Question Bank - 100 CAT level questions on Time, Speed and Distance topic


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    Q83) Ram Kumar, an overworked executive in Delhi, has to decide on the travel plan for attending his friend’s marriage in Ajmer, Rajasthan. Barely managing to get leave from his boss, he has to make sure that he reaches at least on the day of the marriage. Since it has been quite some time since he got a break, he also planned to visit a few tourist spots so that he could de-stress himself after a year of demanding executive work-life. As per his plan, Ram would start from Delhi. He would first pay a visit to Bharatpur bird sanctuary where he would stay in the forest guest house for sometime. After that he planned to visit Jodhpur and would do some sightseeing for a day or two. From Jodhpur, he would travel to Jaipur and spend few days visiting different places in the city. After that he would make a move towards Ajmer where his friend’s marriage would take place. Bharatpur can be reached from Delhi by bus, taxi or train. The probabilities of reaching the destination on time by each mode of travel, Ram reasoned based on his experience of travelling extensively in India, were 0.65, 0.75 and 0.9 respectively. All three modes of travel require 12 hours. From Bharatpur to Jodhpur he could opt for travel by train, bus or private taxi with the corresponding probabilities of 0.9, 0.8 and 0.85. The travel time, he reasoned, would be 12 hours by train, 16 hours by bus and 14 hours by taxi. Jaipur can be reached from Jodhpur by either by a flight, train, bus or taxi with the corresponding probabilities of reaching on time 0.85, 0.9, 0.65 and 0.7 respectively. The flight would take 2 hours, while the train would entail 10 hours; the travel by bus and taxi would take the same time of 15 hours. The last leg of the journey to Ajmer could be covered by train, bus or taxi with respective probabilities of 0.75, 0.55 and 0.55. Bus and taxi require 5 hours to reach Ajmer from Jodhpur while the train takes an hour less. Since both Jaipur and Jodhpur had the facility of airports, he could travel directly to either of these places by taking a flight from Delhi,or use the flight option mid-way along with a combination of land transport.

    1. The second best option (in terms of travel time) gives a total travel time of ________ hours for the entire itinerary.
      a. 29
      b. 30
      c. 31
      d. 32
      e. 33

    2. Due to winter fog, flights out of Delhi have become uncertain and unreliable. Given this constraint,the itinerary Ram should adopt to have the best probability of reaching Ajmer on time is:
      a. Delhi-Bharatpur by train; Bharatpur to Jodhpur by taxi, Jodhpur to Jaipur by bus;
      Jaipur to Ajmer by train
      b. Delhi-Bharatpur by Taxi; Bharatpur to Jodhpur by train, Jodhpur to Jaipur by
      flight; Jaipur to Ajmer by train.
      c. Delhi-Bharatpur by train; Bharatpur to Jodhpur by train, Jodhpur to Jaipur by
      train; Jaipur to Ajmer by train
      d. Delhi-Bharatpur by train; Bharatpur to Jodhpur by taxi, Jodhpur to Jaipur by
      train; Jaipur to Ajmer by train
      e. Delhi-Bharatpur by train; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
      flight; Jaipur to Ajmer by train

    3. Ram’s younger brother Shyam gets to know of Ram’s travel plans and wants to come along. As against his brother, Shyam enjoys scenery enroute and wants Ram to maximize the travel time. To do so, the itinerary that Ram should decide upon is:
      I. Delhi-Bharatpur by train; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
      bus; Jaipur to Ajmer by bus
      II. Delhi-Bharatpur by bus; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
      taxi; Jaipur to Ajmer by taxi
      III. Delhi-Bharatpur by bus; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
      bus; Jaipur to Ajmer by bus
      IV. Delhi-Bharatpur by taxi; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
      taxi; Jaipur to Ajmer by bus
      V. Delhi-Bharatpur by taxi; Bharatpur to Jodhpur by taxi, Jodhpur to Jaipur by
      taxi; Jaipur to Ajmer by taxi
      a. I
      b. I, II
      c. I, II and III
      d. I, II, III and IV
      e. I, II, III, IV and V


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    Q84) A farmer leaves his home at 8 a.m. and heads towards the village temple. His target is to reach the temple at 12 noon. His speed decreases by 20% (of the original speed at the beginning of his journey) for every hour travelled by him and then remains constant for the next 1 hour. At the end of three hours, he has travelled only 70% of the distance. By what percent should he increase his speed for the last one hour (as compared to his third hour speed), so that he reaches the village temple in time?
    a) 49.33
    b) 49.34
    c) 71.41
    d) 71.42
    e) 71.44


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    Q85) Arjun is traveling from Andheri to Dadar by car and Bharat is traveling from Dadar to Andheri by bike (on the same road). Speed of Arjun and Bharat is 60 kmph and 15 kmph. Arjun and Bharat meet at Bandra, somewhere between Andheri and Dadar. After reaching Dadar Arjun takes a rest of 1 hour and then returns to Andheri. The total time taken by Arjun to travel from Andheri to Dadar and then from Dadar to Andheri (including the halt) is 10 minutes more than the time required by Bharat to travel from Bandra to Andheri. What could be the distance between Andheri and Dadar? [Note: Speed of Arjun's car and Bharat's Bike is constant throught the journey]
    a) 20 km
    b) 10 km
    c) 12.5 km
    d) 30 km
    e) 15 km


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    Q86) The speed of three cars in the ratio 2:3:4. the ratio between the times taken by these cars to travel the same distance is
    a) 2:3:4
    b) 4:3:2
    c) 4:3:6
    d) 6:4:3


