- 1. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:

Options- A. 70 km/hr
- B. 75 km/hr
- C. 84 km/hr
- D. 87.5 km/hr

Correct Answer: 87.5 km/hr

Let the speed of two trains be 7*x* and 8*x* km/hr.

Then, 8x = |
❨ | 400 | ❩ | = 100 |

4 |

⟹ x = |
❨ | 100 | ❩ | = 12.5 |

8 |

∴ Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.

- 2. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Options- A. 220 km
- B. 224 km
- C. 230 km
- D. 234 km

Correct Answer: 224 km

(1/2)x |
+ | (1/2)x |
= 10 |

21 | 24 |

⟹ | x |
+ | x |
= 20 |

21 | 24 |

⟹ 15*x* = 168 x 20

⟹ x = |
❨ | 168 x 20 | ❩ | = 224 km. |

15 |

- 3. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:

Options- A. 50 km
- B. 56 km
- C. 70 km
- D. 80 km

Correct Answer: 50 km

Let the actual distance travelled be *x* km.

Then, | x |
= | x + 20 |

10 | 14 |

⟹ 14*x* = 10*x* + 200

⟹ 4*x* = 200

⟹ *x* = 50 km.

- 4. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is:

Options- A. 1 hour
- B. 2 hours
- C. 3 hours
- D. 4 hours

Correct Answer: 1 hour

Let the duration of the flight be *x* hours.

Then, | 600 | - | 600 | = 200 |

x |
x + (1/2) |

⟹ | 600 | - | 1200 | = 200 |

x |
2x + 1 |

⟹ *x*(2*x* + 1) = 3

⟹ 2*x*^{2} + *x* - 3 = 0

⟹ (2*x* + 3)(*x* - 1) = 0

⟹ *x* = 1 hr. [neglecting the -ve value of *x*]

- 5. A car travelling with 5⁄7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.

Options- A.
17 6 km/hr 7 - B. 25 km/hr
- C. 30 km/hr
- D. 35 km/hr

Correct Answer: 35 km/hr

Time taken = 1 hr 40 min 48 sec = 1 hr 40 | 4 | min = 1 | 51 | hrs = | 126 | hrs. |

5 | 75 | 75 |

Let the actual speed be *x* km/hr.

Then, | 5 | x x |
126 | = 42 |

7 | 75 |

⟹ x = |
❨ | 42 x 7 x 75 | ❩ | = 35 km/hr. |

5 x 126 |

- 6. A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is:

Options- A. 100 kmph
- B. 110 kmph
- C. 120 kmph
- D. 130 kmph

Correct Answer: 120 kmph

Let speed of the car be *x* kmph.

Then, speed of the train = | 150 | x |
= | ❨ | 3 | x |
❩kmph. |

100 | 2 |

∴ | 75 | - | 75 | = | 125 |

x |
(3/2)x |
10 x 60 |

⟹ | 75 | - | 50 | = | 5 |

x |
x |
24 |

⟹ x = |
❨ | 25 x24 | ❩ | = 120 kmph. |

5 |

- 7. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1⅔ hours, it must travel at a speed of:

Options- A. 300 kmph
- B. 360 kmph
- C. 600 kmph
- D. 720 kmph

Correct Answer: 720 kmph

Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr. [We can write 1⅔ hours as 5/3 hours]

∴ Required speed = | ❨ | 1200 x | 3 | ❩km/hr | = 720 km/hr. |

5 |

- 8. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

Options- A. 14 km
- B. 15 km
- C. 16 km
- D. 17 km

Correct Answer: 16 km

Let the distance travelled on foot be *x* km.

Then, distance travelled on bicycle = (61 -*x*) km.

So, | x |
+ | (61 -x) |
= 9 |

4 | 9 |

⟹ 9*x* + 4(61 -*x*) = 9 x 36

⟹ 5*x* = 80

⟹ *x* = 16 km.

- 9. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

Options- A. 3.6
- B. 7.2
- C. 8.4
- D. 10

Correct Answer: 7.2

Speed = | ❨ | 600 | ❩m/sec. |

5 x 60 |

= 2 m/sec.

Converting m/sec to km/hr (see important formulas section)

= | ❨ | 2 x | 18 | ❩ | km/hr |

5 |

= 7.2 km/hr.

- 10. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:

Options- A. 35.55 km/hr
- B. 36 km/hr
- C. 71.11 km/hr
- D. 71 km/hr

Correct Answer: 71.11 km/hr

Total time taken = | ❨ | 160 | + | 160 | ❩hrs. | = | 9 | hrs. |

64 | 80 | 2 |

∴ Average speed = | ❨ | 320 x | 2 | ❩km/hr | = 71.11 km/hr. |

9 |

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