Define the speeds

Given the train speed without stoppages is $45$ km/h and with stoppages is $36$ km/h.

$V_{original} = 45\ km/h, V_{actual} = 36\ km/h$

Calculate speed loss per hour

The reduction in distance covered due to stoppages in one hour is $45 - 36 = 9$ km.

$\text{Loss} = 45 - 36 = 9\ km$

Calculate time taken for the lost distance

The train would have covered this $9$ km distance at the original speed of $45$ km/h. Thus, the stoppage time in hours is $\frac{9}{45}$.

$\text{Time} = \frac{9}{45} = \frac{1}{5} hours$

Convert time to minutes

To find the time in minutes, multiply the result by $60$.

$\text{Time} = \frac{1}{5} \times 60 = 12\ minutes$