Time Speed Distance CAT Questions

Time Speed and Distance Questions PDF consists of the Important Time, Speed and Distance problems and concepts to solve them. This Time and Work CAT questions and answers PDF will be very helpful for Quantitative aptitude section of CAT.

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Question 1:

Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide.

A. 1/12

B. 1/6

C. 1/4

D. 1/3

Question 2:

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what sped must he cycle to get there at noon?

A. 11 km/hr

B. 12 km/hr

C. 13 km/hr

D. 14 km/hr

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Question 3:

Karan and Arjun run a 100-meter race, where Karan beats Arjun 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

A. Karan and Arjun reach the finishing line simultaneously.

B. Arjun beats Karan by 1 metre

C. Arjun beats Karan by 11 metres.

D. Karan beats Arjun by 1 metre.

Question 4:

A sprinter starts running on a circular path of radius r metres. Her average speed (in metres/minute) is πr during the first 30 seconds, π r/2 during next one minute, π r/4 during next 2 minutes, π r/8 during next 4 minutes, and so on. What is the ratio of the time taken for the nth round to that for the previous round?

A. 4

B. 8

C. 16

D. 32

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Question 5:

In a 4000 meter race around a circular stadium having a circumference of 1000 meters, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

A. 20 min

B. 15 min

C. 10 min

D. 5 min

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Answers and Solutions for Time Speed Distance CAT Problems:

Answer 1:

The relative speed is 15 km/hr = 15 km/60 min = 0.25 km/min = 250 m/min.
Therefore, one minute before they collide, they are at a distance of 250m.

Answer 2:

Let the distance to be travelled be D.

In the first case, D/10 = t

In the second case, D/15 = t-2

=> D/15 = D/10 – 2

=> 2D = 3D – 60

=> D = 60 km and T = 6 hours

Therefore, to get there at noon, he has to travel at 60/5 = 12 km/hr

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Answer 3:

The speeds of Karan and Arjun are in the ratio 10:9. Let the speeds be 10s and 9s.
Time taken by Karan to cover 110 m = 110/10s = 11/s
Time taken by Arjun to cover 100 m = 100/9s = 11.11/s
Therefore, Karan reaches the finish line before Arjun. From the options, the only possible answer is d).

Answer 4:

Let radius be 1 units and p = 3.14 or π. So circumference is 2∗π

According to given condition distance covered in first 1/2 mins = π/2 km, distance covered in next 1 min = π/2 km, distance covered in next 2 mins = π/2 km and finally distance covered in next 4 minutes = π/2 km.

Time taken to cover first round = 1/2 + 1 + 2 + 4 = 7.5 minutes.

Now time taken to cover π/2 is in GP.

For the second round the time taken is = 8+16+32+64 = 120

Ratio = 120/7.5 = 16

Answer 5:

Let A , B and f,s be the distance traveled and speed of the fastest and the slowest person respectively. Also f=2s so in the given time A=2B. Since the ration of the speeds is 2:1, they will meet at 2-1 points = 1 pont.

Both meet each other for first time at starting point . let b travel distance equal to 1 circumference i.e. 1000m so A=2000m . Both meet after 5 min so speed of slowest is 1000/5=200m/min . So speed of the fastest is 400m/min. So time taken by A to complete race 4000/400 = 10 min.

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