Problems on Trains
Q31. A train 80m long moving at a speed of 40 km/hr crosses a train 100 m long comming from opposite direction on parallel tracks in 5 sec. The speed of the second train is
(a) 72.2 km/hr
(b) 77.5 km/hr
(c) 83.7 km/hr
(d) 89.6 km/hr
Answer: (d) 89.6 km/hr
Let, the speed of the second train be x km/hr
∴ Relative speed = (40 + x) km/hr
| Total length of the trains = 80 + 100 m = 180 m = | 180 m | km = | 18 | km |
| 1000 | 100 |
| Time taken for crossing = | 18/100 | h |
| 40 + x |
| ⇒ | 5 | h = | 18 | h |
| 60 X 60 | 100 (40 + x) |
| ⇒ | 5 | = | 18 |
| 3600 | 4000 + 100x |
⇒ 20000 + 500x = 64800
⇒ 500x = 44800
⇒ x = 89.6 km/hr
Q32. A train is running at the rate of 60 km/hr. A man is going in the same direction parallel to the train at 20 km/hr. If the train crosses the man in 18 seconds, the length of the train be
(a) 200 m
(b) 220 m
(c) 225 m
(d) 245 m
Answer: (a) 200 m
Let the length of the train be x meter
| ∴ Relative speed = (60 - 20) km/hr = 40 km/hr = | 40000 m | = | 100 m |
| 60 X 60 sec | 9 sec |
| Time taken for crossing = | x | sec |
| 100/9 sec |
| ⇒ 18 sec = | 9x | sec |
| 100 |
| ⇒ x = | 18 X 100 | = 200 m |
| 9 |
Q33. A 120 m long train takes 10 seconds to cross a man standing on a platform. The speed of the train is
(a) 6 m/sec
(b) 12 m/sec
(c) 16 m/sec
(d) 20 m/sec
Answer: (b) 12 m/sec
| Speed = | 120 m | = 12 m/sec |
| 10 sec |
Q34. Two trains running in opposite directions cross a man standing on the platform in 25 secs and 15 seconds respectively and they cross each other in 20 seconds. The ratio of their speed is
(a) 1 : 1
(b) 1 : 2
(c) 2 : 1
(d) 2 : 3
Answer: (a) 1 : 1
Let, the speed of the trains be x m/sec and y m/sec
Length of the first train = x m/sec X 25 sec = 25x m
Length of the 2nd train = y m/sec X 15 sec = 15y m
| A/Q | 25x + 15y | = 20 |
| x + y |
⇒ 25x + 15y = 20x + 20y
⇒ 5x = 5y
⇒ x/y = 5/5 = 1/1
∴ Ratio of their speed = 1 : 1
Q35. Convert 20 m/sec into km/hr
(a) 65 km/hr
(b) 68 km/hr
(c) 72 km/hr
(d) 79 km/hr
Answer: (c) 72 km/hr
| Speed = 20 m/sec = | 20 m | = | 20/1000 km | = | 20 X 3600 | km/hr = 72 km/hr |
| 1 sec | 1/60 X60 h | 1000 |
Q36. A train travelling at 40 km/hr completely crosses another train having half its length and travelling in the opposite direction at 60 km/hr. in 9 seonds. If it passes a platform in 2 minutes, the length of the platform is
(a) 1076.32 m
(b) 1132.12 m
(c) 1166.66 m
(d) 1197.16 m
Answer: (c) 1166.66 m
Let the length of the slower train be x meters
∴ The length of the faster train = x/2 meters
| Relative speed = (40 + 60) km/hr = 100 km/hr = | 100 X 1000 m | = | 1000 | m/sec |
| 60 X 60 sec | 36 |
| Now | x + x/2 | = 9 |
| 1000/36 |
| ⇒ | 3x X 36 | = 9 |
| 2 X 1000 |
| ⇒ x = | 9 X 2000 | = 500/3 m |
| 3 X 36 |
Length of the slower train = 500/3 m
Let, the length of the platform be y miles
| 500/3 + y | = 120 |
| 40X1000/60X60 |
| ⇒ | 9 (500 + 3y) | = 120 |
| 100 X 3 |
⇒ 1500 + 9y = 12000
⇒ 9y = 10500
⇒ y = 10500/9 = 1166.66 m
Q37. A train 150 m long takes 10 seconds to cross a man walking at 5 km/hr in the direction opposite to that of the train. Find the speed of the train.
(a) 45 km/hr
(b) 49 km/hr
(c) 53 km/hr
(d) 55 km/hr
Answer: (b) 49 km/hr
Let, the speed of the train be x km/hr
Relative speed = (x + 5) km/hr = 5(x + 5)/18 m/sec
Distance covered in passing the man = 150m
| Now | 150 | = 10 |
| 5(x + 5)/18 |
| ⇒ | 150 X 18 | = 10 |
| 5(x + 5) |
⇒ 540 = 10(x + 5)
⇒ 540 = 10x + 50
⇒ 10x = 490
⇒ x = 49 km/hr
Q38. A 80 m long train is running at 72 km/hr. In how much time will it cross an electric pole ?
(a) 4 sec
(b) 5 sec
(c) 6 sec
(d) 7 sec
Answer: (a) 4 sec
| Speed of the train = (72 X | 5 | ) m/sec = 20 m/sec |
| 18 |
| Required time = | 80 m | = 4 sec |
| 20 m/sec |
Practice Test Exam