Explanation

(b)
$K_{C_{1}}$ for $H_{2} + I_{2} \rightleftharpoons 2HI\ is\ 50$
$K_{C_{2}}$ for $2HI\ \rightleftharpoons H_{2} + I_{2}$
$K_{C_{1}} = \frac{\lbrack HI\rbrack^{2}}{\left\lbrack H_{2} \right\rbrack\left\lbrack I_{2} \right\rbrack}$ …(i)
$K_{C_{2}} = \frac{\left\lbrack H_{2} \right\rbrack\left\lbrack I_{2} \right\rbrack}{\lbrack HI\rbrack^{2}}$ …(ii)
On reversing Eq.(i)
$\frac{1}{K_{c_{1}}} = \frac{\left\lbrack H_{2} \right\rbrack\left\lbrack I_{2} \right\rbrack}{\lbrack HI\rbrack^{2}}$ …(iii)
From Eqs. (ii) and (iii)
$K_{c_{2}} + \frac{1}{K_{c_{1}}} = \frac{1}{50} = 0.02\$