Time and Distance – Trains

1. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
   A.310 m
   B.350 m
   C.600 m
   D.490 m
   E.None of these
   
   Answer

   Answer – B (350 m)
   Explanation – when it cross a pole actually it is crossing itself
   so, S = 300/18
   let length of platform be “p”
   relative speed = total lengths/time
   speed of train = [300 + p ]/39
   (300/18)x39=300 +p
   650 -300=p
   p=350 m
   Note : in this type of question one thing is pole,man and other is of considerable length like platform ,bridge.
   when train crosses pole,man it crosses itself

2.Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A.1 : 3
B.3 : 4
C.3 : 2
D.Data inadequate
E.None of these

Answer

Answer – C (3 : 2)
Explanation – Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y metres.
relative speed = total lengths/time
y – x = [27x + 17 y ]/23
23y -23x = 27x + 17 y
27x+23x= 23 y-17y
4x=6y
x/y=6/4=3/2= 3:2

3.Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
A. 1: 2
B. 4 : 3
C. 7 : 8
D. 3 : 4
E. none of these

Answer

Answer- B (4:3)
Explanation:
Let us name the trains as A and B. Then,
trick formula
(A’s speed) : (B’s speed) = square root of b : square-root of a =square-root of 16 : square-root of 9 = 4 : 3.

4.The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
A.10:30 am
B.10:45 am
C.11 am
D.11:25 am
E.None of these

Answer

Answer – C (11 am)
Explanation – Suppose they meet x hrs after 8 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs] = 330
60x + 75(x – 1) = 330
x = 3
So, they meet at (8 + 3), i.e. 11 a.m

5.A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
A.59 km/hr
B.65 km/hr
C.70 km/hr
D.81 km/hr
E. None of these

Answer

Answer-D (81 km/hr)
Explanation-
4.5 km/hr =(4.5 x 5/18)m/sec =5m/4sec = 1.25 m/sec, and
5.4 km/hr =(5.4 x 5/18)m/sec =3m/2sec = 1.5 m/sec.
Let the speed of the train be x m/sec.
Then, (x – 1.25) x 8.4 = (x – 1.5) x 8.5
=> 8.4x – 10.5 = 8.5x – 12.75
=> 0.1x = 2.25
=> x = 22.5
Therefore Speed of the train =(22.5 x18 /5)km/hr = 81 km/hr.