"__v":0},{"_id":"68962072a399ed435f0ee95c","question_id":"68962072a399ed435f0ee958","option_type":"text","option_text":"20 hours","path_url":null,"__v":0},{"_id":"68962072a399ed435f0ee95e","question_id":"68962072a399ed435f0ee958","option_type":"text","option_text":"24 hours","path_url":null,"__v":0},{"_id":"68962072a399ed435f0ee960","question_id":"68962072a399ed435f0ee958","option_type":"text","option_text":"30 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961d4fa399ed435f0ee8cc","question":"

Two pipes A and B can fill a tank in 12 and 18 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"7.2 minutes","explanation":"

Pipe A fills the tank in 12 minutes, so its rate is 1/12 of the tank per minute.

Pipe B fills the tank in 18 minutes, so its rate is 1/18 per minute.

Add the rates of both pipes:

1/12 + 1/18

Find the LCM of 12 and 18, which is 36.

Convert each fraction:

1/12 = 3/36

1/18 = 2/36

Total rate = 3/36 + 2/36 = 5/36

Since 5/36 of the tank is filled in 1 minute, the full tank will be filled in 36/5 minutes, which is 7.2 minutes or 7 minutes 12 seconds.

","createdAt":"2025-08-08T15:52:47.190Z","updatedAt":"2025-08-08T15:52:47.190Z","__v":0},"options":[{"_id":"68961d4fa399ed435f0ee8ce","question_id":"68961d4fa399ed435f0ee8cc","option_type":"text","option_text":"6.5 minutes","path_url":null,"__v":0},{"_id":"68961d4fa399ed435f0ee8d0","question_id":"68961d4fa399ed435f0ee8cc","option_type":"text","option_text":"7.2 minutes","path_url":null,"__v":0},{"_id":"68961d4fa399ed435f0ee8d2","question_id":"68961d4fa399ed435f0ee8cc","option_type":"text","option_text":"8.0 minutes","path_url":null,"__v":0},{"_id":"68961d4fa399ed435f0ee8d4","question_id":"68961d4fa399ed435f0ee8cc","option_type":"text","option_text":"9.5 minutes","path_url":null,"__v":0}]},{"question":{"_id":"68962118a399ed435f0ee976","question":"

A tank has 3 pipes. Pipe A fills the tank in 6 hours, pipe B fills in 8 hours, and pipe C empties in 12 hours. If A and C are opened for 2 hours, then A is closed and B and C work together, how long will it take from the beginning to fill the tank completely?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"22 hours","explanation":"$26","createdAt":"2025-08-08T16:08:56.392Z","updatedAt":"2025-08-08T16:08:56.392Z","__v":0},"options":[{"_id":"68962118a399ed435f0ee978","question_id":"68962118a399ed435f0ee976","option_type":"text","option_text":"14 hours","path_url":null,"__v":0},{"_id":"68962118a399ed435f0ee97a","question_id":"68962118a399ed435f0ee976","option_type":"text","option_text":"22 hours","path_url":null,"__v":0},{"_id":"68962118a399ed435f0ee97c","question_id":"68962118a399ed435f0ee976","option_type":"text","option_text":"18 hours","path_url":null,"__v":0},{"_id":"68962118a399ed435f0ee97e","question_id":"68962118a399ed435f0ee976","option_type":"text","option_text":"20 hours","path_url":null,"__v":0}]},{"question":{"_id":"689620a1a399ed435f0ee962","question":"

A cistern has an inlet pipe that fills it in 8 hours and an outlet pipe that empties it in 10 hours. If the cistern is initially empty and both pipes are opened, how long will it take to fill 3/4 of the cistern?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"30 hours","explanation":"

Inlet pipe fills the cistern in 8 hours → rate = 1/8 per hour
Outlet pipe empties the cistern in 10 hours → rate = -1/10 per hour
Net rate = 1/8 - 1/10
LCM of 8 and 10 is 40
1/8 = 5/40
1/10 = 4/40
Net rate = 5/40 - 4/40 = 1/40 per hour
Time to fill 3/4 of the cistern = (3/4) ÷ (1/40) = (3/4) × 40 = 30 hours

