Problems on Trains
Exercise:: Problems on Trains-General Questions 3. Time taken by a train of length l metres to pass a pole or stranding man or a signal post is equal to the time taken by the train to cover l meters. 4. Time taken by atrain of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l+b) metres. 5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u>v, then their relative speed is (u-v) m/s. 6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is (u+v) m/s. 7. If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = (a+b)/(u+v) sec. 8. If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then the time taken by the faster train to cross the slower train = (a+b)/(u-v) sec. 9. If two trains or bodies start at the same from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A’s speed): (B’s speed) = (√b: √a)
1. a km/hr = (a x 5/18)m/s
2. a m/s =(a x 18/5)km/hr
1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres
Answer: Option D
Explanation:
Speed= 60 x 5/18 m/sec = 50/3 m/sec.
Length of the train = (Speed x Time).
Length of the train = 50/3 x 9 m = 150 m
2. A train, 130 m long is running at the speed of 45 km/hr crosses a bridge in 30 seconds. What is the length of the bridge?
A. 145 metres
B. 245 metres
C. 325 metres
D. 215 metres
Answer: Option B
Explanation:
The distance travelled by train to cross the bridges is equal to the total length of train and bridge.
Speed = 45 x 5/18 m/sec = 25/2 m/sec.
Time = 30 sec
Total Distance Travelled = (25/2) x 30 = 375 m
Length of the bridge = 375 -130= 245 m
3. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
A. 45 km/hr
B. 50 km/hr
C. 54 km/hr
D. 55 km/hr
Relative Speed= 125/10 m/s =12.5 x 18/5 km/hr = 45 km/hr
Answer: Option B
Explanation:
When the train and man are in same direction then relative speed will be the difference between their individual speeds.
Now, let the speed of the train = x km/h.
So, Relative speed= 45 km/hr = x -5
Speed of the train x = 45+5= 50 km/hr
4. A train moving at 50 km/hr crosses a bridge in 45 seconds.The length of train is 150 m. Find the length of bridge :
A. 445 m
B. 455 m
C. 465 m
D. 475 m
Answer: Option D
Explanation:
The distance travelled by train to cross the bridges is equal to the total length of train and bridge.
speed of train= 50 km/h = 50 x 5/18 m/s= 125/9 m/s
Time = 45 sec
Total distance travelled by train to cross the bridge= (125/9)X45 = 625 m
Length of bridge= total distance travelled - Length of train = 625-150= 475 m
5. A train, 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
A. 40 sec
B. 42 sec
C. 45 sec
D. 48 sec
Answer: Option A
Explanation:
Speed of train= 45 km/h = 45 x 5/18 m/s= 25/2 m/s
Total distance travelled = 360 + 140 = 500 m
Time Taken = Total Distance/ Speed = 500/(25/2) = 40 sec
6. A train of length 110 m is running at a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to the train?
A. 8 sec
B. 10 sec
C. 6 sec
D. 15 sec
Time taken = Distance/Speed = 110/ (55/3) = 6 sec
Answer: Option C
Explanation:
Distance = 110 m
Relative speed = 60 + 6 = 66 km/hr = 66 x (5/18) = 55/3 m/s
7. A train 100 m long is running at the speed of 30 km/hr. Find the time taken by train to pass a man standing near the railway line.
A. 8 sec
B. 12 sec
C. 15 sec
D. 16 sec
Time taken = Distance/Speed = 100/ (25/3) = 12 sec
Answer: Option B
Explanation:
Speed of the train = 30 km/hr = 30 x 5/18 m/s = (25/3) m/s
Distance= Length of train = 100 m
8. A train 100 m long is moving at a speed of 50 km/hr crosses a train 120 m long coming from opposite direction in 6 seconds. The speed of second train is :
A. 45 km/h
B. 132 km/h
C. 63 km/h
D. 82 km/h
Hence, Speed of second train =x km/h = 82 km/h
Answer: Option D
Explanation:
Let the Speed of second train = x km/h
Relative speed = (50 + x ) km/h
Total Distance covered= (100 m + 120 m) = 220 m = 0.22 km
Time = 6 sec = 6/ (60 x 60) hr =1/600 hr
Now, Speed = Distance/ Time
(50 + x ) =0.22 / (1/600)
50 + x =132
x = 82 km/h
9. A train moving with uniform speed crosses a man standing at platform in 2 seconds and a bridge of length 250 m in 7 seconds.The length of train is :
A. 75 m
B. 85 m
C. 100 m
D. 107 m
Answer: Option C
Explanation:
Let the length of train = x m
Speed of train = x/2 = ( x +250)/7
7x = 2 (x + 250)
7x = 2 x + 500
5x = 500
x = 100 m
Hence, length of train =x m = 100 m
10. A train 150 m long is running with a speed of 68 km/h. In what time will it pass a man running at 8 km/h in the same direction to the train.
A. 5 sec
B. 7 sec
C. 9 sec
D. 12 sec
Answer: Option C
Explanation:
Relative Speed = (68 - 8) km/h = 60 km/h
Convert speed into m/s = 60 km/h x (5/18) = (50/3) m/s
Time taken by train to cross the man = Distance/ Speed
= 150/ (50/3)
= 150 x 3/50
= 9 sec
Hence, Time taken = 9 sec