Pipes Cisterns - Solutions

Have given below solutions to the questions on Pipes Cisterns

1) Pipe A, B and C are kept open and together 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 pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?

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 alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in a minute. So, in a minute, B can fill 1/t - 1/3t = 2/3t. Or, B takes 3t/2 minutes to fill an entire tank

To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.

t/2 = t - 10, t = 20 minutes.

A takes 60 mins 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 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes.


2) Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if

i) A is kept open first, followed by B and then C
Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters

In the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15 seconds. So, it would take 279 mins and 15 seconds to fill the tank.

The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

ii) B first, followed by A, and then C

Each cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank would have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters

In the 280th minute, pipe B would be open and it would fill the remaining 25 liters in one minutes. So, it would take 280 mins.

iii) B first, followed by C, and then A
In this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is a small catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1 minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the third minute, the tank would be 100 liters full.

6 mins - 170 liters
9 mins - 250 liters
30 mins - 775 liters
270 mins - 6775 liters
273 mins - 6850 liters
276 mins - 6925 liters
279 minutes - 7000 liters

So, it would take 279 mins and 15 seconds to fill the tank.

The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

3) 4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete a task twice as difficult as this one?

4m and 6w finish in 24 days.
In one day, 4m + 6w = 1/24 of task

In these questions, just substitute extreme values to get the whole range
If a woman is half as efficient as man
4m + 3m = 1/24, 7m = 1/24, m = 1/168
6w + 2m = 3m + 2m = 5m, 5m will take 168/5 days = 33.6 days

If a woman is as efficient as a man
4m + 6w finish in 24 days
10m finish 1/24 of task in a day
6w + 2m = 8m, 8m will take 240/8 = 30 days to finish the task.

So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task.

4) A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
1) 32 2) 54 3) 29 4) 40

3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4. Both 54 and 29 are possible.

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IIM CAT Preparation Tips: Pipes Cisterns - Solutions

Jan 5, 2011

Pipes Cisterns - Solutions

Have given below solutions to the questions on Pipes Cisterns

1) Pipe A, B and C are kept open and together 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 pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?

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 alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in a minute. So, in a minute, B can fill 1/t - 1/3t = 2/3t. Or, B takes 3t/2 minutes to fill an entire tank

To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.

t/2 = t - 10, t = 20 minutes.

A takes 60 mins 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 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes.


2) Pipe A fills a tank at the rate of 100lit/min, Pipe B fills at the rate of 25 lit/min, pipe C drains at the rate of 50 lit/min. The three pipes are kept open for one minute each, one after the other. If the capacity of the tank is 7000 liters, how long will it take to fill the tank if

i) A is kept open first, followed by B and then C
Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters

In the 280th minute, pipe A would be open and it would fill the remaining 25 liters in 15 seconds. So, it would take 279 mins and 15 seconds to fill the tank.

The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

ii) B first, followed by A, and then C

Each cycle of 3 minutes, 75 liters get filled. 25 + 100 - 50. So, after 3 minutes the tank would have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
279 mins - 6975 liters

In the 280th minute, pipe B would be open and it would fill the remaining 25 liters in one minutes. So, it would take 280 mins.

iii) B first, followed by C, and then A
In this case also, Each cycle of 3 minutes, 75 liters get filled. 25 -50 + 100. But there is a small catch here. In the first set of 3 minutes, we would fill up to about 100 liters. After 1 minute, we would be at 25 liters, after 2 minutes, we would be at 0 liters and in the third minute, the tank would be 100 liters full.

6 mins - 170 liters
9 mins - 250 liters
30 mins - 775 liters
270 mins - 6775 liters
273 mins - 6850 liters
276 mins - 6925 liters
279 minutes - 7000 liters

So, it would take 279 mins and 15 seconds to fill the tank.

The most important thing in these type of questions is to think in terms of cycles till we reach close to the required target and then think in simple steps.

3) 4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete a task twice as difficult as this one?

4m and 6w finish in 24 days.
In one day, 4m + 6w = 1/24 of task

In these questions, just substitute extreme values to get the whole range
If a woman is half as efficient as man
4m + 3m = 1/24, 7m = 1/24, m = 1/168
6w + 2m = 3m + 2m = 5m, 5m will take 168/5 days = 33.6 days

If a woman is as efficient as a man
4m + 6w finish in 24 days
10m finish 1/24 of task in a day
6w + 2m = 8m, 8m will take 240/8 = 30 days to finish the task.

So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task.

4) A fill pipe can fill a tank in 20 hours, a drain pipe can drain a tank in 30 hours. If a system of n pipes (fill pipes and drain pipes put together) can fill the tank in exactly 5 hours, which of the following are possible values of n (More than one option could be correct)?
1) 32 2) 54 3) 29 4) 40

3 fill pipes cancel out 2 drain pipes. Plus, you need an additional 4 fill pipes fill the tank in 5 hours. so the answer has to be 5k + 4. Both 54 and 29 are possible.

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3 Comments:

At 7:48 AM , Blogger RadhikaTalluri said...

Thanks for posting the questions with answers.

Where can I get the complete CAT course material?

Thanks in advance,
Radhika

 
At 5:00 PM , Blogger Bee said...

You can get the complete material from 2iim.com. This is the relevant link -
http://www.2iim.com/IIM_CAT_classes_correspondence_courses/CAT_correspondence_course.shtml

 
At 2:16 PM , Blogger ballasatya said...

For question 2, We should stop before the last cycle mentioned here and go by minutes
Eg : i) A is kept open first, followed by B and then C
Each cycle of 3 minutes, 75 liters get filled. 100 + 25 - 50. So, after 3 minutes the tank would have 75 liters
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
276 mins - 6900 liters
Stop here, now 277th minute Tap A will be opened and fills 100lts…
That’s it now tank is filled.
Ans given as 279 min and 15 sec, this will lead to following
6 mins - 150 liters
9 mins - 225 liters
30 mins - 750 liters
270 mins - 6750 liters
273 mins - 6825 liters
276 mins - 6900 liters
277 mins – 7000liters
278 mins- 7000liters(B tries to fill 25 liters but it overflows)
279 mins – 6950liters
279 mins 15 secs – 6975liters(A fills 25 liters in 15 secs)
Now we have only 6975liters in tank but not full.
Just want to share my thoughts

 

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