If 75% of a first order reaction gets completed in 32 minutes, time t…

The correct answer is Option (1) → 16 minutes

For a first order reaction, the half-life does not depend on the starting concentration:

    \( \displaystyle t_{1/2}=\frac{0.693}{k} \)

So the same time is needed to go from 100% to 50% as from 50% to 25%. When 75% of the reaction is complete, 25% of the reactant is left, which is two half-lives:

    \( \displaystyle 100\%\xrightarrow{t_{1/2}}50\%\xrightarrow{t_{1/2}}25\% \)

The same result from the integrated rate equation:

    \( \displaystyle t_{75\%}=\frac{2.303}{k}\log\frac{100}{25}=\frac{2.303\times0.602}{k}=\frac{1.386}{k}=2\,t_{1/2} \)

    \( \displaystyle t_{1/2}=\frac{32\ \mathrm{min}}{2}=16\ \mathrm{min} \)

So 50% of the reaction is completed in 16 minutes.

NCERT (2026-27 edition):
Half-Life of a Reaction – …

Note: The same/similar question has been asked in different years by NTA as per the details given below: