When the burner in a hot air balloon is turned on, the temperature of the air in the balloon causing its volume to and the balloon

This is a very poorly written question.

The choice they want is 'B'.  But that's a terrible way to describe
what happens.

The volume of the balloon never needs to change.

When the burner turned on, it creates some fiery hot air
right above the flame.  The fiery hot air quickly rises to
the top of the balloon, forcing some not-so-hot air out
at the bottom. 

The fiery hot air is less dense than the air that got forced out,
so now, the average density of all the air in the balloon has
decreased. 

Since its volume hasn't changed but its average density has
decreased, the buoyant force on it (it's floating in air) has
increased.  The balloon either descends slower than before,
or else rises faster than before.

A,d, and e on edgunuity

The correct answer for the first question is a. because if cold air is denser then the warm air will be pushed out of the way. the coreect answer for the 2nd question is a.