Taps X, Y and Z alone would fill a tank in 20, 30 and 60 minutes respectively. X and Y are opened at the start, and Z is opened 6 minutes later. How long does the tank take to fill?

Take the tank as 60 units: X gives 3 units a minute, Y gives 2 and Z gives 1. In the first 6 minutes X and Y put in $5\times 6=30$ units, leaving 30. With Z open the three deliver 6 units a minute, so 30 ÷ 6 = 5 more minutes. Total 6 + 5 = 11 minutes. 10 minutes assumes all three ran from the start (60 ÷ 6). 12 minutes leaves Z out entirely (60 ÷ 5). 16 minutes adds the all-three time of 10 minutes onto the opening 6, counting the first stretch twice.