For a first order reaction, the time taken to reduce initial concentration by a factor of 1/4 is 10 min. The time required to reduce initial concentration by a factor of 1/16 will be

The time required to reduce the initial concentration to a factor 1/4 is 10 min.
So, half life of the reaction is $\left(t_{\frac{1}{2}}\right)$ = 5 min.
∴ The time required to reduce the initial concentration to a factor 1/16 i.e. 4 half lives is = (5×4) min = 20 min.

For a first order reaction, time required to reduce the concentration by the same factor is constant.