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Two numbers a and b are inversely proportional to each other. If a increases by 100%, then b decreases by:
Inverse proportionality is expressed as follows :
$$a\propto \frac{1}{b}$$
$$\Rightarrow$$ a*b = constant
When value of a changes, the value of b changes accordingly such that their product remains same.
Thus, new value of a $$a^{'} = a + a = 2a $$
Thus, the new value of b $$b^{'}$$ can be solved by :
$$a^{'}*b^{'}=a*b$$
$$\Rightarrow 2a*b^{'}= a*b $$
$$\Rightarrow b^{'}= \frac{b}{2} $$
Thus b decreases by 50%.
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