# Problems on Trains Questions

**FACTS AND FORMULAE FOR PROBLEMS ON TRAINS**

**1. **a km/hr = [a x (5/18)] m/s.

**2. **a m/s = [a x (18/5)] km/hr.

**3.** Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.

**4.** Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + 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 relatives speed = (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 = (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 = 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 = sec.

**9. **If two trains (or bodies) start at the same time 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) =

A) 60 | B) 62 |

C) 64 | D) 65 |

Explanation:

Relative speed = m / sec = kmph = 112 kmph.

Speed of goods train = (112 - 50) kmph = 62 kmph.

A) 48 | B) 24 |

C) 38 | D) 36 |

Explanation:

Less Cogs more turns and less time less turns

Number of turns required=80 × × = 24 times

A) 10 | B) 8 |

C) 6 | D) 4 |

Explanation:

Distance = 110 m

Relative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)

= m/sec = m/sec

Time taken to pass the man = = 6 s

A) 69.5 km/hr | B) 70 km/hr |

C) 79 km/hr | D) 79.2 km/hr |

Explanation:

Let the length of the train be x metres and its speed by y m/sec.

Then,

Now,

8y + 264 = 20y

y = 22.

Speed = 22 m/sec =km/hr = 79.2 km/hr.

A) 10 | B) 25 |

C) 12 | D) 20 |

Explanation:

Speed of train 1 = = 12 m/sec

Speed of train 2 = = 8 m/sec

if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec

distance covered = 120 + 120 = 240 m

time = distance/speed = 240/20 = 12 sec