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

Q3) Three boys A, B and C start running at constant speeds from the same point P along the circumference of a circular track. The speeds of A, B and C are in the ratio 5:1:1. A and B run clockwise while C runs in the anticlockwise direction. Each time A meets B or C on the track he gives them a card. What is the difference in the number of cards received by B and C if A distributes 33 cards in all?
(a) 3
(b) 7
(c) 5
(d) 11

Q4) A bike running at 80 km/h initially is slowed down to 60 km/h as soon as the fuel indicator touches the half level mark. It keeps running at this speed till it runs out of fuel, thereby covering a total distance of 640 km in 10 hours. If the bike consumes 2 litres of fuel per hour, what is the capacity (in litres) of the fuel tank of the bike?

Q5) P and Q are two points on a river, and the direction of current is from P to Q. A motorboat goes from P to Q in 4 hours and comes back to P in 6 hours. Had the motorboat started at its usual speed and increased its speed at the beginning of each subsequent hours, starting from the second hour, by 40% of its starting speed, how long would the motorboat have taken to travel from P to Q?
a. 3 hours
b. 3.5 hours
c. 2.5 hours
d. Cannot be determined

Q6) A goods train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 s, whereas a passenger on the passenger train observes that he crosses the goods train in 40 s. If the speeds of the goods train and passanger train are in the ratio 1 : 2, then the ratio of the lengths of the goods train and that of the passenger train is
a. 1 : 3
b. 2 : 3
c. 4 : 3
d. 2 : 1

Q7) Lucknow Mail, which runs between Lucknow and Delhi, leaves Lucknow at 8.30 a.m. and travels at 80 km/hr towards Mathura situated 300 km away from Lucknow. Satabdi Express, runs between Lucknow and Delhi, leaves Lucknow at 9.00 a.m. and travels at 100 km/hr. Just when Satabdi crosses Lucknow Mail, Prayagraj Express travelling at 50 km/hr leaves Mathura towards Lucknow. When will Prayagraj Express meet Satabdi Express?
a. 11.50 a.m.
b. 11.40 a.m.
c. 11.00 a.m.
d. none

Q8) Mr. Perumal decided to walk down the escalator of a tube station. He found that if he walks 26 steps, he requires 30 s to reach the bottom. However, if he walks 34 steps he would only require 18 s to reach to the bottom. If the escalator is moving downwards, find the number of steps in the escalator.
a. 42
b. 46
c. 56
d. 58

Q9) Vijay went from A to B at a certain speed and came back to A from B at a speed that was 12 times the speed at which he went from A to B. The entire journey took 9 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?

Q10) A junction of two highways is patrolled by two cars, one on each road. Each car covers a distance of 5 km on either side of the junction on its road. If the speeds of the 2 cars are 50 km/hr and 75 km/hr and they start from the junction at 6 a.m. from the same point, when will they meet next time?
a. 6 : 16 a.m.
b. 6 : 24 a.m.
c. 6 : 30 a.m.
d. 6 : 48 a.m.

Q11) A swimmer started swimming from Baghbazar Ghat towards Ahiritola Ghat against the stream. At Ahiritola Ghat he saw a floating log. He continued swimming, in the same direction as before,till Howrah Ghat and after reaching there, he immediately turned and started swimming back. Coincidentally the log and the swimmer both reached Baghbazar Ghat at the same time. If Howrah Ghat is 20 km away from the Ahiritola Ghat and the swimmer took thrice the time for ongoing journey that he took while coming back, then what is the distance between Baghbazar Ghat and Ahiritola Ghat?
a. 60 km
b. 20 km
c. 10 km
d. 40 km

Q12) Two friends – Prakash and Arpit – started running simultaneously from a point P in the same direction along a straight running track. The ratio of the speeds of Prakash and Arpit was 2 : 5 respectively. Two hours later, Arpit turned back and started running backwards at onefifth of his original speed. He met Prakash at a distance of 10 km from the point P. What was Prakash’s running speed?
a. 1.25 km/hr
b. 2.5 km/hr
c. 3.75 km/hr
d. 6.25 km/hr

Q13) An escalator is moving downwards at a speed of 4 steps/minute. Neerja takes 6 minutes less to reach the bottom from the top of the escalator, if he comes down on the moving escalator, as compared to when he does so on the stationary escalator. Gia takes 6 more min to reach the top from the bottom of the escalator if he goes up on the escalator moving downward as compared to when he does so on the stationary escalator. They start simultaneously from the top and the bottom of the escalator, moving downward, respectively and meet after 4 minutes. How many steps are there in the escalator?
a. 60
b. 56
c. 48
d. Cannot be determined

Q14) Neha wants to visit Nitin’s house, hence she calls up Nitin and asks him to come to her residence and pick her up. Nitin asks her to leave immediately and start walking towards his house. At the same time he also leaves by car, meets Neha on the way, picks her up and drives back to his house, thereby taking a total of 30 mins. Had Nitin driven all the way to pick Neha from her home, he would have taken a total of 40 mins. What is the ratio of speed at which Neha walks to the speed at which Nitin drives the car?
a. 1 : 4
b. 1 : 5
c. 1 : 3
d. 2 : 3

Q15) Three motorcycles started simultaneously from point P to point Q along the same highway. The second motorcycle travelled at a speed of 30 km/hr higher than that of the first motorcycle and arrived at Q 3 hr earlier than the first motorcycle. The third motorcycle arrived at Q 2 hr earlier than the first motorcycle, travelling half the time with the speed of the first motorcycle and the other half at the speed of the second motorcycle. The distance between P and Q is
a. 120 km
b. 150 km
c. 180 km
d. 210 km

Q16) A and B started walking, at the same time, from the top of an escalator, which was coming down, and reached the bottom end. The ratio of the speeds of A and B is 2 : 1. A took 60 steps while B took 40 to get off the escalator. Find the number of steps in the escalator when it is stationary.

Q17) Two runners A and B started running simultaneously from points P and Q for Q and P respectively. They met at a point, S, and after that they took 18/5 min and 10 min respectively to reach their respective destinations. After how much time, from the start, did they meet each other at point S?
a. 6.4 min
b. 3.2 min
c. 6 min
d. 3 min

Q18) Santosh was walking to and fro on a railway platform. He was walking at a uniform speed of 4 km/ hr in a straight path and he reverses his direction of motion at the end of fourth, seventh, ninth and thirteenth minutes, how far will he be from the starting point at the end of the tenth minute?
a. 2/15 km
b. 3/15 km
c. 4/15 km
d. 0 km

Q19) Two persons – A and B – start running simultaneously around a circular track – with speeds 4 m/sec and 12 m/sec respectively. What is the minimum number of rounds that A has to make in order to meet B once at the starting point?
a. 1
b. 12
c. 3
d. 4

Q20) Two cyclists are travelling at 3 km/hr and 10 km/hr around a circular track. What should be the ratio of number of distinct points that they would meet on that track if they first travel 10 rounds in same direction and then 10 rounds in opposite direction?
a. 7 : 13
b. 3 : 10
c. 3 : 7
d. 30 : 13

Q21) Two cars P and Q are moving at uniform speeds, 50 km/hr and 25 km/hr respectively, on two straight roads intersecting at right angle to each other. P passes the intersecting point of the roads when Q has still to travel 50 km to reach it. What is the shortest distance between the cars during the journey?
a. 20√5 km
b. 50 km
c. 25 km
d. 25√2 km

Q22) 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?
a. 6 hour
b. 4.5 hour
c. 4.2 hour
d. 3.6 hour