","createdAt":"2025-08-08T16:06:57.117Z","updatedAt":"2025-08-08T16:06:57.117Z","__v":0},"options":[{"_id":"689620a1a399ed435f0ee964","question_id":"689620a1a399ed435f0ee962","option_type":"text","option_text":"25 hours","path_url":null,"__v":0},{"_id":"689620a1a399ed435f0ee966","question_id":"689620a1a399ed435f0ee962","option_type":"text","option_text":"30 hours","path_url":null,"__v":0},{"_id":"689620a1a399ed435f0ee968","question_id":"689620a1a399ed435f0ee962","option_type":"text","option_text":"35 hours","path_url":null,"__v":0},{"_id":"689620a1a399ed435f0ee96a","question_id":"689620a1a399ed435f0ee962","option_type":"text","option_text":"40 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961dd8a399ed435f0ee8e0","question":"

Three pipes X, Y, and Z can fill a cistern in 10, 15, and 30 hours respectively. All three pipes are opened together, but after 2 hours, pipe Z is closed. How much more time will be needed to fill the cistern?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"4 hours","explanation":"$27","createdAt":"2025-08-08T15:55:04.338Z","updatedAt":"2025-08-08T15:55:04.338Z","__v":0},"options":[{"_id":"68961dd8a399ed435f0ee8e2","question_id":"68961dd8a399ed435f0ee8e0","option_type":"text","option_text":"4 hours","path_url":null,"__v":0},{"_id":"68961dd8a399ed435f0ee8e4","question_id":"68961dd8a399ed435f0ee8e0","option_type":"text","option_text":"5 hours","path_url":null,"__v":0},{"_id":"68961dd8a399ed435f0ee8e6","question_id":"68961dd8a399ed435f0ee8e0","option_type":"text","option_text":"6 hours","path_url":null,"__v":0},{"_id":"68961dd8a399ed435f0ee8e8","question_id":"68961dd8a399ed435f0ee8e0","option_type":"text","option_text":"7 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961d8aa399ed435f0ee8d6","question":"

A tank has an inlet pipe that can fill it in 6 hours. It also has an outlet pipe that can empty the full tank in 8 hours. If both pipes are opened simultaneously when the tank is empty, how long will it take to fill the tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"24 hours","explanation":"

The inlet pipe fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.

The outlet pipe empties the tank in 8 hours, so its rate is -1/8 per hour.

Add the rates of both pipes:

1/6 - 1/8

Find the LCM of 6 and 8, which is 24.

Convert each fraction:

1/6 = 4/24

1/8 = 3/24

Total rate = 4/24 - 3/24 = 1/24

Since 1/24 of the tank is filled in 1 hour, the full tank will be filled in 24 hours.

","createdAt":"2025-08-08T15:53:46.385Z","updatedAt":"2025-08-08T15:53:46.385Z","__v":0},"options":[{"_id":"68961d8aa399ed435f0ee8d8","question_id":"68961d8aa399ed435f0ee8d6","option_type":"text","option_text":"20 hours","path_url":null,"__v":0},{"_id":"68961d8aa399ed435f0ee8da","question_id":"68961d8aa399ed435f0ee8d6","option_type":"text","option_text":"24 hours","path_url":null,"__v":0},{"_id":"68961d8aa399ed435f0ee8dc","question_id":"68961d8aa399ed435f0ee8d6","option_type":"text","option_text":"28 hours","path_url":null,"__v":0},{"_id":"68961d8aa399ed435f0ee8de","question_id":"68961d8aa399ed435f0ee8d6","option_type":"text","option_text":"32 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961cffa399ed435f0ee8c2","question":"

A cistern can be filled by pipe S in 8 hours and by pipe T in 12 hours. There is also a drain pipe U that can empty the cistern in 6 hours. If the cistern is initially empty and all pipes are opened simultaneously, what will happen?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"Fills in 24 hours","explanation":"

Pipe S fills the cistern in 8 hours, so its rate is 1/8 of the tank per hour.

