Aptitude Hack#86(20-5-19)

Question:

 A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed?

   A )   52 km
   B )   53 km
   C )   54 km
   D )   55 km

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Train Formulas

Conversion:

km/hr to m/s conversion:

m/s to km/hr conversion:

Formulas for finding Speed, Time and Distance 

1.     Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
 
 
2.     Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.
 
 
3.     Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.
 
 
4.     Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
 
 
5.     If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
 

Time taken by the trains to cross each other=

 
 
6.     If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:

Time taken by the faster train to cross the Slow Train=

7.     If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:
      (A's speed) : (B's speed) = (b : a)

Example sum

1) A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Speed = [ 60 * (5 / 18 ) ] m/sec
= ( 50 / 3 ) m/sec
Length of the train = ( Speed * Time )
= [( 50/3)*9 ] m= 150m



2) A train 125 m long passes a man, running at 5 km/hr in the same direction in whichthe train is going, in 10 seconds. Find the speed of the train?
Speed of the train relativeto man = ( 125 /10 ) m/sec
= ( 25 / 2 ) m/sec
= [(25/2) * ( 18/5) ] km/hr
= 45 km/hr
Let the speed of the train be x km/hr.
Relative speed = (x - 5 ) km/hr.
(x-5)=45
x = 45+5x 
= 50 km/hr

Basic Formulas

If two trains of p meters and q meters are moving in same direction at the speed of x m/s and y m/s ( x > y ) respectively then time taken by the faster train to overtake slower train is given by = [ (p + q)/ (x -y)]

Example sum

3)Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr.The faster trainpasses the slower train in 36 seconds.Find the length of each train?
Let the length of each train be x metres.
Distance covered = 2x metres.
Relative speed = ( 46 - 36 ) km/hr
= [ 10*(5/18) ] m/sec
= ( 25/9) m/sec
=  ( 2x/36) = ( 25/9)
= 2x=100  
 x = 50
Basic Formulas

If two trains of p meters and q meters are moving in opposite direction at the speed of x m/s and y m/s respectively then time taken by trains to cross each other is given by = [ (p + (x + y)]


Example sum

4) Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Speed of the first train = ( 120 / 10 )m/sec
= 12 m/sec
Speed of the second train = ( 120 / 15 )m/sec
= 8 m/sec
Relative speed = ( 12 + 8 )
= 20 m/sec  
Required time = [ ( 120 + 120 ) / 20 ] sec
= 12 sec  

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Aptitude Hack#38(2-4-19)

Question:

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

A) 130

B) 360

C) 500

D) 540

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Aptitude Hack#18(13-3-19)

Question:
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr
B. 50 km/hr
C. 54 km/hr
D. 55 km/hr

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Aptitude Hack#4(27-2-19)

Question:

Three friends started running together on a circular track at 8:00:00 am. Time taken by them to complete one round of the track is 15 min, 20 min, 30 min respectively. If they run continuously without any halts, then at what time will they meet again at the starting point for the fourth time?

A )  8:30:00 am

B )  9:00:00 pm

C  )12:00:00 pm

D )12:00:00 am

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