The total time taken to fill the bucket completely is 3 hours 45 minutes
The time taken to fill the bucket by one tap= 6 hours
Then the time take by one tap to fill half of the bucket= 3 hours
Part filled by one tap in one hour =
Part filled by four taps in one hour =
Given, that after half the bucket is filled, three more similar taps are opened
Then the remaining part = 
Time taken to fill the half of the bucket=
hours
Convert the hours to minutes
minutes
Therefore,
Total time taken to fill the bucket= The time taken by one tap to fill half of the bucket+ Time taken by 4 taps to fill the half of the bucket
=3 hours+ 45 minutes
=3 hours 45 minutes
Hence, The total time taken to fill the bucket completely is 3 hours 45 minutes
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