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CAT Exam  >  CAT Test  >  Quantitative Aptitude (Quant)  >  CAT Practice: Time, Speed and Distance - 1 - CAT MCQ

CAT Practice: Time, Speed and Distance - 1 - Free MCQ Test with solutions


MCQ Practice Test & Solutions: CAT Practice: Time, Speed and Distance - 1 (10 Questions)

You can prepare effectively for CAT Quantitative Aptitude (Quant) with this dedicated MCQ Practice Test (available with solutions) on the important topic of "CAT Practice: Time, Speed and Distance - 1". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 18 minutes
  • - Number of Questions: 10

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*Answer can only contain numeric values
CAT Practice: Time, Speed and Distance - 1 - Question 1
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An escalator is moving up. Rohit and his girlfriend walk up the moving escalator. Rohit has a walking speed one and half times that of his girlfriend. Rohit reaches the top after taking 40 steps, while his girlfriend does so after taking 30 steps. If the escalator is switched off, how many steps would Rohit take to walk up to the top?


Detailed Solution: Question 1

Let the walking speed of Rohit be 1.5x and that of his girlfriend be x. Let the speed of the escalator be S steps/unit time, and the number of steps on the escalator be N.
As per information provided for Rohit, we can say that N = (40/1.5x) * (1.5x+S) --(i)
As per information provided for Rohit's girlfriend, N = (30/x) * (x+S) --(ii)
Equating the two we get S = 3x
After Putting the value of S in equation 1 , we get 
Hence number of steps on the escalator is N = 120.

*Answer can only contain numeric values
CAT Practice: Time, Speed and Distance - 1 - Question 2
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A person travels from A to B and returns. He has two stops (C and D) to reach his destination and AC = CD = DB. In onward journey, his speed from A to C is 20 kmph, from C to D is 25 kmph, and from D to B is 10 kmph. While returning to A, his speed from B to D is 20 kmph; from D to C, he takes a different route which increases his driving distance by 10 km but allows him to drive at 40 kmph along his route; and from C to A, his speed is 25 kmph. If his return journey takes 3 minutes less than his onward journey, find the distance (in km) between A and B.


Detailed Solution: Question 2

Let the distance between A and B be 3x.
AC = CD = DB = x km
Time taken for going from A to C in onward journey = x/20
Time taken for going from C to D in onward journey = x/25
Time taken for going from D to B in onward journey = x/10
Time taken for going back from B to D in return journey = x/20
Time taken for going back from D to C in return journey = (x + 10)/40
Time taken for going back from C to A in return journey = x/25
It is given that he takes 3 minutes (1/20 hours) less in the return journey.
Hence, according to the question:

Thus, distance between A and B = 3x = 12 km

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CAT Practice: Time, Speed and Distance - 1 - Question 3
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An escalator moves at a constant rate from one floor up to the next floor. Jack walks up 29 steps while traveling on the escalator between the floors. Jill takes twice as long to travel between the floors and walks up only 11 steps. When it is stopped, how many steps does the escalator has between the two floors?


Detailed Solution: Question 3

Suppose that the escalator was two floors long, instead of just one, and that Jack and Jill start walking at the same time. Then Jack will reach the second floor at the same time Jill reaches the first floor (since it takes Jill twice as long to climb one floor). In that time,

Jack will have climbed 2(29)steps and Jill will have climbed 11 steps, so there will be

47 = 2(29) − 11 steps between them on the escalator.

These 47 steps represent the distance between two floors, or the length of the escalator.

*Answer can only contain numeric values
CAT Practice: Time, Speed and Distance - 1 - Question 4
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Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then the time, in seconds, needed to finish riding the escalator is


CAT Practice: Time, Speed and Distance - 1 - Question 5
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Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

Detailed Solution: Question 5

Let the speeds of Anil and Sunil be a and s respectively.

(a + s) × 1.5 = 45
⇒ a + s = 30     ... (i)

Let the time taken by Sunil after crossing = t hours.
So, time taken by Anil = (t + 5/4) hours.

