# Solution

The two trains would have collided head-on twenty minutes after 7.30 am, that is at 7.50 am, had no corrective action been taken.

The blunder was realised by Mr Kumar at 7.30 am. Till then, the "Gujarat Queen" had travelled for an hour while the "Vadodara Express" had travelled for 30 minutes. Therefore, the "Gujarat Queen" had covered a distance of 50 kilometres while the "Vadodara Express" had covered a distance of 20 kilometres. The distance between Ahmedabad and Vadodara has been stated to be 100 kilometres. Thus, at 7.30 am, the distance between the two trains was 30 kilometres.

Suppose the trains had collided "t" minutes after 7.30 am, then "Gujarat Queen" would have covered a distance of say d1 in "t" minutes while "Vadodara Express" would have covered a distance of say d2 in the same time.

Speed=distance/time. We have considered "t" in minutes, so we have to make the necessary conversions. The "Gujarat Queen" is travelling at 50 kilometres per hour, that is 50 kilometres in 60 minutes. Therefore, in "t" minutes, it would travel 50t/60 kilometres. Likewise, "Vadodara Express" will travel 40t/60 kilometres. Thus, d1=50t/60 and d2=40t/60.

The two trains will collide when both of them together have covered a total distance of 30 kilometres because that is the distance that remains between them at 7.30 am. Therefore, d1+d2=30.

Thus, 50t/60+40t/60=30.

Thus, 50t+40t=1800.

So, t=20.

The accident, therefore, would have occurred 20 minutes after 7.30 am, that is at 7.50 am

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in