The distance between two railway stations is 1176 km. To cover this distance, an express train takes 5 hours less than a passenger train while the average speed of the passenger train is 70 km/h less than that of the express train. The time taken by the passenger train to complete the travel is:

Given,

Distance between two railway stations = 1176 km

Let the time taken by passenger train to cover the distance = t

$$=$$> Time taken by express train to cover the distance = t - 5

The average speed of the passenger train is 70 km/h less than that of the express train

$$=$$>  $$\frac{1176}{t-5}-\frac{1176}{t}=70$$

$$=$$>  $$\frac{168}{t-5}-\frac{168}{t}=10$$

$$=$$>  $$168\left[\frac{t-t+5}{\left(t-5\right)t}\right]=10$$

$$=$$>  $$168\left[\frac{5}{\left(t-5\right)t}\right]=10$$

$$=$$>  $$t^2-5t-84=0$$

$$=$$>  $$t^2-12t+7t-84=0$$

$$=$$>  $$t\left(t-12\right)+7\left(t-12\right)=0$$

$$=$$>  $$\left(t-12\right)\left(t+7\right)=0$$

$$=$$>  $$t-12=0$$  or   $$t+7=0$$

$$=$$>   $$t=12$$  or   $$t=-7$$

t cannot be negative

$$=$$>  $$t=12$$

$$\therefore\ $$The time taken by the passenger train to complete the travel = 12 hours

Hence, the correct answer is Option A