12 minutes
To determine how many minutes per hour the train stops, we start by comparing the average speeds with and without stoppages.
The average speed without stoppages is 60 km/h, and with stoppages, it is 48 km/h. The difference in these speeds is due to the time lost because of stoppages.
Let's assume the train covers a certain distance \( D \) in one hour.
- The time taken to cover the distance \( D \) without stoppages is given by: \(T_{\text{no stoppage}} = \frac{D}{60}\) hours.
- The time taken to cover the same distance \( D \) with stoppages is: \(T_{\text{with stoppage}} = \frac{D}{48}\) hours.
- The additional time taken due to stoppages is: \(T_{\text{stoppage}} = T_{\text{with stoppage}} - T_{\text{no stoppage}} = \frac{D}{48} - \frac{D}{60}\).
- Simplifying, we calculate: \(T_{\text{stoppage}} = \frac{5D}{240} = \frac{D}{48}\) hours.
- In terms of minutes, since there are 60 minutes in an hour, the stoppage time is: \(T_{\text{stoppage}} \times 60 = \frac{D}{48} \times 60 = \frac{60D}{48} = \frac{5D}{4}\) minutes.
- Since the train travels distance \( D \) in one hour, the effective stoppage time per hour is: \(\frac{60}{5} = 12\) minutes.
Therefore, the train stops for 12 minutes per hour.
This confirms that the correct option is 12 minutes.
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