Question

The average speed of a train while travelling from station A to station B is 25% more than the average speed of the train travelling back from station B to station A. The train halts for one hour on station B. The total time taken for the complete to and fro journey is 19 hours, and the distance between stations A and B is 450 km. Find the speed of the train while travelling from station A to station B.

• A. 45 km/h
• B. 54 km/h
• C. 55.55 km/h
• D. 56.25 km/h

Answer 1

The correct option is D 56.25 km/h

Let the speed of the train from B to $A=S$, then the speed of the train from A to B will
be $=1.25S$
Total time taken to cover the distance from A to B and back (excluding the halting time of 1 hour) $=19-1=18$ hours
Time taken to travel from A to B $\to \frac{450}{1.25S}=t1$
Time taken to travel from B to A $\to \frac{450}{S}=t2$
$t1+t2=\frac{450}{1.25S}+\frac{450}{S}=18$
$\Rightarrow \frac{360}{S}+\frac{450}{S}=18$
$\Rightarrow 810=18S\Rightarrow S=45$
Hence, speed from A to B $=1.25\times 45=56.25$ km/h