An Acid – Base indicator has k_a value of $3\times {10}^{-5}$  the acid form of indicator is red and basic form is blue. The [H⁺] required to change the indicator from 75% red to 75% blue is 

$\begin{array}{l}HIn\stackrel{ }{\rightleftharpoons }{H}^{+}+I{n}^{-}\\ Acid Base\\ \mathrm{Re}dBlue\end{array}$

$k_a=\frac{\left[H^{+}\right]\left[I{n}^{-}\right]}{HIn}$

$\left[H^{+}\right]=\frac{k_a.\left|HIn\right|}{\left|I{n}^{-}\right|}$

1^st case Acid from 75% Base 25%

$\left|H^{+}\right|=\frac{3\times {10}^{-5}\times 75}{25}=9\times {10}^{-5}$

2^nd case acid from 25% Base 75%

$\left|H^{+}\right|=\frac{3\times {10}^{-5}\times 25}{75}=1\times {10}^{-5}$

$\therefore \Delta \left|H^{+}\right|=9\times {10}^{-5}-1\times {10}^{-5}$

$=8\times {10}^{-5}$