Question

Choose the correct answer from the alternatives given.
Two trains for Bhopal leave Delhi at 9 am and 8:30 am and travel at 90km/hr. and 80km/hr. respectively. How many kilometers from Delhi will the two trains be together?
A) 360 km
B) 320 km
C) 270 km
D) 280 km

Answer 1

Hint: We need to find the distance from Delhi at which the two trains will meet. Since both the trains are travelling in the same direction but with different speeds and have started at different times from Bhopal, one 30 minutes later than the other, so we will use the concept of relative speed to find the distance at which the trains meet.

Complete step by step answer:
Now, the first train leaves from Bhopal at 8:30 am and travels at a speed of 80km/hr. while the second train starts from Bhopal 30 minutes later at 9 am and travels at a speed of 90km/hr.
So the first train has already covered some distance in half an hour before the second train has started.
So the distance travelled by the first train in these 30 minutes before the second train has started from Bhopal = Speed of first train x Time.
$$\begin{gathered} =80\times {\displaystyle \frac{30}{60}} \\ =40km \end{gathered}$$
So, the second train will have to cover this 40km at a relative speed with respect to the first train.
Now, since both the trains are travelling in the same direction,
So relative speed of the second train:
$$\begin{gathered} =(90-80)km/hr \\ =10km/hr \end{gathered}$$
Now time taken by second train to cover the extra 40km will be
$$\begin{gathered} time={\displaystyle \frac{di\tan ce}{relativespeed}} \\ ={\displaystyle \frac{40}{10}} \\ =4hours \end{gathered}$$
So, the distance at which both trains will now meet will be
$$\begin{gathered} di\tan ce=time\times speedof\sec ondtrain \\ =4\times 90 \\ =360km \end{gathered}$$
So, the two trains will now meet when they are 360km away from Delhi.
Hence the correct answer is option A.

Note: The concept of relative speed has to be applied and the difference in distance due to the different times of departures of trains from Bhopal have to be considered carefully. Also the formulae for speed and motion need to be applied correctly.