Aquantity a varies inversely as a quantity b, if, when b changes, a changes in the inverse ratio. what happens to the quantity a if the quantity b doubles? (site 1)

Let us write the inverse variation in the given in an equation form,
 
                                             a = k / b

where k is the constant of proportion. 
If the value of b is double, there should be a corresponding change in a. 

                                            (x)(a) = k / 2b
                                         (x)(a) = (1/2)(k/b)

The value of x is 1/2. Therefore, the value of a is halved.