**Time and Distance** Aptitude Questions and Answers – Formulas & Tricks

**Time and Distance Formula:**

- Distance = Speed * Time,
- Time = Distance / Speed
- Speed = Distance / Time
- Average Speed = 2xy / (x + y)
- Convert Km/h to M/s =Km/h * (5/18)
- Convert m/sec to Km/hr = m/sec * (18/5)
- If the ratio of the speed of A and B is a : b, then the ratio of the times taken by them to cover the same distance is (1 / a) : (1 / b) or b : a
- Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is (2xy / (x + y))km/hr.
- Using this formula, all basic problems can be handled. However, we need to make sure about the correct usage of units while using the formula
- Speed is inversely proportional to the time taken when distance travelled is constant. So When speed increases, time decreases and vice versa.
- Two persons may walk in same direction or in opposite direction

**Relative Speed:**

Relative Speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.

Time and Distance Aptitude Questions and Answers With Detailed Explanation – Quantitative Aptitude

## Time and Distance

Question 1 |

The speed of a train is 90kmph. What is the distance covered by it in 10mins?

15kmph | |

12kmph | |

10kmph | |

5kmph |

Question 1 Explanation:

**Answer: Option A**

__Explanation:__

90 * (10/60) = 15kmph

Question 2 |

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

50km | |

56km | |

70km | |

80km |

Question 2 Explanation:

**Answer: Option A**

__Explanation:__

Let the actual distance travelled by x km.

Then, (x+10) = ((x+20)/14)

14x = 10x + 200

4x = 200

**x = 50km**

Question 3 |

In covering a distance of 30km, Abhay takes 2hrs more than Sameer. If Abahy doubles his speed, then he would take 1hr less than Sameer. Abhay's Speed is:

5kmph | |

6kmph | |

6.25kmph | |

7.5kmph |

Question 3 Explanation:

**Answer: Option A**

__Explanation:__

Let Abhay's speed be x km/hr

Then, (30 / x) - (30 / 2x) = 3

=> 6x = 30

**x = 5km/hr**

Question 4 |

Robert is travelling on his cycle and has calculated to reach point A at 2PM. if he travels at 10kmph, he will reach there at 12 noon if he travels at 15kmph. At what speed must he travel to reach A at 1 P.M?

8kmph | |

11kmph | |

12kmph | |

14kmph |

Question 4 Explanation:

**Answer: Option C**

__Explanation:__

Let the distance travelled by x km.

Then, (x/10) - (x/15) = 2

3x - 2x = 60

x = 60km.

Time taken to travel 60km at 10km/hr = (60/10)hrs = 6hrs

So, Robert started 6hrs before 2PM. i.e., at 8AM

Therefore, Required Speed = (60/5)kmph

**Required Speed = 12kmph**

Question 5 |

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

14km | |

15km | |

16km | |

17km |

Question 5 Explanation:

**Answer: Option C**

__Explanation:__

So,

9x + 4(61-x) = 9 * 36

5x = 80

**x = 16km**

Question 6 |

How long does a train 110m long travelling at 60kmph takes to cross a bridge of 170m in length?

16.8sec | |

15sec | |

16sec | |

16.8sec |

Question 6 Explanation:

**Answer: Option D**

__Explanation:__

D = 110 + 170 = 280m

S = 60 * (5/18) = 50/3

T = 280 * (3/50) = 16.8sec

Question 7 |

A thief is noticed by a policeman from a distance of 200m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10km and 11km per hour respectively. What is the distance between them after 6mins?

100m | |

150m | |

190m | |

200m |

Question 7 Explanation:

**Answer: Option A**

__Explanation:__

Relative speed of the thief and policeman = (11 - 10)km/hr = 1km/hr

Distance Covered in 6mins = (1/60) * 6km = 1/10km=100m

Therefore, Distance between the thief and policeman = (200 - 100)m = 100m.

Question 8 |

How long will a boy take to run round a square field of side 35meter, if he runs at the rate of 9km/hr?

50sec | |

52sec | |

54sec | |

56sec |

Question 8 Explanation:

**Answer: Option D**

__Explanation:__

Speed = 9km/hr = 9 *(5 / 18)m/sec = (5/2)m/sec

Distance = (35 *4)m = 140m

Time taken = 140 * (2/5)sec = 56 sec

Question 9 |

The ratio between the speeds of two trains is 7:8. If the second train runs 400kms in 4hrs, then the speed of the first train is?

83.5km/hr | |

84.5 km/hr | |

86.5 km/hr | |

87.5 km/hr |

Question 9 Explanation:

**Answer: Option D**

__Explanation:__

Let the speeds of two trains be 7x and 8x km/hr

8x = 400/4

x = 12.5km/hr

So, Speed of first train is 12.5 * 7 = 87.5km/hr

Question 10 |

The number of degrees that the hour hand of a clock moves though between noon and 2.30 in the afternoon of the same day is.

720 | |

180 | |

75 | |

65 |

Question 10 Explanation:

**Answer: Option C**

__Explanation:__

The hour hand moves from pointing to 12 to pointing to half way between 2 and 3.

The angle covered between each hour marking on the clock is 360/12.

Since, the hand has covered 2.5 of these divisions the angle moved through is 75.

There are 10 questions to complete.