But the upthrust the car derived from displacing air is negligible. The magnitude of the upthrust is the weight of the displaced air, which can be safely ignored for this question. So the weight of the car must be supported by the upthrust exerted by water.
xmPhysics 
mr chua, doesnt the car also displace air so shouldnt by that logic the bridge also not need to support W of the car
But the upthrust the car derived from displacing air is negligible. The magnitude of the upthrust is the weight of the displaced air, which can be safely ignored for this question. So the weight of the car must be supported by the upthrust exerted by water.