Tap 1 fills (1/10)th of the tub in a minute

Tap 2 fills (1/15)th of the tub in a minute

Tap 3 fills (1/30)th of the tub in a minute

(1/10)+(1/15)+(1/30)=(3/30)+(2/30)+(1/30)=(6/30)

The three taps will fill the tub in 30/6=5 mins