b
(b) Suppose in the following figure, equilibrium of charge \(B\) is considered. Hence for it's equilibrium \(|{F_A}|\, = \,|{F_C}|\)
\(==>\) \(\frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Q^2}}}{{4{x^2}}} = \)\(\frac{1}{{4\pi {\varepsilon _0}}}\frac{{qQ}}{{{x^2}}}\) \(==>\) \(q = \frac{{ - \,Q}}{4}\)

Short Trick : For such type of problem the magnitude of middle charge can be determined if either of the extreme charge is in equilibrium by using the following formula.
If charge \(A\) is in equilibrium then \(q\) \(= -\) \({Q_B}\,{\left( {\frac{{{x_1}}}{x}} \right)^2}\)
If charge \(B \) is in equilibrium then \(q = - {Q_A}\,\,{\left( {\frac{{{x_2}}}{x}} \right)^2}\)
If the whole system is in equilibrium then use either of the above formula.