# Quantitative Aptitude on Times and Distance

Q21. A car completes a certain journey in 8 hours. It coveres half of the distance at 30 km/hr and the rest at 50 km/hr. The length of the journey is

(a) 250 km

(b) 265 km

(c) 280 km

(d) 300 km

**Answer:** (d) 300 km

Let, the length of the journey be x Km

A/Q | x | X | 1 | + | x | X | 1 | = 8 |

2 | 30 | 2 | 50 |

⇒ | x | + | x | = 8 |

60 | 100 |

⇒ | 5x + 3x | = 8 |

300 |

⇒ 8x = 8 X 300

⇒ x = 300 km

Q22. A man walking at 3 km/hr crosses a square field diagonally in 4 minutes. The area of the field is

(a) 15000 m^{2}

(b) 17000 m^{2}

(c) 20000 m^{2}

(d) 25000 m^{2}

**Answer:** (c) 20000 m^{2}

Speed = 3 km/hr = | 3 km | = | 3000 m | = 50 m/minute |

1 hr | 60 minute |

∴ Distance covered in 4 minutes = 4 X 50 meter = 200 meter

∴ Length of the diagonal = 200 meters

∴ Area = ½ X diagonal^{2} = ½ X 2000^{2} = ½ X 200 X 200 = 20000 m^{2}

Q23. Convert 60 km/hr into m/sec

(a) 15½ m/sec

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

(c) 16¼ m/sec

(d) 17¾ m/sec

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

Speed = 60 km/hr = | 60 km | = | 60 X 1000 m | = | 100 | m/sec = 16^{4}/_{6} m/sec = 16^{2}/_{3} m/sec |

1 hr | 60 X 60 sec | 6 |

Q24. Convert 20 m/sec into km/hr

(a) 55 km/hr

(b) 59 km/hr

(c) 63 km/hr

(d) 72 km/hr

**Answer:** (d) 72 km/hr

Speed = | 20 m | = | ^{20}/_{1000} km |
= | 20 X 60 X 60 | km/hr = 72 km/hr |

1 sec | ^{1}/_{60 X 60} hr |
1000 |

Q25. A man walks from his house to the railway station. If he walks at 6 km/h, he misses a train by 6 minutes. However, if he walks at 7 km/h, he reaches the station 4 minutes before the diparture of the train. Find the distance covered by him to reach the station.

(a) 7 km

(b) 9 km

(c) 10 km

(d) 12 km

**Answer:** (a) 7 km

Let, the required distance be x km

Now | x | - | x | = | 6 + 4 | = | 10 |

6 | 7 | 60 | 60 |

⇒ | x | - | x | = | 1 |

6 | 7 | 6 |

⇒ | 7x - 6x | = | 1 |

42 | 6 |

⇒ x = ^{1}/_{6} X 42 = 7 km

Q26. A man covers a certain distance by walk at 6 km/hr and returns back to the starting point riding on scooter at 50 km/hr. Find his average speed of the whole journey.

(a) 32.48 km/h

(b) 49.12 km/h

(c) 54.54 km/h

(d) 59.65 km/h

**Answer:** (c) 54.54 km/h

Average Speed = | 2xy | Km/h = | 2 X 60 X 50 | Km/h |

x + y | 60 + 50 |

= | 2 X 60 X 50 | Km/h = | 600 | Km/h = 54.54 Km/h |

110 | 11 |

Q27. A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 km/h. This train catches up the goods train in 4 hours. Find the speed of the goods train.

(a) 29 km/h

(b) 32 km/h

(c) 36 km/h

(d) 41 km/h

**Answer:** (c) 36 km/h

Let, the speed of the goods train be x km/h

Distance covered by goods train in 10 hours = Distance covered by express train in 4 hours

⇒ 10x = 4 X 90

⇒ x = ^{(4X90)}/_{10} = 36 km/h

Q28. The ratio between the speeds of two trains is 4:6. If the first train runs 280 km in 4 hours, the speed of the second train is

(a) 85 km/h

(b) 89 km/h

(c) 98 km/h

(d) 105 km/h

**Answer:** (d) 105 km/h

Let, the speed of the second train be 6x km/h

∴ the speed of the first train be 4x km/h

A/Q 4x = | 280 |

4 |

⇒ 4x = 70

⇒ x = ^{70}/_{4} = ^{35}/_{2}

∴ Speed of the second train = 6 X ^{35}/_{2} = 3 X 35 = 105 km/h

Q29. Excluding stoppages, the speed of a bus is 50 km/h and including stoppages, it is 40 km/h. For how many minutes does the bus stop per hour ?

(a) 12 min

(b) 16 min

(c) 18 min

(d) 21 min

**Answer:** (a) 12 min

Due to stoppages, it covers (50 - 40) i.e 10 km less per hour

∴ Time taken to cover 10 km = (^{10}/_{50} X 60) min = 12 min

Q30. X and Y are two stations 600 km apart. A train starts from X and moves towards Y at a speed 30 km/h. Another train starts from Y at the same time and moves towards X at 40 km/h. How far from X will they cross each other ?

(a) 257.11 km

(b) 266.22 km

(c) 312.35 km

(d) 323.39 km

**Answer:** (a) 257.11 km

Suppose, they meet x km from X

Now | x | = | 600 - x |

30 | 40 |

⇒ | x | = | 600 - x |

3 | 4 |

⇒ 4x = 1800 - 3x

⇒ 7x = 1800

⇒ x = 257.11 Km