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## Monday, 29 April 2019

22. A 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds. What is the length of the platform?
A. 150 m                     B. 350 m                 C. 420 m                D. 600 m
Explanation :
Length of the train
= distance covered in crossing the post
= speed × time
= speed × 18
ie,300= speed × 18
Speed of the train = 300/18 m/s = 50/3 m/s
Time taken to cross the platform = 39 s
(300+x)/(50/3) = 39 s where x is the length of the platform
300+x = (39 × 50) / 3 = 650 meter
x = 650-300 = 350 meter

23. A train crosses a post in 15 seconds and a platform 100 m long in 25 seconds. Its length is
A. 150 m                    B. 300 m                  C. 400 m                     D. 180 m
Explanation :
Assume x is the length of the train and v is the speed x/v = 15
=> v = x/15
(x+100)/v = 25
=> v = (x+100)/25
Ie, x/15 = (x+100)/25
=> 5x = 3x+ 300
=> x = 300/2 = 150

24. A train , 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?
A. 440 m                     B. 500 m                    C. 260 m                  D. 430 m
Explanation :
Distance = 800+x meter where x is the length of the tunnel
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s
Distance/time = speed
(800+x)/60 = 65/3
=> 800+x = 20×65 = 1300
=> x = 1300 - 800 = 500 meter

25. Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/ hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is
A. 50 sec                  B. 58 sec               C. 24 sec                D. 22 sec
Explanation :
Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s
We are calculating the time taken by the slower train to pass the driver of the faster one
Hence the distance = length of the smaller train = 500 m
Time = distance/speed = 500/(125/6) = 24 s

26. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is
A. 42                   B. 36                     C. 28                    D. 20
Explanation :
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v+v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10×36/10 km/hr = 36 km/hr

27. A train 108 m long is moving at a speed of 50 km/hr . It crosses a train 112 m long coming from opposite direction in 6 seconds. What is the speed of the second train?
A. 82 kmph                  B. 76 kmph                  C. 44 kmph               D. 58 kmph
Explanation :
Total distance = 108+112 = 220 m
Time = 6s
Relative speed = distance/time = 220/6 m/s = 110/3 m/s
= (110/3) × (18/5) km/hr = 132 km/hr
=> 50 + speed of second train = 132 km/hr
=> Speed of second train = 132-50 = 82 km/hr

28. How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
A. 42                          B. 50                            C. 30                    D. 28
Explanation :
Distance = 500m
Speed = 63 -3 km/hr = 60 km/hr = 600/36 m/s =
50/3 m/s
Time taken = distance/speed= 500/(50/3) = 30 s
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