A train without stop page travels with an average speed of 65 km/h and with stoppage,it travels with an average speed of 52 km/h. For how many minutes does the train stop on an average per hour?

Let the total distance traveled by the train =d

And total time taken t=1 hour

so, if train is not getting stop at any stoppage then average speed of the train $$65=\dfrac{d}{1}-------(i)$$km/hour
If train is getting stop at the stoppage for the time $$t_1$$

Then average speed of the train $$52=\dfrac{d}{1+t_1}-----(ii)$$

from equation (i) and (ii)

$$\Rightarrow \dfrac{65}{52}=\dfrac{1+t_1}{1}$$
$$\Rightarrow t_1=1.25-1=0.25$$

$$\Rightarrow t_1=0.25$$hour= $$\dfrac{25}{100}=\dfrac{1}{4}$$hour
$$\Rightarrow t_1=\dfrac{60}{4}=15$$ min