Two taps can fill a cistern in 2 hours and 47 hours respectively. A third tap can empty it
in 47 hours. How long (in hours) will it take to fill the empty cistern, if all of them are
opened together?
Correct Answer:
D. 2
Explanation:
The correct answer is Option D: 2.
To find the total time required to fill the cistern, we calculate the combined rate of all three taps. The first tap fills the cistern in 2 hours, so its rate is 1/2 of the cistern per hour. The second tap fills it in 47 hours, contributing a rate of 1/47 per hour. The third tap empties the cistern in 47 hours, which acts as a negative rate of -1/47 per hour. When all three taps operate simultaneously, the positive and negative rates of the 47-hour taps cancel each other out (1/47 - 1/47 = 0). This leaves only the rate of the first tap, which is 1/2. Therefore, the cistern will be filled in exactly 2 hours.
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