Pipe T fills it in 12 hours, so its rate is 1/12 per hour.

Drain pipe U empties the cistern in 6 hours, so its rate is -1/6 per hour.

Add the rates of all three pipes:

1/8 + 1/12 - 1/6

Find the LCM of 8, 12, and 6, which is 24.

Convert each fraction:

1/8 = 3/24

1/12 = 2/24

1/6 = 4/24

So, the total rate is:

3/24 + 2/24 - 4/24 = 1/24

Since the net rate is 1/24, 1/24 of the cistern is filled in one hour.

Therefore, the cistern will be filled in 24 hours.

","createdAt":"2025-08-08T15:51:27.342Z","updatedAt":"2025-08-08T15:51:27.342Z","__v":0},"options":[{"_id":"68961cffa399ed435f0ee8c4","question_id":"68961cffa399ed435f0ee8c2","option_type":"text","option_text":"Fills in 24 hours","path_url":null,"__v":0},{"_id":"68961cffa399ed435f0ee8c6","question_id":"68961cffa399ed435f0ee8c2","option_type":"text","option_text":"Never fills","path_url":null,"__v":0},{"_id":"68961cffa399ed435f0ee8c8","question_id":"68961cffa399ed435f0ee8c2","option_type":"text","option_text":"Fills in 12 hours","path_url":null,"__v":0},{"_id":"68961cffa399ed435f0ee8ca","question_id":"68961cffa399ed435f0ee8c2","option_type":"text","option_text":"Empties completely","path_url":null,"__v":0}]},{"question":{"_id":"68961fa4a399ed435f0ee930","question":"

A water tank has 5 outlet pipes that can empty the tank in 4, 6, 8, 12, and 24 hours respectively. If all pipes are opened together, how long will it take to empty the full tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"1.5 hours","explanation":"$28","createdAt":"2025-08-08T16:02:44.345Z","updatedAt":"2025-08-08T16:02:44.345Z","__v":0},"options":[{"_id":"68961fa4a399ed435f0ee932","question_id":"68961fa4a399ed435f0ee930","option_type":"text","option_text":"2 hours","path_url":null,"__v":0},{"_id":"68961fa4a399ed435f0ee934","question_id":"68961fa4a399ed435f0ee930","option_type":"text","option_text":"1.5 hours","path_url":null,"__v":0},{"_id":"68961fa4a399ed435f0ee936","question_id":"68961fa4a399ed435f0ee930","option_type":"text","option_text":"2.4 hours","path_url":null,"__v":0},{"_id":"68961fa4a399ed435f0ee938","question_id":"68961fa4a399ed435f0ee930","option_type":"text","option_text":"3 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961ccfa399ed435f0ee8b8","question":"

A water reservoir has two inlet pipes P and Q, and one outlet pipe R. Pipe P fills the reservoir in 15 hours, pipe Q fills it in 20 hours, and pipe R can empty the full reservoir in 12 hours. If all three pipes are opened together when the reservoir is empty, how long will it take to fill the reservoir completely?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"30 hours","explanation":"

Pipe P fills the reservoir in 15 hours, so its rate is 1/15 of the tank per hour.

Pipe Q fills it in 20 hours, so its rate is 1/20 per hour.

Pipe R empties it in 12 hours, so its rate is -1/12 per hour.

Add the rates of all three pipes:

1/15 + 1/20 - 1/12

To add them, find the LCM of 15, 20, and 12 which is 60.

Convert each fraction:

1/15 = 4/60

1/20 = 3/60

1/12 = 5/60

So, the total rate is:

4/60 + 3/60 - 5/60 = 2/60 = 1/30

Since 1/30 of the reservoir is filled in one hour, the reservoir will be completely filled in 30 hours.

