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

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

Q23) Two men are walking towards each other alongside a railway track. A freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction. The train passes this man is 18 seconds. Assume the velocities are constant throughout. How long after the train has passed the second man will the two men meet?
A. 89.7 minutes
B. 90 minutes
C. 90.3 seconds
D. 91 seconds

Q24) A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
A. 5 : 6
B. 6 : 5
C. 8 : 3
D. 3 : 8

Q25) A boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes. How long will it take to go 5 km in stationary water?
A. 2 hr 30 min
B. 2 hr
C. 4 hr
D. 1 hr 15 min

Q26) A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
A. 1 km/hr.
B. 2 km/hr.
C. 1.5 km/hr.
D. 2.5 km/hr.

Q27) In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
A. 12 km/hr
B. 11 km/hr
C. 10 km/hr
D. 8 km/hr

Q28) A plane travelled a certain distance at a uniform speed. Had the speed been 216 kmph more, the journey would have taken one hour less and had the speed been 108 kmph less, the journey would have taken one hour more. Find the distance travelled by the plane.

Q29) 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.
If PQ = 100 km, then find the distance between the floating cork and A when A reaches Q.
a. 11 km
b. 12 km
c. 13 km
d. 14 km
e. None of these

Q30) Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

Q31) Anwar leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Anwar, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Anwar is 30 km\hr, find the speed of his son.