a
Let solubility of \(\bar AgCl = x\,mole/L\)

\(AgCl \rightleftharpoons A{g^ + } + C{l^ - }\)

i.e., \({K_{sp(AgCl)}} = x \times x\)

\(KCl \to {K^ + } + \mathop {C{l^ - }}\limits_{0.1} \)

\([C{l^ - }]\,\) from \(KCl = 0.1\,m\)

Total \([C{l^ - }]\) in solution \( = x + 0.1\)

\({K_{sp}}(AgCl) = [A{g^ + }][C{l^ - }] = x(x + 0.1)\)

\(1.0 \times {10^{ - 10}} = x(x + 0.1)\)

\(1.0 \times {10^{ - 10}} = {x^2} + 0.1x\)

\(1.0 \times {10^{ - 10}} = 0.1x\)      (as \({x^2} <  < 1\))

\(x = 1.0 \times {10^{ - 9}}\,mol/L\)