","createdAt":"2025-08-08T15:50:39.081Z","updatedAt":"2025-08-08T15:50:39.081Z","__v":0},"options":[{"_id":"68961ccfa399ed435f0ee8ba","question_id":"68961ccfa399ed435f0ee8b8","option_type":"text","option_text":"30 hours","path_url":null,"__v":0},{"_id":"68961ccfa399ed435f0ee8bc","question_id":"68961ccfa399ed435f0ee8b8","option_type":"text","option_text":"60 hours","path_url":null,"__v":0},{"_id":"68961ccfa399ed435f0ee8be","question_id":"68961ccfa399ed435f0ee8b8","option_type":"text","option_text":"45 hours","path_url":null,"__v":0},{"_id":"68961ccfa399ed435f0ee8c0","question_id":"68961ccfa399ed435f0ee8b8","option_type":"text","option_text":"Never fills","path_url":null,"__v":0}]},{"question":{"_id":"68961f40a399ed435f0ee91c","question":"

A cistern can be filled by two pipes in 15 and 20 minutes respectively. Both pipes are opened together but after 5 minutes, the slower pipe is turned off. How much more time will be needed to fill the cistern?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"6.25 minutes","explanation":"$29","createdAt":"2025-08-08T16:01:04.930Z","updatedAt":"2025-08-08T16:01:04.930Z","__v":0},"options":[{"_id":"68961f40a399ed435f0ee91e","question_id":"68961f40a399ed435f0ee91c","option_type":"text","option_text":"5 minutes","path_url":null,"__v":0},{"_id":"68961f40a399ed435f0ee920","question_id":"68961f40a399ed435f0ee91c","option_type":"text","option_text":"6.25 minutes","path_url":null,"__v":0},{"_id":"68961f40a399ed435f0ee922","question_id":"68961f40a399ed435f0ee91c","option_type":"text","option_text":"8 minutes","path_url":null,"__v":0},{"_id":"68961f40a399ed435f0ee924","question_id":"68961f40a399ed435f0ee91c","option_type":"text","option_text":"7 minutes","path_url":null,"__v":0}]},{"question":{"_id":"68961e50a399ed435f0ee8f4","question":"

Two pipes can fill a pool in 8 and 12 hours respectively. A third pipe can empty the pool in 6 hours. If all three pipes work together, how long will it take to fill the empty pool?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"24 hours","explanation":"$2a","createdAt":"2025-08-08T15:57:04.411Z","updatedAt":"2025-08-08T15:57:04.411Z","__v":0},"options":[{"_id":"68961e50a399ed435f0ee8f6","question_id":"68961e50a399ed435f0ee8f4","option_type":"text","option_text":"Pool will never fill","path_url":null,"__v":0},{"_id":"68961e50a399ed435f0ee8f8","question_id":"68961e50a399ed435f0ee8f4","option_type":"text","option_text":"24 hours","path_url":null,"__v":0},{"_id":"68961e50a399ed435f0ee8fa","question_id":"68961e50a399ed435f0ee8f4","option_type":"text","option_text":"18 hours","path_url":null,"__v":0},{"_id":"68961e50a399ed435f0ee8fc","question_id":"68961e50a399ed435f0ee8f4","option_type":"text","option_text":"12 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961f05a399ed435f0ee912","question":"

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"14 hours","explanation":"$2b","createdAt":"2025-08-08T16:00:05.941Z","updatedAt":"2025-08-08T16:00:05.941Z","__v":0},"options":[{"_id":"68961f05a399ed435f0ee914","question_id":"68961f05a399ed435f0ee912","option_type":"text","option_text":"12 hours","path_url":null,"__v":0},{"_id":"68961f05a399ed435f0ee916","question_id":"68961f05a399ed435f0ee912","option_type":"text","option_text":"14 hours","path_url":null,"__v":0},{"_id":"68961f05a399ed435f0ee918","question_id":"68961f05a399ed435f0ee912","option_type":"text","option_text":"16 hours","path_url":null,"__v":0},{"_id":"68961f05a399ed435f0ee91a","question_id":"68961f05a399ed435f0ee912","option_type":"text","option_text":"18 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961c4fa399ed435f0ee8ae","question":"

A swimming pool has three filling pipes M, N, and O. Pipe M can fill the pool in 20 hours, pipe N can fill it in 30 hours, and pipe O can fill it in 60 hours. If all three pipes are opened simultaneously, how long will it take to fill the empty pool?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"10 hours","explanation":"

