Explanation

(c)
(i)20 mL of 0.5 N $HCl$
0.5N$\Rightarrow 1000\ mL\ of\ 0.5\ mol\ of\ HCl$
HCl present in 20 mL=$\frac{20 \times 0.5}{1000} = 1.0 \times 10^{- 2}$
(ii)35mL of 0.1 N NaOH
0.1 N$\Rightarrow 1000$ mL of 0.1 mol of NaOH
$\Rightarrow$ $NaOH\ \ present\ in\ 35\ mol = \frac{3.5 \times 0.1}{1000}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 0.35 \times 10^{- 2}$
Total volume = 20+35=55 mL
$\Rightarrow$ Resulting mole in solution,
$(1.0 - 0.35)10^{- 2} = 0.65 \times 10^{- 2}\ mol\ HCl$
$HCl = H^{+} + Cl^{-}$
$\lbrack HCl\rbrack = \left\lbrack H^{+} \right\rbrack + \lbrack Cl^{-}\rbrack$
55 mL contains $0.65 \times 10^{- 2}\ mole\ of\ H^{+}\ ions$
$1000\ mL = \frac{0.65 \times 10^{- 2} \times 10^{3}}{55} = \frac{6.5}{55}$
$pH = - \log{\left\lbrack H^{+} \right\rbrack = - \log\left( \frac{6.5}{55} \right)}$
$= \log{55 - \log{6.5 = 0.92}}$
Due to acidic nature of solution the colour of phenolphthalein becomes pink.