CAT Practice : Pipes cisterns, Work time

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The following topics are covered in the CAT quant section from Arithmetic in Pipes cisterns and work time. Detailed explanatory answers, solution videos and slide decks are also provided.
1. Fill pipes and drain pipes

A drain pipe can drain a tank in 12 hours, and a fill pipe can fill the same tank in 6 hours. A total of n pipes – which include a few fill pipes and the remaining drain pipes – can fill the entire tank in 2 hours. How many of the following values could ‘n’ take?
a)   24               b)   16               c)   33               d)   13               e)   9                 f)   8

1. 3
2. 4
3. 2
4. 1
2. Three Pipes

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. How long will C alone take to fill the tank?

1. 18
2. 36
3. 27
4. 24
3. Three Pipes

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.
ii.   B first, followed by A, and then C.
iii.  B first, followed by C, and then A.

1. 279.25 mins, 280 mins and 280 mins
2. 280 mins, 280 mins and 279.25 mins
3. 279 mins, 280 mins and 279.25 mins
4. 277 mins, 277 mins and 45 secs and 279 mins
277 mins, 277 mins and 45 secs and 279 mins
• PIpes opened alternately
• Hard
4. Work Time

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 the same task?

1. 30 to 33.6 days
2. 32 to 35 days
3. 33.6 to 35 days
4. 30 to 35 days
5. Fill pipes and drain pipes

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

1. 1 and 2 only
2. 1 and 3 only
3. 2 and 4 only
4. 2 and 3 only
2 and 3 only
• Pipes Cisterns
• Medium
6. Pipes Cisterns - Algebra

Consider three friends A, B and C who work at differing speeds. When the slowest two work together they take n days to finish a task. When the quickest two work together they take m days to finish a task. One of them, if he worked alone would take thrice as much time as it would take when all three work together. How much time would it take if all three worked together?

1. ${3mn \over 2(m + n)}$
2. ${2mn \over m + n}$
3. ${4mn \over 3(m + n)}$
4. ${5mn \over 3(m + n)}$
${4mn \over 3(m + n)}$
• Indirect Proportion
• Hard
7. Pipes Cisterns - Filling Tank

Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?

1. 40 minutes
2. 28 minutes
3. 30 minutes
4. 36 minutes
8. Pipes Cisterns - Work Time

B takes 12 more days than A to finish a task. B and A start this task and A leaves the task 12 days before the task is finished. B completes 60% of the overall task. How long would B have taken to finish the task if he had worked independently?

1. 48 days
2. 36 days
3. 28 days
4. 32 days
9. Pipes Cisterns - Work Time

A and B together can finish a task in 12 days. If A worked half as efficiently as he usually does and B works thrice as efficiently as he usually does, the task gets completed in 9 days. How long would A take to finish the task if he worked independently?

1. 12 days
2. 24 days
3. 27 days
4. 18 days
10. Pipes Cisterns - Work Time

B takes 12 more hours than A to complete a task. If they work together, they take 16 fewer hours than B would take to complete the task. How long will it take A and B together to complete a task twice as difficult as the first one?

1. 16 hrs
2. 12 hrs
3. 14 hrs
4. 18 hrs
11. Pipe flow rate

Pipe A can fill a tank in 12 hours. When it works along with Pipe B, it can fill the tank in 8 hours. In how many hours can pipe B fill the same tank independently?.

1. 8 hrs
2. 12 hrs
3. 24 hrs
4. 16 hrs
12. Pipes Cisterns - Work Time

Number of units of a good that can be produced by a factory is directly proportional to the square of the number of workers, square root of the number of machines and to the number of hours put in. The factory produces 200 goods when 4 people work for 8 hours each with 4 machines. When 3 people work for 12 hours each with 9 machines, how many goods will be produced?.

1. ${K = \frac{25}{32}}$
2. ${K = \frac{100}{163}}$
3. ${K = \frac{25}{256}}$
4. ${K = \frac{16}{29}}$
${K = \frac{25}{32}}$
• Work Time
• Medium
13. Pipes Cisterns - Work Time

A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?

