# 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 |