A quantity 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 doubts?

quantity a is halfed

Corrected question;

A quantity 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?

Step-by-step explanation:

Analysing the question;

A quantity a varies inversely as a quantity b,

a ∝ 1/b

a = k/b ... 1

when b changes a changes in the inverse ratio;

Since the change at the same ratio but inversely, k = 1

So, equation 1 becomes;

a = 1/b

If the quantity b doubles,

ab = 1

a1b1 = a2b2

When b doubles, b2 = 2b1

a1b1 = a2 (2b1)

Making a2 the subject of formula;

a2 = a1b1 / (2b1)

a2 = a1/2

Therefore, when b doubles, a will be divided by 2, that means a is halfed.