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    Q87) A car travels a distance of 170 km in 2 hours, partly at 100 km/hr and partly at 50 km/hr. Find the distance travelléd at 50 km/hr.
    a) 140 km
    b) 50 km
    c) 40 km
    d) None of these


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    Q88) A person is standing in the middle of the platform of length 300m.Two trains 'B' and 'C' of length 120 m and 250m running with a speed 54kmph and 72 kmph respectively enter platform from opposite ends at the same time on parallel tracks. How much length of the train C does the Person A see while it passes him if the train 'B' comes in between 'A' and 'C' to block the view?
    a. 60m
    b. 50m
    c. 90m
    d. 80m


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    Q89) A tortoise can complete a full round on a circular track in 8 min, while a rabbit can do the same on the circular track in 5 minutes. If the tortoise has a 5 minute lead, when would they meet for the first time at the Starting Point, given that both of them have started from the same point in the same direction.


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    Q90) A ran for a certain distance around a circular track and found that he had run exactly half a round more than an intefral number of rounds around the track,he also figures that if he runs 11 times the earlier distance on the same track,he would fall short of exactly 100m for completing an integral number of rounds around the track.Find the length of the track?


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    Q91) A man completes a journey in 20 hours. He travels half of the journey’s distance at the rate of 84 km/hr and the other half of the journey’s distance at the rate of 96 km/hr. Find the total distance that the man covered during the journey?


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    Q92) Four people A, B, C, and D are running around a circular ground in a 432 km race of 2 laps. Initially they all are separated by 1/4th of the circumference of the ground and their speeds are 10 m/s, 20 m/s, 30 m/s and 40 m/s respectively. After every hour they all exchange their speeds such that A takes B's speed, B takes D's speed, C takes A's speed and D takes C's speed. Find the time taken by the winner to finish the race.


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    Q93) A railway track runs parallel to a road and a cyclist whose speed is 12kmph meets a trains at the crossing,same time everyday. One day cyclist started 25min late and met the train 6km ahead of the crossing. What is the speed of the train?
    a. 60
    b. 72
    c. 90
    d. 84


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    Q94) Rohan, Shikha’s boyfriend, had to pick her from her home for a live concert on her 23rd birthday. The venue of the concert and Shikha’s home were in opposite directions from Rohan’s office. He got late because of some work at office and realised that if he goes to pick Shikha from her home, which was a 48-minute drive from his office, they would be late for the show by 16 minutes. He asked her to start from her home towards his office in an auto-rickshaw and himself started driving towards her home. Both of them started simultaneously, he picked her as soon as they met and they managed to reach the venue just in time for the concert. If Rohan drives at an average speed of 60 km/hr, find the speed (in km/hr) of the auto-rickshaw.


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    Q95) A starts from Bombay to Delhi. After a while he realizes he would cover 3/4 th of the distance in scheduled time and hence doubles his speed and reaches on time. He would have been late by 3 hours if he didn't change the speed. So after how much time from the start he changes the speed ?


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    Q96) Two motorists leave from opposite ends of a road at the same time and travel at constant but different speeds. They pass each other 700 meters from one end and continue to the other end of the road, where they turn around. On their return trip the motorists pass again—this time 400 meters from the opposite end of the road. How wide is the road?


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    Q97) Two guns were fired from the same place at an interval of 12min;but a person in the train approaching the place hears the second shot 10 min after the first. The speed of the train, if speed of sound is 330m/s


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    Q98) P and U stay next to each other and study in the same school. P and U start walking towards their school at the speed of 2km/hr and 3 km /hr respectively. The faster of the two reaches the school first and turns around and starts walking back. If P and U meet 200m away from the home, what is the distance between their residence and the school?
    a) 260m
    b) 240m
    c) 200m
    d) 250m


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    Q99) A bird is sitting on a train A moving at a Speed of 40 kmph. It sees another train B at a Distance of 200 ms with Speed of 60 kmph coming from the opposite direction on the same rail track. It flies with an average Speed of 10kmph and sits on another train. Again immediately it flies back to the first train and again to the second train and so on. It does so before the two trains crash. What is the total Distance traveled by the bird?


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    Q100) Rishi Kapoor can swim a certain course against the river flow in 84 minutes; he can swim the same course with the river flow in 9 minutes less than he can swim in still water. How long would he take to swim the course with the river flow?


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    total steps be T
    T/N -T/(N+4) =6
    3N^2+12N-2T=0 N=-12+rt (144+24T) /6 --(1)
    and T/(G-4)-T/G = 6
    3G^2 -12G-2T=0
    G= 12+rt (144+24T) /6 ---(2)
    relative speed = N+G
    so T= 4N+4G --(3)
    using 1 and 2,
    T = 4 * rt (144+24T)/3
    9T^2 = 16 (144+24T)
    9T^2 - 384T-2304 = 0
    T = (384 + 480)/18 = 48 steps


  • BITS Pilani | CAT 2016 - 99.93 percentile in Quant


    P's distance be Y, Q's be X
    Y/50 = (X-50)/25
    Y=2X-100
    say Y=100, X=100
    distance at any time=d
    d^2 = (100-50t)^2 + (100-25t)^2
    diff wrt t for minima
    (100-50t)*2 +(100-25t) = 0
    t=12/5
    d^2 = 20^2 + 40^2 = 2000 so d= 20 rt 5


 

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