CAT Question Bank  Time, Speed & Distance

Q3) A man jogging inside a railway tunnel at a constant speed hears a train approaching the tunnel from behind at a speed of 30 km/h, when he is one third of the way inside the tunnel. Whether he keeps running forward or turns back, he will reach the end of the tunnel at the same time the train reaches that end. The speed at which the man is running is

Q4) Rohan and Sohan start simultaneously from a point A on a circular track and run in the same direction. The speed of Rohan is 9 times the speed of Sohan. How many times are they diametrically opposite to each other by the time Sohan completes 3 complete rounds on the track?

Q5) Everyday father arrives at the school at 5:00 PM by car to pick up his son. Today his car engine fails so he stops to repair. At 5:10 PM, his son begin to walk to the home. On the way, son meets with his father and get on the incoming repaired car. They arrive home 30 minutes later than the usual time. The ratio of car speed to walking speed is 6:1. How many minutes are used to repair the car on the way?

Q6) A man's speed is 15km/hr. His speed increases by 0.5 km/hr after every 2 min. How much time he would take to travel 375 km?

Q7) Raj started from his house towards his friend Brij’s house, 24 km away. After sometime, Brij also started
moving towards Raj’s house, traveling at one and a half times the speed of Raj. If when they met, the duration
for which Raj had traveled was three times that for which Brij had traveled, at what distance from Brij’s house
did they meet?

Q8) Two trains travelling on the same track, in opposite directions, are separated from each other by a distance of 100 km. One train travels from Bombay to Thane at a speed of 25 kmph and the second train travels from Thane to Bombay at a speed of 15 kmph. At this moment, a crow starts from the first train and flies along the track to the second train, at a speed of 50 kmph, and then flies back to the first train. It repeats this process continually till the two trains collide head on. What is the total distance travelled by the crow in direction of the first train n in the direction of the 2nd second train?

Q9) A train has to travel the distance between Aurangabad and Daulatabad, equal to 20 km, at a constant speed. It travelled half the way with the specified speed and stopped for three minutes, to arrive at Daulatabad on time, it had to increase its speed by 10 km/h for the rest of the way. Next time the train stopped halfway for five minute. By what speed must it increase its speed for the remaining half of the distance to arrive at Daulatabad as per the schedule.

Q10) A is planning to attend the marriage of B.He starts at a specific speed and time so as to be there at the wedding at the exact time. A was driving exactly for 1 hr when he had a flat tyre. He changed the tyre in exactly 10 minutes.He started driving the remaining distance at a speed of 30km/hr. Consequently he was late for wedding by 30 min. If the puncture had happened 20km later he would be late for the wedding by only 20 min. Total distance travelled by A in km
a) 60
b) 70
c) 100
d) 80

Q11) P starts from Delhi to Pune. 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 ?

Q12) Shyam went from Delhi to Shimla via Chandigarh by car. The distance from Delhi to Chandigarh is 3/4 times the distance from Chandigarh to Shimla. The average speed from Delhi to Chandigarh was half as much again as that from Chandigarh to Shimla. If the average speed for the entire journey was 49 kmph. What was the average speed from Chandigarh to Shimla?
(a) 39.2 kmph
(b) 63 kmph
(c) 42 kmph
(d) None of thes

Q13) Two vehicles A and B start from the same point at the same time but move in opposite directions along a circular track of radius 14 km .The initial speed of A is thrice that of B. Every time they meet , they reverse their directions and exchange their speeds. Find the shortest distance between their starting point and third meeting point.

Q14) Vinay fires two bullets from the same place at an interval of 12 minutes but raju sitting in a train approaching the place hears the second report 11 minutes 30 seconds after the first. What is the speed of train in which raju is sitting? (Speed of sound 330 meters per second)

Q15) A road passes through the town of sangamner and yeotmal. A cyclist started from sangamner in the direction of yeotmal. At the same time, two pedestrians started from yeotmal travelling at the same speed, the first of them towards sangamner and the other in the opposite direction. The cyclist covered the distance between the two towns in half and hour and continued ahead in the same direction. He over took the second pedestrian, 1.2 hours after he met the first pedestrian. Find the time the cyclist spends travelling from sangamner to the point of meeting with the first pedestrian?

Q16) Karan and Arjun run a 100metre race, where Karan beats Arjun by 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.

Q17) Two cyclists start simultaneously towards each other from Aurangabad and Ellora, Which are 28 km part, An hour later they meet and keep pedalling with the same speed without stopping. The second cyclist arrives at Ellora 35 minutes later the first arrives at Aurangabad. Find the speed of the cyclist who started from Ellora.

Q18) A bus covers a journey at an average speed of 90 km/h. If the time for which the bus stops during the journey is excluded, then the average speed for the journey becomes 108 km/h. For how much time, on an average, does the bus stop every hour?
(a) 12 minutes
(b) 10 minutes
(c) 15 minutes
(d) 7.5 minutes

Q19) Arif, Bill and Chetan were classmates and wanted to watch a movie at South City Mall right after their
class got over. Bill had an Activa bike which could accommodate a rnaximurn of two persons at a time and they wanted to reach the mall in the minimum time possible. They started simultaneously from their college, Bill and Arif on the bike and Chetan on foot. Bill dropped Arif at a certain point along the route to the mall, turned back and on his way met Chetan. He picked up Chetan and then traveled towards the mal! such that all three of them reached the mall simultaneously. Whai is the total time (in minutes) taken by them to reach the mall from their college, if the speed of the bike was 30 krn/hr, the walking speed of each of them was 6 km/hr and the distance between their college and the mall was 22.5.

Q20) Sachin and Sunil started with a speed of 40 km/hr and 18 km/hr respectively on their bikes for Patna at 8 a.m. from the same place. Sunil completed the entire journey with the same speed with which he had started. At 9:30 a.m., Sachin was stuck in traffic and had to reduce his speed. So in the next 30 minutes, he could cover only 15 km and covered the remaining distance with a speed equal in magnitude to the total time taken by Sunil in hours to cover the entire journey and reached Patna at the same time as Sunil and in broad daylight. At what time did both of them reach Patna?

Q21) Vijay went from A to B at a certain speed and came back to A from B at a speed that was 4 times the speed at which he went from A to B. The entire journey took 3 hr. Had Vijay come back at a speed that was only half the speed at which he actually returned, how long would it have taken him for the entire journey?

Q22) Two motorcyclst 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 kmph and 19 kmph resp. Every time ajay overtakes vijay (anywhere on track); both of them decrease there speed by 1kmph. If the length of the track is 1 Km. How many times do they meet at the starting point before vijay comes to rest?