July 2014



Kiran Musunuru Vaccination against heart attacks: Harvard Stem Cell Institute (HSCI) scientists collaborating with researchers at the University of Pennsylvania have developed a "genome-editing" approach for permanently reducing cholesterol levels in mice through a single injection, a development that could reduce the risk of heart attacks in humans by 40 to 90 percent. Read more ....

Electric eel 'Shocking' truth: Scientists have found how the electric fish evolved its jolt. Writing in the journal Science, a team of researchers led by Michael Sussman of the University of Wisconsin-Madison, Harold Zakon of the University of Texas at Austin and Manoj Samanta of the Systemix Institute in Redmond, Washington identifies the regulatory molecules involved in the genetic and developmental pathways that electric fish have used to convert a simple muscle into an organ capable of generating a potent electrical field. Read more ....

Football Football physics: It happens every four years: The World Cup begins and some of the world's most skilled players carefully line up free kicks, take aim - and shoot way over the goal. The players are all trying to bend the ball into a top corner of the goal, often over a wall of defensive players and away from the reach of a lunging goalkeeper. Yet when such shots go awry in the World Cup, a blame game usually sets in. Players, fans, and pundits all suggest that the new official tournament ball, introduced every four years, is the cause. Read more .....

Penguins Warming and penguins: A study of how penguin populations have changed over the last 30,000 years has shown that between the last ice age and up to around 1,000 years ago penguin populations benefitted from climate warming and retreating ice. This suggests that recent declines in penguins may be because ice is now retreating too far or too fast. Read more ....

Football Splendid kick-off: On June 12, during the opening of the FIFA 2014 World Cup in Brazil, a paralyzed person wearing a brain-controlled robotic exoskeleton made the first kick of the football championship. For those who were watching the opening ceremony on television sets, it was a fleeting glimpse. Read more ....




Solution

Okay, we know the speed of Train A is 45 kmph.

Let speed of Train B be "s" kmph

Let the trains meet after "t" hours.

Let Train A cover a distance d1 when it meets Train B, and correspondingly, let Train B cover a distance d2 when it meets Train A.

Speed of Train A is 45 kmph, so it will take d1/45 hours to cover distance d1. Now this is "t". So, t = d1/45.

Similarly, speed of Train B is "s" kmph, so it will take d2/s hours to cover distance d2. Now this is also "t" because the trains have traveled for "t" hours before meeting.

So, t = d2/s.

Therefore, d1/45 = d2/s, or d1/d2 = 45/s.

After meeting, Train A has to cover d2 kms and train B has to cover d1 kms to reach their destinations (because the trains are travelling in opposite directions and, therefore, d1+d2 is the total distance of the journey).

Train A has already covered d1, so it has to cover d2 now. Likewise, Train B has to cover d1. Train A covers d2 in 90 minutes while Train B covers d1 in 40 minutes.

Now, Train A covers d2 in 90 minutes, or 90/60 hours. Speed of Train A is 45kmph, so it will cover d2 in d2/45 hrs. So d2/45 = 90/60. Therefore, d2 = (90 x 45)/60.

Likewise, speed of Train B is "s" kmph, so it will cover d1 kms in d1/s hours. But this is 40 minutes, or 40/60 hrs. So, d1/s = 40/60. Therefore, d1 = 40s/60.

Therefore d1/d2 = (40s/60) / [(90 x 45)/60]. That is d1/d2 = 40s/ (90 x 45).

But d1/d2 = 45/s.

Therefore 45/s = 40s/ (90 x 45).

So, 40s2 = 45 x 90 x 45.

Therefore, s2 = (45 x 90 x 45) / 40.

Therefore s = square-root of (45 x 90 x 45 / 40).

Now we are considering speed, so only positive values need to be taken.

Therefore s = 45 x 3/2.

Or, s = 67.5 kmph. Therefore, speed of Train B is 67.5 kmph.

Seems you could have applied a simple formula to arrive at the answer. The formula is:

Speed of Train A/ speed of Train B = square-root (time taken by Train B to reach destination after meeting)/ square-root (time taken by Train A to reach destination after meeting). Thus, 45/s = square-root(40)/square-root(90).

Now, for the total distance between Udaipur and Chittorgarh: The total distance is d1 + d2; d1 = 40s/60, and "s" we have found out is 67.5. Therefore, d1 = 40 x 67.5 / 60 = 45. We know d2 = (90 x 45)/60 = 67.5. Therefore d1 + d2 = 45 + 67.5 = 112.5 kilometers.

The trains meet after "t" hours after starting. Take any of the equations involving "t" to find it. Let's take t = d2/s. Thus, t = 67.5 / 67.5 = 1. So, the trains meet one hour after starting.

I hope I have got it right!



Some useful links for
your career:


  • 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
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu

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