1. The fastest and Shortest way for Four of them to cross the bridge is to find a way for 7 and 10 to cross the bridge together, only once and never come back. So here is it,

2. Let 1 and 2 cross the bridge, 2 comes back, 7 and 10 go across, 1 comes back then 1 and 2 go across.

3 So the Total Time taken for Four to cross = 2 + 2 + 10 + 1 + 2 = 17 mins