1. 10.8 days
2. 14.33 days
3. 11 days
4. 8.4 days
14. Pipes Cisterns - Work Time

A can complete a task 4 hours lesser time than B takes to complete the same. If A and B together can complete the task in 288 minutes, how long does B alone take to complete the task?

1. 1 hr
2. 2 hrs
3. 3 hrs
4. 12 hrs
15. Pipe Leakage

Two pipes can fill a tank in 12 hrs and 18 hrs respectively. The pipes are opened together but due to a pipe leakage , it takes 48 minutes extra to fill the tank, If the tank is full, what time will it take to completely empty due to the leakage.

1. 72 hrs
2. 84 hrs
3. 96 hrs
4. 112 hrs
16. Pipes

A cistern of capacity 40 litres has an inlet and an outlet pipe. When both the pipes are opened at once, it takes 8 minutes to fill the cistern. However, if the outflow rate is increased 1.5 times, the cistern never gets filled. Which of the following can be the outflow rate?

1. 8 litres/minute
2. 6 litres/minute
3. 12 litres/minute
4. 9 litres/minute
17. Two Pipes

A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.

1. 10 h
2. 14 h
3. 16 h
4. 20 h
18. Mining

A mining team made a plan to mine up to 300 m in a certain number of days. After working as per plan for 5 days, they added new members to the team and hence could mine 5 m more per day. In this way, 4 days before the planned date, they had mined 295 m. How many meters of mining was initially planned for each day?

1. 30 m
2. 12.5 m
3. 15 m
4. 7.5 m
19. Watering A Garden

Ajay and Suraj can water a garden in 45 minutes and 40 minutes respectively. They started working together but after some time Ajay left to watch a cricket match. Suraj hurriedly finished the work in next 23 minutes and joined Ajay. After how many minutes had Ajay left?

1. 9 min
2. 8 min
3. 7 min
4. 10 min
20. Fetching Water

Bibhor takes 3 hours to fetch as much water as Ahmed can fetch in 2 hours. Deepak takes 5 hours to fetch as much water as Bibhor can fetch in 4 hours. A tank takes 20 hours to fill if all work together. What time would Bibhor take to fill the tank alone?

1. 50 h
2. 56 h
3. 77 h
4. 66 h
21. Laying Wires

Anuj, Bibhuti and Chandu can lay 432 m of wires together in 8 days. In a day, Chandu can lay as many more meters of wire than Bibhuti as Bibhuti can lay more than Anuj. Chandu’s 5 days of work is equivalent to Anuj’s 7 days of work. How many meters of wire can Anuj alone lay in a day?

1. 9 m
2. 15 m
3. 18 m
4. 21 m
22. Typing Pages

A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?

1. 22.5 days
2. 45 days
3. 30 days
4. 20 days
23. Toys

A, B and C are to make 100 toys. In a day, they can together make 25 toys. A starts to work alone and makes 32 toys in some days. A then leaves and B and C works to make the remaining toys. It takes 8 days overall to make the 100 toys. How many days will it take for A to make 256 toys alone?

1. 16 days
2. 32 days
3. 64 days
4. 30 days
24. Amar, Akbar and Anthony

Amar, Akbar and Anthony set out to complete a work. Anthony being the eldest would take 1 day less than Amar if he were to complete the work alone. All three together could complete the work in a day. However, Anthony was kidnapped by Shakal. Amar and Akbar began the work in his absence. After a day, Amar was also kidnapped. Akbar took 3 more days to finish the work. How much portion of the work Anthony could do in a day?

1. $\frac{2}{3}$
2. $\frac{1}{6}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$
25. Iphone 16s

It’s year 2025 and iphone16 has just been launched. Apple has claimed that it is the best iphone they have created so far. It’s 4 charging inlets have completely revolutionized the mobile market. If only top and bottom inlets are used, it takes 20 mins to fully charge. If the right, left and bottom inlet are used, it takes 15 mins to fully charge. If top, left and right inlets are used, it takes 12 mins to charge.. What is the fastest possible time in which the iphone16 can be fully charged?

1. 12 min
2. 8 min
3. 11 min
4. 10 min

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