Arithmatical  Problems on Trains
DIRECTIONS : Problems based on Trains.
1. 
A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line. 

A. 10 sec. 

B. 12 sec. 

C. 14 sec. 

D. 16 sec. 
Solution 
Speed of the train  = (30 x 5/18)m/sec 
= (25 / 3) m/sec. 
Distance moved in passing the standing man  = 100 m. 
Required time taken  = 100 /( 25 / 3) 
=(100 x 3 / 25) sec 
= 12 sec. 

2. 
A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed? 

A. 52 kmph. 

B. 62 kmph. 

C. 72 kmph. 

D. 80 kmph. 
Solution 
Relative Speed  = (280 / 9)m/sec 
= (280/9 x 18/5) 
= 112 kmph. 
Speed of the train  = (112  50)kmph 
= 62 kmph. 

3. 
A train 150 m long is running with a apecd of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going? 

A. 6 sec. 

B. 7 sec. 

C. 9 sec. 

D. 11 sec. 
Solution 
Speed of the train relative to man  =( 68  8 ) 
= 60 Kmph 
= 60 x 5 / 18 
=50/3 m/sec. 
Time taken by it to cover 150 m at (50 /3)m/sec  = (112  50)kmph 
= (150 x 3/50)sec 
= 9 sec. 

4. 
A train moves with a speed of 108 kmph. Its speed in metres per second is 

A. 10.8 

B. 18 

C. 30 

D. 38.8 
Solution 
Speed  = 108 Kmph 
= (108 x 5/18)m/sec 
= 30 m/sec. 

5. 
Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is 

A. 80 m 

B. 100 m 

C. 120 m 

D. 180 m 
Solution 
Relative Speed  = (36 + 45) km/hr 
= (81 x 5/18) m/sec 
= (45/2) m/sec 
Length of the train  = (45 / 2 x 8) m 
= 180 m. 
