Question

Only a single rail track exists between stations A and B on a railway line. One hour after the north-bound 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 S to that of the super fast train so that the passenger train S reaches exactly at the scheduled time at A on that day?

• A. 1 : 3
• B. 1 : 4
• C. 1 : 5
• D. 1 : 6

Hint:

When dealing with speed-time-distance problems, remember that doubling speed reduces time taken by half.

Answer 1

The Correct Option is C

Let the speed of the super fast train \( N \) be \( v \), and the speed of the passenger train \( S \) be \( \frac{v}{2} \), and the speed of normal express train \( E \) be \( \frac{v}{2} \). - The distance between A and B is fixed. - Train N leaves 20 minutes behind schedule. - To catch up, the super-fast train needs to travel 20 minutes faster. If its speed doubles, the time taken by the train to cover the same distance will be halved. Thus, the speed ratio of S to N will be \( 1:5 \), maintaining the schedule. Hence, the Correct Answer is 1:5.