Assume the distance travelled by train is equal to its speed (with stoppages) in an hour which is $60 \hspace {0.1cm} km$. Then , we can find the stoppage time of the train in an hour.
∴ In $80 \hspace {0.1cm} km/hr$ speed (without stoppages) train covers the distance in $\dfrac{60}{80} \hspace {0.1cm} hr = \dfrac{6}{8} \hspace {0.1cm} hr = \dfrac{3}{4} \times 60 \hspace {0.1cm} min = 3 \times 15 \hspace {0.1cm} min = 45 \hspace {0.1cm} min$ $\qquad \left [ \because Distance = Speed \times Time \\ \qquad \qquad Or, Time = \dfrac{Distance}{Speed} \right ]$
whereas, in $60 \hspace {0.1cm} km/hr$ speed train covers the distance in $1 \hspace {0.1cm} hr$.
$\color{maroon}{\text{So, In an hour the train stops for}}$ $\color{green}{ \left ( 60 - 45 \hspace {0.1cm} min \right ) = 15 \hspace {0.1cm} min}$