woops!! ...
Tank is full at $180$ minutes after $1/15$th part is drained by last minute. If we look oppositely, $1$ (or full tank) in $180$ the minute, $1+1/15$ in $179$, $1+1/15 - 1/30$ in $178$, $1+1/15 - 1/30-1/20$ in $177$ ..
If we look oppositely it is essentially the time required to build up extra $1/15$ th in $179$the minute volume and drain it in the last. The filling up equation from opposite will be of the following form. So we are trying to find the least positive integer solution of one of these equations. $ {n \over 15} - {n \over 30} - {n \over 20} = -{1 \over 15} \\ {n +1\over 15} - {n \over 30} - {n \over 20} = -{1 \over 15}\\ {n +1\over 15} - {n+1 \over 30} - {n \over 20} = -{1 \over 15} $ So we have $n = 4$ for the first equaton so $4 + 4 + 4 = 12$, (from opposite view) it takes $12$ minute to build up $1 /15$ th volume and another min to drain it. So, $180 - 13 = 167$.