# Problems on Trains

Q21. How much time will a train 180 m long take to cross a bridge 300 m long, if it is running at a speed of 50 km/hr

(a) 31.21 sec

(b) 34.56 sec

(c) 37.15 sec

(d) 39.59 sec

**Answer:** (b) 34.56 sec

Speed = 50 km/hr = | 50 X 1000 m | = | 500 | m/sec = | 125 | m/sec |

60 X 60 sec | 36 | 9 |

Required Time = | 180 + 300 m | = | 480 X 9 | sec = 34.56 Sec |

125/9 m/sec | 125 |

Q22. Two goods train each 400 m long are running in opposite directions on parallel tracks. Their speeds are 400 km/hr and 30 km/hr respectively. The time taken by the slower train to pass the driver of the faster one is

(a) 32.87 sec

(b) 36.15 sec

(c) 39.33 sec

(d) 41.14 sec

**Answer:** (d) 41.14 sec

Relative Speed = (40 + 30) km/hr = 70 km/hr = | 70 X 1000 m | = | 700 m | = | 175 | m/sec |

60 X 60 sec | 36 sec | 9 |

Distance covered = 400 + 400 = 800 m

Required Time = | 800 | Sec = | 800 X 9 | sec = 41.14 Sec |

175/9 | 175 |

Q23. A 150 m long train crosses a man walking at the speed of 5 km/hr in the opposite direction in 5 seconds. The speed of the train is

(a) 95 km/hr

(b) 98 km/hr

(c) 101 km/hr

(d) 103 km/hr

**Answer:** (d) 103 km/hr

Let, the speed of the train be x km/hr

Relative Speed = (x + 5) km/hr = | (x + 5) X 1000 m | = | 5(x+5) | m/sec |

60 X 60 sec | 18 |

A/Q | 150 | = 5 |

5(x + 5)/18 |

⇒ 150 = 5 X | 5(x + 5) |

18 |

⇒ 150 X 18 = 25x + 125

⇒ 2700 = 25x + 125

⇒ 25x = 2575

⇒ x = 2575/25 = 103 km/hr

Q24. A train passes two persons walking in the same direction in which the train is going. These persons are walking at the rate of 2 km/hr and 4 km/hr respectively and the train passes them completely in 10 seconds and 12 seconds respectively. The speed of the train is

(a) 14 km/hr

(b) 19 km/hr

(c) 23 km/hr

(d) 27 km/hr

**Answer:** (a) 14 km/hr

Let the length of the train be x km and speed be y km/hr

Speed of the train relative to first man = (y - 2) km/hr

speed of the train relative to second man = (y - 4) km/hr

Now = | x | = | 10 |

y - 2 | 60 X 60 |

⇒ | x | = | 1 |

y - 2 | 360 |

⇒ 360x = y - 2 -------- (1)

And | x | = | 12 |

y - 4 | 60 X 60 |

⇒ | x | = | 1 |

y - 4 | 300 |

⇒ 300x = y - 4 -------- (2)

(1) - (2) ⇒ 60x = 2

⇒ x = 2/60 = 1/30

(1) ⇒ 360 X ^{1}/_{30} = y - 2

⇒ 12 = y - 2

⇒ y = 14 km/hr

Q25. A train moving at the rate of 40 km/hr crosses a standing man in 10 seconds. It will crosses a plateform 60m long in

(a) 15.40 sec

(b) 18.56 sec

(c) 22.29 sec

(d) 25.14 sec

**Answer:** (a) 15.40 sec

Speed = 40 km/hr = | 40 X 1000 m | = | 400 | m/sec = | 100 | m/sec |

60 X 60 sec | 36 | 9 |

Length of the train = Speed X time = | 100 | X 10 m = | 1000 | m |

9 | 9 |

∴ Required time of the train to cross the platform = | (1000/9 + 60) m |

100/9 m/sec |

= | (1000+540)/9 | = 1540/100 = 15.40 sec |

100/9 |

Q26. Two trains travel in opposite directions at 35 km/hr and 40 km/hr. A man sitting in the slower train passes the faster train in 10 seconds. The length of the faster train is

(a) 188.13 m

(b) 192.62 m

(c) 201.45 m

(d) 208.33 m

**Answer:** (d) 208.33 m

Relative Speed = (35 + 40) km/hr = 75 km/hr = | 75 X 1000 m | = | 750 | m/sec = | 375 | m/sec |

60 X 60 sec | 36 | 18 |

Length of the train = Distance covered in 10 second at 375/18 m/sec speed =

375 | X 10 m = | 3750 | m = 208.33 m |

18 | 18 |

Q27. Two trains running in opposite directions at 36 km/hr and 45 km/hr cross each other in 20 seconds. If one of the train is 200 m long, the length of the other train is

(a) 235 m

(b) 245 m

(c) 250 m

(d) 265 m

**Answer:** (c) 250 m

Let, the length of the other train be x meters

Sum of their length = (200 + x) m

Relative Speed = (36 + 45) km/hr = 81 km/hr = | 81 X 1000 m | = | 45 | m/sec |

60 X 60 sec | 2 |

A/Q | 200 +x | = 20 |

45/2 |

⇒ 2 (200 + x) = 20 X 45

⇒ 400 + 2x = 900

⇒ 2x = 500

⇒ x = 250 m

Q28. Two trains each 100 m long, moving in opposite directions cross each other in 10 seconds. If one is moving twice as fast as the other, then the speed of the faster train is

(a) 48 km/hr

(b) 53 km/hr

(c) 58 km/hr

(d) 67 km/hr

**Answer:** (a) 48 km/hr

Let, the speed of the trains be x m/sec and 2x m/sec respectively.

Relative speed = (x + 2x) m/sec = 3x m/sec

Total length of the train = 100 + 100 = 200 m

A/Q 200/10 = 3x

⇒ 3x = 20

⇒ x = 20/3

∴ Speed of the faster train = 2x m/sec = 2 X | 20 | = | 40 | m/sec |

3 | 3 |

= | 40/1000 km | = | 40 X 3600 | km/h = 48 km/hr |

3/(60 X 60) h | 3 X 1000 |

Q29. A train 100 m long is running at 50 km/h. In what time will it pass a man running in the direction opposite to that of the train at 5 km/h ?

(a) 5 ^{3}/_{11} sec

(b) 5 ^{6}/_{11} sec

(c) 6 ^{6}/_{11} sec

(d) 7 ^{9}/_{11} sec

**Answer:** (c) 6 ^{6}/_{11} sec

Relative speed = u + v km/h = 50 + 5 km/h = 55 km/h = | 55 X 1000 m |

60 X 60 sec |

Distance covered in passing the man = 100 m

∴ Time taken = | 100 | = | 360 | sec = 6 | 6 | sec |

^{55000}/_{3600} sec |
55 | 11 |

Q30. Two trains 110 m and 95 m long run at the speed of 40 km and 70 km per hour respectively in opposite directions on parallel tracks. The time which they thake to cross each other is

(a) 6.20 sec

(b) 6.70 sec

(c) 7.25 sec

(d) 7.38 sec

**Answer:** (b) 6.70 sec

Relative speed = (40 + 70) km/h = 110 km/h = | 110000 m | = | 75 m |

60 X 60 sec | 9 sec |

Total Distance of the trains = (110 + 95)m = 205 m

∴ Required Time = | 205 | sec = | 205 X 9 | sec = | 369 | sec = 6.70 sec |

^{275}/_{9} |
275 | 55 |