ANSWERS -HURDLE 12 : TRAINS

Ans 1.90 sec

Ans 2.The speed of train B remains unchanged.

Ans 3.Option D

Ans 4. 360M and 120 m travelling at 20 m/s and 4 m /s

Ans 5.125 m at 32 m/s

Ans 6. 14 sec and 7 sec

Ans7. 52 m/s and 26 m/s

Ans8.11 m/s , 168 m in length

Ans 9. 26 sec and 15 sec

Ans 10. 684 m and 456 m traveling at 34 m/s and 4 m/s

Ans 11.552 m at 8 m/s

Ans12. 21s and 14 sec

Ans13. 84 m/s and 49 m/s

Ans14. 221 m at 9 m/s

Ans15. 36 sec and 18 sec

Ans16. 384 m and 224 m at 57 m/s and 19 m/s

Ans17. 225 at 38 m/s

Ans18. 48 sec and 16 sec

Ans19. H , Ans20. C , Ans21. D , Ans22. J , Ans23. K , Ans24. M , Ans25. A

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FORMULS'S FOR TRAINS :

Let Train Length= L
Let Train Speed-S

1. When the Train passes a stationary point, the time taken will be T = L/S

2. When Train passes a moving object (A man walking, a bird flying etc).
Let the speed of moving object be S2
Time taken to pass the moving object :
If in same direction : T = L/ (S-S2)
If in opposite directions T = L/(S+S2)


3. When Train crosses certain length ( Another stationery train , platform, bridge etc) (UrPercentile.com)
Length of Stationary Object = L2
Time taken to cross the length :
T = ( L + L2)/ S


4. Train passes another moving object with significant length ( Another moving train)
Length of other train= L2
Speed of other train= S2

Time taken when moving in same direction:
T = (L +L2)/ (S-S2)

Time taken when moving in opposite direction:
T = (L +L2)/ (S+S2)

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HERE ARE SOLUTIONS OF SOME OF THE QUESTIONS, THE REST MAY BE SOLVED USING THE SAME METHOD.

Solution1.
Total distance to travel : 2100 +600 = 2700 Mt
Speed = 30 Mt/s
Time = 2700/30 = 90 seconds.

Solution2.
The other train is stationery , that is speed is 0 m/s.
(UrPercentile.com)
The speed remains unchanged and so the second train will take same amount of time in both direction.

Solution3.
Only option d is correct.
"a" is not possible.
"b" is not true as the train will not be able to pass each other anytime. .
"c" is not correct as the maximum distance will be when the train are travelling opposite to each other i.e, at 180 degrees.

Solution4. SHORT CUT
let Total Length of two train = D
let Time taken to cross in opposite direction = T1
let Time taken to cross in same direction = T2
then S1= |(D/T1)+ (D/T2)| / 2
and S2= |(D/T1)-(D/T2)| / 2
Let the length of Train 1 be L and that of Train 2 be L2.
Now L+L2= 480 and L1-L2= 240 . so solving the two equation we get L=360 and L2= 120.
Now S1= |(D/T1)+ (D/T2)| / 2
and S2= |(D/T1)-(D/T2)| / 2
D=480
T1= 30 and T2=20. (UrPercentile.com)
so S1= |(480/30) +(480/20) |/2 = 20
and S2= |(480/30) -(480/20) |/2 = 4

Solution5.
Train T1 - 275 m long
Speed of T1 - 48 m/sec
Train T2 - D2 m long
Speed of T2 - S2 m/sec
(275+D2)/25 = S1-S2 (Relative speed when the two trains are travelling in same direction )
(240+D2)/5 = S1+S2 (Relative speed when the two trains are travelling in opp direction )
=> S2 = 32 m/sec , D2 = 125 m

Solution6.
Train T1 - 588 m long
Speed of T1 - 105 m/sec
Train T2 - 392 m long
Speed of T2 - 35 m/sec
Time taken to cross each other while travelling in the same direction - t1
Time taken to cross each other while travelling in the opp direction - t2
Total Distance covered by 2 trains = 588+392 = 980 m
980/t1 = 105 - 35
980/t2 = 105 + 35
=> t1 = 980/70 = 14 sec
t2 = 980/140 = 7 sec

Solution9.
Train T1 - 468 m long
Speed of T1 - 41 m/sec
Train T2 - 312 m long
Speed of T2 - 11 m/sec
Time taken to cross each other while travelling in the same direction - t1
Time taken to cross each other while travelling in the opp direction - t2
Total Distance covered by 2 trains = 468+312 = 780 m
780/t1 = 41 - 11
780/t2 = 41 + 11
=> t1 = 780/30 = 26 sec
t2 = 780/52 = 15 sec