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

Q71) Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyoms steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
a. 40
b. 50
c. 60
d. 80

Q72) Ram and Shyam started simultaneously from the same point on a circular track 1800m long in opposite directions with speeds of 6m/sec and 12 m/sec respectively .after every crossing they exchanged their speeds and continued to travel in the same direction .find the distance between them (measured along the track) when ram completes 3.5 rounds
a) 600m
b) 450m
c) 750m
d) 300m

Q73) Rajat started walking from point A to point B and Manoj started walking from point B to point A, both at 6 a.m. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then, both continued their journey. Since they had just had their breakfast, their speeds reduced to half of their initial speeds. After 1 hour, Manoj realised that their keys got exchanged, so he started running towards Rajat at two and a half times his present speed. If the ratio of Rajat’s and Manoj’s initial speeds was 3:2, at what time would Manoj meet Rajat?

Q74) A and B start swimming simultaneously from two points P and Q respectively, on a river towards each other. A crosses a floating cork at a point S and B crosses the floating cork at a point T which is at a distance of 8 km from point S. A and B cross each other at a distance of 2 km from T. It is given that the direction of flow of the river is from P to Q and in still water, the ratio of speeds of A and B is 3 : 1. P, S, T and Q ( in that order) are on the same straight line and assume that A, B and the floating cork move along that line.Find the ratio of the upstream speed of A to the downstream speed of B.
a) 9:7
b) 6:5
c) 5:4
d) Cannot be determined

Q75) A and B start swimming simultaneously from two points P and Q respectively, on a river towards each other. A crosses a floating cork at a point S and B crosses the floating cork at a point T which is at a distance of 8 km from point S. A and B cross each other at a distance of 2 km from T. It is given that the direction of flow of the river is from P to Q and in still water, the ratio of speeds of A and B is 3 : 1. P, S, T and Q ( in that order) are on the same straight line and assume that A, B and the floating cork move along that line.Find the ratio of the upstream speed of A to the downstream speed of B.
a) 9:7
b) 6:5
c) 5:4
d) Cannot be determined

Q76) DESISpiderman has to chase a gang of robbers riding on a car after looting a nearby bank . Spiderman is having coffee at a distance 36 kms south of the car initially when his spider senses give him an inkling. So he heads for the car immediately at a velocity of 50 km/hr as soon as the car also starts at a velocity of 40 km/hr. The gangsters drive the car towards the east with 40 km/hr. Spiderman keeps moving towards the car following his inkling. (i.e. the direction of Spiderman keeps changing and he keeps following the shortest path to the car.) The time in hours after which Spiderman reaches upto car and gives gangster the treatment is
(1) 1.5
(2) 2
(3) 2.5
(4) 3
(5) none of these

Q77) Bus A leaves the terminus every 20 minutes, it travels a distance 1 km to a circular road of length 10 km and goes clockwise around the road, and then back along the same road to the terminus (a total distance of 12 km). The journey takes 20 minutes and the bus travels at constant speed. Having reached the terminus it immediately repeats the journey. Bus B does the same except that it leaves the terminus 10 minutes after Bus A and travels the opposite way round the circular road. The time taken to pick up or set down passengers is negligible. A man wants to catch a bus a distance 0 < x < 12 km from the terminus (along the route of Bus A). Let f(x) the maximum time his journey can take. The value of x for which f(x) is a maximum is
(1) 3
(2) 5
(3) 8
(4) 10
(5) none

Q78) Three friends, Raghu, Amit and Ninad are cycling around a circular track of length 1.2 km at different speeds. They start from the same place at the same time and Raghu and Amit reverse their directions every time they meet. Raghu meets Amit and Ninad for the first time after 40 seconds and 56 seconds respectively while Amit and Ninad meet for the first time after 30 seconds. What is the ratio of speeds of Raghu, Ninad and Amit?

Q79) A and B run around a circular track starting at the same point simultaneously and in the same direction. A runs at 30m/s. It is known that the speed of B is positive integer and is not more than 50m/s. If A and B meet at exactly 4 points including the starting point on the circular track and if they run forever , how many different values can the speed of B take ?

Q80) A file of soldiers two – kilometer long is walking one behind the other at a uniform speed. An inspecting officer starts at the rear, moves forward till he reaches the front. Then he starts back with the same speed till he reaches the last man at the rear. When he gets to the last man, the last man has reached exactly the spot where the man at the front was when the officer started his inspection. What is the total distance travelled by the officer in this whole operation?
a) 4.24km
b) 4.42km
c) 4.62km
d) 4.82km

Q81) A man travels 51 km in 61 minutes and 30 seconds with a usual speed of 50km hr There are some speed breakers on the road Each speed breaker reduces his speed to 80% of his usual speed for a distance of 50m about the speed breaker Find the number of speed breakers that he crossed
a. 20
b. 25
c. 30
d. 35

Q82) Two motorcyclists, Ajay and Vijay, start simultaneously from a point S on an oval track and drive around the track in the same direction, with speeds of 29 km/hr and 19 km/hr respectively. Every time Ajay overtakes Vijay (anywhere on the track), both of them decrease their respective speeds by 1 km/hr. If the length of the track is 1 km, how many times do they meet at the starting point before Vijay comes to rest

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 destress himself after a year of demanding executive worklife. 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 midway along with a combination of land transport.
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. 33Due 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. DelhiBharatpur by train; Bharatpur to Jodhpur by taxi, Jodhpur to Jaipur by bus;
Jaipur to Ajmer by train
b. DelhiBharatpur by Taxi; Bharatpur to Jodhpur by train, Jodhpur to Jaipur by
flight; Jaipur to Ajmer by train.
c. DelhiBharatpur by train; Bharatpur to Jodhpur by train, Jodhpur to Jaipur by
train; Jaipur to Ajmer by train
d. DelhiBharatpur by train; Bharatpur to Jodhpur by taxi, Jodhpur to Jaipur by
train; Jaipur to Ajmer by train
e. DelhiBharatpur by train; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
flight; Jaipur to Ajmer by trainRam’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. DelhiBharatpur by train; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
bus; Jaipur to Ajmer by bus
II. DelhiBharatpur by bus; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
taxi; Jaipur to Ajmer by taxi
III. DelhiBharatpur by bus; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
bus; Jaipur to Ajmer by bus
IV. DelhiBharatpur by taxi; Bharatpur to Jodhpur by bus, Jodhpur to Jaipur by
taxi; Jaipur to Ajmer by bus
V. DelhiBharatpur 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

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

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

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

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

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

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.

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?