Rate of M = 1/20, Rate of N = 1/30

Rate of O = 1/60 Combined rate = 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10

Time = 1 ÷ (1/10) = 10 hours

","createdAt":"2025-08-08T15:48:31.165Z","updatedAt":"2025-08-08T15:48:31.165Z","__v":0},"options":[{"_id":"68961c4fa399ed435f0ee8b0","question_id":"68961c4fa399ed435f0ee8ae","option_type":"text","option_text":"8 hours","path_url":null,"__v":0},{"_id":"68961c4fa399ed435f0ee8b2","question_id":"68961c4fa399ed435f0ee8ae","option_type":"text","option_text":"10 hours","path_url":null,"__v":0},{"_id":"68961c4fa399ed435f0ee8b4","question_id":"68961c4fa399ed435f0ee8ae","option_type":"text","option_text":"12 hours","path_url":null,"__v":0},{"_id":"68961c4fa399ed435f0ee8b6","question_id":"68961c4fa399ed435f0ee8ae","option_type":"text","option_text":"15 hours","path_url":null,"__v":0}]},{"question":{"_id":"68961e9aa399ed435f0ee8fe","question":"

A tank has 4 inlet pipes. Pipes A, B, C can fill the tank individually in 2, 3, and 6 hours respectively. Pipe D can empty the full tank in 4 hours. If all pipes are opened together, how long will it take to fill the tank?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"1.2 hours","explanation":"$2c","createdAt":"2025-08-08T15:58:18.434Z","updatedAt":"2025-08-08T15:58:18.434Z","__v":0},"options":[{"_id":"68961e9aa399ed435f0ee900","question_id":"68961e9aa399ed435f0ee8fe","option_type":"text","option_text":"1.2 hours","path_url":null,"__v":0},{"_id":"68961e9aa399ed435f0ee902","question_id":"68961e9aa399ed435f0ee8fe","option_type":"text","option_text":"2 hours","path_url":null,"__v":0},{"_id":"68961e9aa399ed435f0ee904","question_id":"68961e9aa399ed435f0ee8fe","option_type":"text","option_text":"2.4 hours","path_url":null,"__v":0},{"_id":"68961e9aa399ed435f0ee906","question_id":"68961e9aa399ed435f0ee8fe","option_type":"text","option_text":"3 hours","path_url":null,"__v":0}]},{"question":{"_id":"68962018a399ed435f0ee944","question":"

A pipe fills a tank in 6 hours. After 3 hours of filling, another pipe that can fill the tank in 4 hours is also opened. How much total time will it take to fill the tank completely?

","question_type":"text","question_image_url":null,"subtopic_id":"68961b9aa399ed435f0ee8a9","exam_ids":[],"answer":"4.2 hours","explanation":"

After 3 hours, work done = 3/6 = 1/2
Remaining work = 1/2
Combined rate = 1/6 + 1/4 = 5/12
Time for remaining = (1/2) ÷ (5/12) = 6/5 = 1.2 hours
Total time = 3 + 1.2 = 4.2 hours

","createdAt":"2025-08-08T16:04:40.327Z","updatedAt":"2025-08-08T16:04:40.327Z","__v":0},"options":[{"_id":"68962018a399ed435f0ee946","question_id":"68962018a399ed435f0ee944","option_type":"text","option_text":"4.2 hours","path_url":null,"__v":0},{"_id":"68962018a399ed435f0ee948","question_id":"68962018a399ed435f0ee944","option_type":"text","option_text":"4.8 hours","path_url":null,"__v":0},{"_id":"68962018a399ed435f0ee94a","question_id":"68962018a399ed435f0ee944","option_type":"text","option_text":"5.1 hours","path_url":null,"__v":0},{"_id":"68962018a399ed435f0ee94c","question_id":"68962018a399ed435f0ee944","option_type":"text","option_text":"5.4 hours","path_url":null,"__v":0}]}],"initialError":""}]]

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Online Test - Pipes And Cisterns

Question 1 of 21