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Select the correct answerTwo pipes A and B can fill a tank in 36 minutes. and 45 minutes. respectively. A water pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. In how much time, the tank is full?radio_button_unchecked51 minradio_button_unchecked42 minradio_button_unchecked39 minradio_button_unchecked46 min

Question

Select the correct answerTwo pipes A and B can fill a tank in 36 minutes. and 45 minutes. respectively. A water pipe C can empty the tank in 30 minutes. First A and B are opened. After 7 minutes, C is also opened. In how much time, the tank is full?radio_button_unchecked51 minradio_button_unchecked42 minradio_button_unchecked39 minradio_button_unchecked46 min

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Solution

Let's solve this step by step:

  1. First, we need to find out how much of the tank each pipe can fill or empty in one minute. Pipe A can fill 1/36 of the tank in one minute, pipe B can fill 1/45 of the tank in one minute, and pipe C can empty 1/30 of the tank in one minute.

  2. If pipes A and B are opened together, they can fill (1/36 + 1/45) = 9/180 + 4/180 = 13/180 of the tank in one minute.

  3. In 7 minutes, pipes A and B together can fill 7 * 13/180 = 91/180 of the tank.

  4. After 7 minutes, pipe C is also opened. Now, all three pipes together can fill or empty (13/180 - 1/30) = 13/180 - 6/180 = 7/180 of the tank in one minute.

  5. Now, we need to find out how much time it will take to fill the remaining part of the tank. The remaining part of the tank is (1 - 91/180) = 89/180 of the tank.

  6. Therefore, the time taken to fill the remaining part of the tank is (89/180) / (7/180) = 89/7 = 12.71 minutes.

  7. So, the total time taken to fill the tank is 7 minutes (when only A and B were opened) + 12.71 minutes (when all three pipes were opened) = 19.71 minutes.

However, none of the given options match this answer. There might be a mistake in the question or the options provided.

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