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A pipe can fill a tank in 45 mints while another pipe can discharge the tank in one hour. In how much time the tank will be filled if both the pipes work on alternate minutes?

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Answer: it will take 360 minutes to fill the tank.

Explanation:

1. First, let's find the rates at which each pipe fills or discharges the tank.

- The first pipe can fill the tank in 45 minutes, so its filling rate is 1/45 of the tank per minute.

- The second pipe can discharge the tank in one hour, which is equivalent to 60 minutes. Therefore, its discharging rate is 1/60 of the tank per minute.

2. Next, let's determine how long it takes for the tank to be filled when the pipes work on alternate minutes.

- Since the pipes work on alternate minutes, each pipe has 1 minute to either fill or discharge the tank.

- In the first minute, the first pipe fills 1/45 of the tank.

- In the second minute, the second pipe discharges 1/60 of the tank.

- This process continues, with the first pipe filling in odd-numbered minutes and the second pipe discharging in even-numbered minutes.

3. To find out when the tank will be completely filled, we need to calculate how many cycles of alternating minutes are required.

- In each cycle of 2 minutes, the net change in the tank's level is (1/45 - 1/60) of the tank.

- Simplifying this expression, we get (4/180 - 3/180) of the tank, which is 1/180 of the tank.

- Therefore, it takes 180 cycles of alternating minutes to fill the entire tank.

4. Finally, let's calculate the total time required to fill the tank.

- Since each cycle of alternating minutes takes 2 minutes, the total time required is 180 cycles multiplied by 2 minutes per cycle.

- Thus, the tank will be filled in 360 minutes.

Therefore, if both pipes work on alternate minutes,

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