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# MATHS (SOLVED IN STEPS) PROBLEMS ON TRAINS - 02

8. Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
A. 10.8 s                    B. 12 s                 C. 9.8 s                       D. 8 s
Explanation :
Distance = 140+160 = 300 m
Relative speed = 60+40 = 100 km/hr =
(100×10)/36 m/s
Time = distance/speed = 300 / (100×10)/36 = 300×36 /1000 = 3×36/10 = 10.8 s

9. Two trains are moving in opposite directions with speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. The slower train cross the faster train in — seconds
A. 56 B.                      48                  C. 47            D. 26
Explanation :
Relative speed = 60+90 = 150 km/hr (Since both trains are moving in opposite directions)
Total distance = 1.1+.9 = 2km
Time = 2/150 hr = 1//75 hr = 3600/75 seconds = 1200/25 = 240/5 = 48 seconds

10. A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
A. None of these           B. 280 meter          C. 240 meter              D. 200 meter
Explanation :
Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 36
=> 300+L = 15×36 = 540
=> L = 540-300 = 240 meter

11. A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
A. 79.2 km/hr             B. 69 km/hr           C. 74 km/hr                 D. 61 km/hr
Explanation :
Let x is the length of the train and v is the speed
Time taken to move the post = 8 s
=> x/v = 8
=> x = 8v — (1)
Time taken to cross the platform 264 m long = 20 s
(x+264)/v = 20
=> x + 264 = 20v —(2)
Substituting equation 1 in equation 2, we get
8v +264 = 20v
=> v = 264/12 = 22 m/s
= 22×36/10 km/hr = 79.2 km/hr

12. Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
A. 10            B. 25               C. 12                    D. 20
Explanation :
speed of train1 = 120/10 = 12 m/s
speed of train2 = 120/15 = 8 m/s
if they travel in opposite direction, relative speed = 12+8 = 20 m/s
distance covered = 120+120 = 240 m
time = distance/speed = 240/20 = 12 s

13. A train having a length of 1/4 mile , is traveling at a speed of 75 mph. It enters a tunnel 3 ½ miles long. How long does it take the train to pass through the tunnel from the moment the front enters to the moment the
rear emerges?
A. 3 min                   B. 4.2 min             C. 3.4 min                   D. 5.5 min
Explanation :
Total distance = 3 ½ + ¼ = 7/2 + ¼ = 15/4 miles
Speed = 75 mph
Time = distance/speed = (15/4) / 75 hr = 1/20 hr = 60/20 minutes = 3 minutes

14. A train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the train?
A. 270 m                    B. 210 m                  C. 340 m                    D. 130 m
Explanation :
Speed= 72 kmph = 72×10/36 = 20 m/s
Distance covered = 250+ x where x is the length of the train
Time = 26 s
(250+x)/26 = 20
250+x = 26×20 = 520 mx = 520-250 = 270 m
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