Explanation

(b)
For first order reaction,
$k = \frac{2.303}{t}\log_{10}\frac{a}{a - x}$
Where, a= initial concentration
X= change in concentration during time‘t’.
If 75% of the reaction was completed in 32 min, then
$k = \frac{2.303}{32}\log_{10}\frac{100}{100 - 75} = \frac{2.033}{32}\log_{10}4$
$k = 0.0433\min^{- 1}$
Hence, time required for the completion of 50% reaction.
$t = \frac{2.303}{0.0433}\log_{10}\frac{100}{100 - 75}$
$= \frac{2.033}{32}\log_{10}2 = 16\ min$