Arithmatical  Problems on Trains
DIRECTIONS : Problems based on trains, speed, distance.
6. 
A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ? 

A. 10 sec. 
B. 12 sec. 

C. 14 sec. 
D. 16 sec. 
Solution 
Speed of the train  = (59 + 7) Kmph 
= (66 x 5/18) m/sec 
= (55 / 3 )m/sec 
Time taken by it cover 220 m  = (220 x 3 /55)sec 
= 12 sec 

7. 
Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ? 

A. 9 a.m 
B. 10 a.m 

C. 1030 a.m 
D. 11 a.m 
Solution 
Distance covered by A in x hours  = 20 x km 
Distance covered by B in (x  1) hours  = 25 (x  1) km 
= 20x + 25 (x  I) 
= 110 
= 45x = 135 
x = 3. So, they meet at 10 a.m 

8. 
A train 108 m long moving at a speed of 50 km / hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is 

A. 48km/hr 
B. 54 km/hr 

C. 66km/hr 
D. 82km/hr 
Solution 
Relative speed  = (x + 50) km/ hr 
=(x + 50) x 5/18 m/sec 
= 250 + 5 x /18]m/sec 
Distance covered  = (108 + 112) m 
= 220 m 

= 220 / (250 + 5x / 18) = 6 
= 250 + 5 x= 660 
= 82 km / hr. 

9. 
How long does a train 110 metres long running at the speed of 72 km / hr take to cross a bridge 132 metres in length ? 

A. 9.8 sec 
B. 12.1 sec 

C. 12.42 sec 
D. 14.3 sec 
Solution 
Speed  = (72 x 5/18 )m/sec 
= 20 m/ sec 
Total Distance covered  = (110 + 132) m 
= 242 m 
Required time  = (242 / 60) sec 
= 12.1 sec 

10. 
In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr ? 

A. 2.5 sec 
B. 4.25 Sec 

C. 5 sec 
D. 12.5 sec 
Solution 
Speed  = (144 x 5 /18) m/sec 
= 40 m / sec 
Time taken  = (100 /40) sec 
= 2.5 sec. 
