The question is from Pipes and Cisterns. The filling rates of three pipes are given and we need to find out the time to fill the tank in three given conditions. Sometimes 100 + 25 - 50 is different from 75. Think about this before going to the solutions. Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.

Question 3: 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

- A is kept open first, followed by B and then C.
- B first, followed by A, and then C.
- B first, followed by C, and then A.

- 279.25 mins, 280 mins and 280 mins
- 280 mins, 280 mins and 279.25 mins
- 279 mins, 280 mins and 279.25 mins
- 277 mins, 277 mins 45 sec and 279 mins

277 mins, 277.45 mins and 279 mins

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**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

Now, A will be open, A can fill 100 liters in a minute.

277 mins - 7000 liters

So, it would take 277 mins 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.**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

276 mins - 6900 liters

Now, B will be open, B can fill 25 liters in a minute.

277 mins - 6925 liters

Now, A will be open, A can fill 100 liters in a minute. Therefore, A can fill 75 liters in 45 seconds.

277 mins 45 sec - 7000 liters

So, it would take 277 mins 45 sec .**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 - 175 liters

9 mins - 250 liters

30 mins - 775 liters

270 mins - 6775 liters

273 mins - 6850 liters

276 mins - 6925 liters

Now, B will be open, B can fill 25 liters in a minute.

277 mins - 6950 liters

Now, C will be open, C will drain 50 liters in a minute.

278 mins - 6900 liters

Now, A will be open, A can fill 100 liters in a minute.

279 mins - 7000 liters

So, it would take 279 mins 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.

The question is **"how long will it take to fill the tank if"**

Choice D is the correct answer.

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