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**Common Admission Test (CAT) Aptitude Questions**

**Work Time, Pipes Cisterns questions appear periodically in the Quant section of CAT**

**Question 1** If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?

**Correct Answer is 30 days**

Explanatory Answer

Let 'a' be the number of days in which A can do the job alone. Therefore, working alone, A will complete 1 by a th of the job in a day.

Similarly, let 'b' be the number of days in which B can do the job alone. Hence, B will complete 1 by bth of the job in a day.

Working together, A and B will complete 1/a + 1/b of the job in a day.

The problem states that working together, A and B will complete the job in 7.5 or 15/2 days. i.e they will complete 2/15th of the job in a day.

Therefore, 1/a + 1/b = 2/15 ...... (1)

From the question, we know that if A completes half the job working alone and B takes over and completes the next half, they will take 20 days.

As A can complete the job working alone in 'a' days, he will complete half the job, working alone, in a/2 days.

Similarly, B will complete the remaining half of the job in b/2 days.

Therefore, a/2 + b/2 = 30 => a + b = 40 or a = 40 - b ...... (2)

From (1) and (2) we get, 1/40-b + 1/b = 2/15 => 600 = 2b(40 - b)

=> 600 = 80b - 2b2

=> b2 - 40b + 300 = 0

=> (b - 30)(b - 10) = 0

=> b = 30 or b = 10.

If b = 30, then a = 40 - 30 = 10 or

If b = 10, then a = 40 - 10 = 30.

As A is more efficient than B, he will take lesser time to do the job alone. Hence A will take only 10 days and B will take 30 days.

Note: Whenever you encounter work time problems, always find out how much of the work can 'A' complete in a unit time (an hour, a day, a month etc). Find out how much of the work can be completed by 'B' in a unit time. Then add the amount of work done by A and B to find the total amount of work that will be completed in a unit time.

If 'A' takes 10 days to do a job, he will do 1/10th of the job in a day. Similarly, if 2/5ths of the job is done in a day, the entire job will be done in 5/2 days.

**Question 2** Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

**Explanatory Answer**

Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minute and Pipe C drains the tank at the rate of 20 litres a minute.

If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres of water at the end of 3 minutes.

After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.

It will take 13 * 3 = 39 minutes for the 13 cycles to be over.

At the end of the 39th minute, Pipe C will be closed and Pipe A will be opened. It will add 40 litres to the tank.

Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 litres of water.

At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened. It will add 30 litres of water in a minute.

Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 litres of water.

But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for a full minute at the end of 40 minutes.

Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a minute to fill 10 litres of water.

Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minute

or 40 minutes 20 seconds.

**Question 3** There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

Correct Answer is 7 pipes

**Explanatory Answer**

Let there be 'n' fill pipes attached to the tank.

Therefore, there will be 12 - n drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours. Therefore, each of the fill pipes will fill 1/8 th of the tank in an hour.

Hence, n fill pipes will fill n/8 of the tank in an hour.

Each drain pipe will drain the tank in 6 hours. Therefore, each of the drain pipes will drain 1/6 th of the tank in an hour.

Hence, (12 - n) drain pipes will drain (12-n)*1/6 th of the tank in an hour.

When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow. Therefore, in an hour 1/24 th of the tank gets filled.

Hence, .

i.e. or 7n - 48 = 1 => 7n = 49 or n = 7.

**Question 4 ** A pump can be used either to fill or to empty a tank. The capacity of the tank is 3600 m3. The emptying capacity of the pump is 10 m3/min higher than its filling capacity. What is the emptying capacity of the pump if the pump needs 12 more minutes to fill the tank than to empty it?

Correct Answer is 60 m3 / min

**Explanatory Answer**

Let 'f' m3/min be the filling capacity of the pump.

Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.

The time taken to fill the tank will be = 3600/f minutes

And the time taken to empty the tank will be = 3600/(f+10).

We know that it takes 12 more minutes to fill the tank than to empty it

i.e 3600/f - 3600/(f+10) = 12

=> 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)

=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2 + 10 f - 3000 = 0.

Solving for positive value of 'f' we get, f = 50.

Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min

**Question 5 ** Two workers A and B manufactured a batch of identical parts. A worked for 2 hours and B worked for 5 hours and they completed half the job. Then they worked together for another 3 hours and they had to do (1/20)th of the job. How much time does B take to complete the job, if he worked alone?

**Explanatory Answer**

Let 'a' hours be the time that worker A will take to complete the job.

Let 'b' hours be the time that worker B takes to complete the job.

When A works for 2 hours and B works for 5 hours half the job is done.

i.e. . ....... (1)

When they work together for the next three hours, 1/20th of the job is yet to be completed.

They have completed half the job earlier and 1/20th is still left.

So by working for 3 hours, they have completed th of the job.

Therefore, ...... (2).

Solving equations (1) and (2), we get b = 15 hours.

**Question 6 ** Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom of the tank it takes thrice as long to fill the tank. How long will the leak at the bottom of the tank take to empty a full tank, when pipe A is kept closed?

Correct Answer is (3/2)a hours

**Explanatory Answer**

Pipe A fills the tank in 'a' hours.

Therefore, 1/a of the tank gets filled in an hour.

On account of the leak it takes 3a hours to fill the tank.

Therefore, 1/3a of the tank gets filled in an hour.

Let the leak at the bottom of the tank take 'x' hours to empty the tank.

Hence, 1/x of the tank gets emptied every hour.

Hence, x = 3a/2

**Question 7** A and B working together can finish a job in T days. If A works alone and completes the job, he will take T + 5 days. If B works alone and completes the same job, he will take T + 45 days. What is T?

**Correct Answer is 15 days
Explanatory Answer**

When A and B work together, they will take under root 225 = 15 days.

Where 5 and 45 are the extra time that A and B take to complete the job if they work alone compared to the time that they will take if they worked together.

Explanatory Answer

If the man takes 60 hours to complete the work, then he will finish 1/60 th of the work in 1 hour.

Let us assume that his son takes x hours to finish the same work.

If they work together for 1 hour they will finish 1/60 + 1/x = 1/40th of the work.

Therefore, 1/x = 1/120

The son, working alone would take 120 hours to complete the work.

Explanatory Answer

Ram completes 40% of work in 12 days.

i.e. another 60% of the work has to be completed by Ram and Ravi. They have taken 12 days to complete 60% of the work.

Therefore, Ram and Ravi, working together, would have completed the entire work in (12/60)*100 = 20 days.

As Ram completes 40% of the work in 12 days, he will take (12/40)*100 = 30 days to complete the entire work

Working alone, we know Ram takes 30 days to complete the entire work. Let us assume that Ravi takes 'x' days to complete the entire work, if he works alone. And together, they complete the entire work in 20 days.

Therefore, 1/30 + 1/x = 1/20

=> (1/x) = (1/20) - (1/30) = (1/60)

Therefore, Ravi will take 60 days to complete the work, if he works alone.

Hence, Ram is 100% more efficient than Ram.