So, the time taken by Anil = 1 + 5/4 = 9/4 hour
Total time taken by Anil = 3/2 + 9/4
= 15/4 hours

Hence, the speed of Anil = 45 ÷ (15/4) = 12

*Answer can only contain numeric values
CAT Practice: Time, Speed and Distance - 1 - Question 6
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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 (in minutes) taken by the fastest runner to finish the race?


Detailed Solution: Question 6

Let the speed of slower runner be x metre/min.
And the speed of faster runner be 2x metre/min.
Thus, for the first time when they meet, when slower runner will move by 1000 metres, faster runner will move by 2000 metres.
 = 5
x = 1000/5 = 200 m/min
Thus, time taken by faster runner to complete the race is:
 
= 10 minutes

CAT Practice: Time, Speed and Distance - 1 - Question 7
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Brishti went on an 8-hour trip in a car. Before the trip, the car had travelled a total of x km till then, where x is a whole number and is palindromic, i.e., x remains unchanged when its digits are reversed. At the end of the trip, the car had travelled a total of 26862 kms till then, this number again being palindromic. If Brishti never drove at more than 110 kmph, then the greatest possible average speed at which she drove during the rip, in kmph was?

Detailed Solution: Question 7

Total distance travelled at the end of the trip = 26,862.
This includes the distance which car had travelled before the trip and the distance it travels in the 8 hours of the trip.

To maximize speed in 8 hours, we need to maximize distance travelled in 8 hours.
∴ We need to minimize the distance travelled by car before the trip starts, hence we need to minimize x.

Since Brishti drove at less than 110 kmph, hence she must have travelled less than 110 × 8 = 880 kms in the last 8 hours.

∴ She must have travelled more than 26862 – 880 = 25,982 kms before the last 8 hours.
⇒ x > 25,982 and it has to be a palindrome.

Least palindrome greater than 25,982 is 26062.

∴ Car travelled at least 26062 kms before the trip, hence maximum distance travelled during the trip = 26862 – 26062 = 800 kms.

⇒ Maximum average speed for the trip = 800/8 = 100 kmph.

Hence, option (d).

CAT Practice: Time, Speed and Distance - 1 - Question 8
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Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all the three cross each other at the same time, is

Detailed Solution: Question 8

Speed of

Ravi = 40 × 5/18 = 100/9 m/s and

Ashok = 50 × 5/18 = 250/18 m/s

Time taken for them to meet 
⇒ Vijay and Ravi should also meet in 9 secs.

⇒ 9V - 100 = 54
⇒ 9V = 154
⇒ V = 154/9 m/s = 154/9 × 18/5 kmph = 61.6 kmph

CAT Practice: Time, Speed and Distance - 1 - Question 9
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A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is?

Detailed Solution: Question 9

Let the speeds of river, faster and slower boats be r, f and s km/hr respectively and distance between A and B be 12 kms.

For Faster boat:
⇒ f + r = 12/2 = 6   ...(1)
⇒ f - r = 12/3 = 4   ...(2)

(1) - (2)
⇒ 2r = 6 - 4 = 2
⇒ r = 1

For Slower boat:


⇒ s2 - 1 = 4s
⇒ s2 - 4s - 1 = 0
= 2 ± √5 = 2 + √5 [negative value of s is rejected]
Now, time taken by the slower boat to go from A to B

Hence, option (c).

CAT Practice: Time, Speed and Distance - 1 - Question 10
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Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X  is

Detailed Solution: Question 10

Let the time taken to meet after starting be t mins.

Time taken by A to reach Y after meeting = (10 – t) mins
Time taken by B to reach X after meeting = 9 mins

⇒ t2 = (10 - t) × 9

⇒ t2 +9t – 90 = 0

⇒ (t + 15)(t - 6) = 0

⇒ t = 6 (-15 is rejected)

Total time taken by B to reach Y = 6 + 9 = 15 mins.

Hence, option (b).

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This test contains 10 MCQs on CAT Practice: Time, Speed and Distance - 1 with detailed solutions for each question. It is part of the Quantitative Aptitude (Quant) course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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