The smallest tap fills 1/20 water-cask in 1 minute.
The middle tap fills 1/12 water-cask in 1 minute.
The largest tap fills 1/5 water-cask in 1 minute.
Together they fill
1/20 + 1/12 + 1/5 = 1/3
water-cask in 1 minute.
Therefore, the whole water-cask is filled in 3 minutes.