# Problems on Trains

Q11. A 230m long train crosses a bridge in 30 seconds at 45 km/hr. The length of the bridge is

(a) 130m

(b) 145m

(c) 245m

(d) 250m

**Answer:** (b) 145m

Let the length of the bridge be x meter

Now speed = | 230 + x | m/sec |

30 |

=> 45 km/hr = | 230 + x | m/sec |

30 |

=> | 45 X 1000 | m/sec = | 230 + x | m/sec |

60 X 60 | 30 |

=> | 25 | = | 230 + x |

2 | 30 |

=> 460 + 2x = 750

=> 2x = 750 - 460

=> x = 290/2 = 145 m

Q12. A train crosses a pole in 15 seconds, while it crosses a 100m long platform in 25 seconds. The length of the train is

(a) 125m

(b) 135m

(c) 150m

(d) 200m

**Answer:** (c) 150m

Let the length of the train be x meter

Now x/15 = (100+x)/25 => 25x = 1500 + 15x

=> 10x = 1500

=> x = 150m

Q13. A fast train takes 3 hours less than the slow train for a journey of 600 km. If the speed of the slow train is 10 km/hr less than the fast train, the speed of the slow train is

(a) 32 km/hr

(b) 40 km/hr

(c) 46 km/hr

(d) 51 km/hr

**Answer:** (b) 40 km/hr

Let the speed of the slow train is x km/hr

∴ the speed of the fast train is (x + 10) km/hr

Fast train takes the time = | 600 km | = | 600 | hr |

(x + 10) km/hr | x + 10 |

Slow train takes the time = | 600 km | = | 600 | hr |

x km/hr | x |

A/Q | 600 | = | 600 | - 3 |

x + 10 | x |

⇒ | 600 | = | 600 - 3x |

x + 10 | x |

⇒ 600x = (600 - 3x)(x + 10)

⇒ 600x = 600x + 6000 - 3x^{2} - 30x

⇒ 3x^{2} + 30x - 6000 = 0

⇒ x^{2} + 10x - 2000 = 0

⇒ x^{2} + 50x - 40x - 2000 = 0

⇒ x(x + 50) - 40(x + 50) = 0

⇒ (x - 40)(x + 50) = 0

∴ x - 40 = 0

⇒ x = 40 km/hr

Q14. Two trains starts from two stations A and B and travel towards each other at 40 km/hr and 50 km/hr respectively. At the time of their meeting, the second train has travelled 110 km more than the first. The distance between A and B is

(a) 850 Km

(b) 870 Km

(c) 935 Km

(d) 990 Km

**Answer:** (d) 990 Km

Let, the two trains meet after x hours

Now 50x = 40x + 110

⇒ 50x - 40x = 110

⇒ 10x = 110

⇒ x = 11

∴ Distance between A and B = (40 X 11 + 50 X 11) Km = (440 + 550) Km = 990 Km

Q15. A train covered a certain distance at a uniform speed. If the train had been 5 km/hr faster, it would have taken 3 hours less than the schedule time. If the train were slower by 5 km/hr, the train would have taken 5 hours more than the schedule time. The length of journey is

(a) 120 Km

(b) 140 Km

(c) 160 Km

(d) 180 Km

**Answer:** (d) 180 Km

Let the required distance be x km and uniform speed be y km/hr

Now | x | - | x | = 3 --------(1) |

y | y + 5 |

Now | x | - | x | = 5 --------(2) |

y - 5 | y |

(1) ⇒ | x(y + 5) - xy | = 3 |

y(y + 5) |

⇒ xy + 5x - xy = 3y^{2} + 15y

⇒ 3y^{2} + 15y = 5x ------ (3)

(2) ⇒ | xy - x(y - 5) | = 5 |

y(y - 5) |

⇒ xy - xy + 5x = 5y^{2} - 25y

⇒ 5y^{2} - 25y = 5x ------ (4)

From (1) and (4) ⇒ 3y^{2} + 15y = 5y^{2} - 25y

⇒ 2y^{2} = 40y

⇒ y = 20

(3) ⇒ 3 X 20^{2} + 15 X 20 = 5x

⇒ 1200 + 300 = 5x

⇒ 5x = 900

⇒ x = 180 km

Q16. Bombay Express left Delhi for Bombay at 14.30 hours travelling at a speed of 70 km/hr and Rajdhani Express left Delhi for Bombay on the same day at 15.30 hours travelling at a speed of 90 km/hr. How far away from Delhi will the two trains meet ?

(a) 285 Km

(b) 290 Km

(c) 315 Km

(d) 345 Km

**Answer:** (c) 315 Km

Let, the trains meet at a distance of x km from Delhi.

Then | x | - | x | = 1 |

70 | 90 |

⇒ | 9x - 7x | = 1 |

630 |

⇒ 2x = 630

⇒ x = 315 km

Q17. A train without stoppages travels at the rate of 60 km/hr and with stopagges it travels at 55 km/hr. How many minutes does the train stop on an average per hour ?

(a) 5 min

(b) 8 min

(c) 10 min

(d) 12 min

**Answer:** (a) 5 min

Due to stoppages it covers 5 Km less per hour

Required Time taken to cover 5 km = (5/60) X 60 min = 5 min

Q18. A train travelled distances of 10 km, 20 km and 30 km at speeds of 50 km/hr, 60 km/hr and 90 km/hr respectively. The average speed of the train was

(a) 67.25 km/hr

(b) 69.23 km/hr

(c) 70.12 km/hr

(d) 72.45 km/hr

**Answer:** (b) 69.23 km/hr

Total distance covered = 10 km + 20 km + 30 km = 60 km

Total Time taken = ( | 10 | + | 20 | + | 30 | ) hr |

50 | 60 | 90 |

= ( | 1 | + | 1 | + | 1 | ) hr |

5 | 3 | 3 |

= | 3 + 5 + 5 | h = | 13 | h |

15 | 15 |

Average Speed = | 60 | km/hr = | 60 X 15 | km/hr = | 900 | km/hr = 69.23 km/hr |

13/15 | 13 | 13 |

Q19. Two trains A and B start running together from the same point in the same directions at 50 km/hr and 60 km/hr respectively. If the length of each train is 200 m, how long will it take for the train B to cross train A.

(a) 121 Sec

(b) 135 Sec

(c) 144 Sec

(d) 156 Sec

**Answer:** (c) 144 Sec

Relative Speed = (60 - 50) km/hr = 10 km/hr = | 10 X 1000 m | = | 100 | m/Sec = | 25 | m/Sec |

60 X 60 Sec | 36 | 9 |

Total Distance covered = 200 + 200 = 400 m

∴ Required time = 400 X (9/25) Sec = 16 X 9 Sec = 144 Sec

Q20. A train 200 m in length passes a milestone in 20 Sec and another train of the same length travelling in opposite direction in 15 Sec. The speed of the second train is

(a) 12 ^{1}/_{3} m/sec

(b) 15 ^{2}/_{5} m/sec

(c) 16 ^{2}/_{3} m/sec

(d) 18 ^{3}/_{5} m/sec

**Answer:** (c) 16 ^{2}/_{3} m/sec

Speed of the first train = 200/20 m/sec = 10 m/sec

Let the speed of the second train be x m/sec

Relative Speed = (10 + x) m/sec

Total distance = 200 + 200 = 400 m

A/Q | 400 | = 15 |

10 + x |

⇒ 400 = 15 (10 + x)

⇒ 400 = 150 + 15x

⇒ 15x = 250

⇒ x = 250/15 = 50/3 = 16 ^{2}/_{3} m/sec