Question 17

Only a single rail track exists between stations A and B on a railway line. One hour after the northbound super fast train N leaves station A for station B, a south-bound passenger train S reaches station A from station B. The speed of the super fast train is twice that of a normal express train E, while the speed of a passenger train S is half that of E. On a particular day, N leaves for B from A, 20 min behind the normal schedule. In order to maintain the schedule, both N and S increased their speeds. If the super fast train doubles its speed, what should be the ratio (approximately) of the speeds of passenger train to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?

Solution

Let the speed of an express train be 4x, normal train be 2x and passenger train be x.
Let the distance between the 2 stations be D.
Since there is only 1 railway track, train N must reach station B before train S leaves.
Therefore, D/4x + D/x = 60
5D/4x = 60
D/x = 48

Train N leaves 20 minutes late. Therefore, the 2 trains must have covered the distance within 40 minutes on this particular day.
Train N doubles its speed. Therefore, speed of train N will be 8x. Let the new speed of the passenger train be y.

D/8x + D/y = 40
48/8 + D/y = 40
D/y = 34.

Speed of super fast train = D/8x = 6
Speed of passenger train = D/y = 34

Ratio of the speeds = 6/34 = 3/17.
The ratio is approximately equal to 1:6. Therefore, option D is the right answer.