Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hours working separately. Pipe C can empty whole the tank in 4 hours. He opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was half-filled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. What is the time difference between both the cases, to fill the tank fully:

Using the combined work formula, pipes A and B together fill 1/4 + 1/6 = 5/12 of the tank per hour. In the intended half-filled case, they take 6/5 hours to fill half, and then adding pipe C alters the rate to 1/4 + 1/6 - 1/4 = 1/6 per hour to fill the second half, taking 3 hours for a total of 4.2 hours. In the mistaken 3/4th filled case, they take 9/5 hours to fill 3/4th of the tank, and then work at the 1/6 per hour rate to fill the remaining 1/4th, taking 1.5 hours for a total of 3.3 hours. The difference is 0.9 hours, which equals 54 minutes.

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