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

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.

Q32) A train leaves a point A at 5 p.m. and reaches another point B a 11 p.m. Another train leaves point B at 7 p.m. and reaches point A at 10 p.m. At what time will the two trains meet?

Q33) Sameer and Sumer started running from the same point in opposite directions on a circular track of length 120 m. Their speeds are 20 m/s and 40 m/s respectively. After every second, Sameer increases his speed by 2 m/s whereas Sumer decreases his speed by 2 m/s. How many times would they have met on the track by the time Sumer comes to rest?

Q34) Three athletes A, B and C run a race, B finished 24 meters ahead of C and 36 m ahead of A, while C finished 16 m ahead of A. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race?

Q35) In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
A. 60 m
B. 40 m
C. 20 m
D. 10 m

Q36) A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is:
A. 5.15 kmph
B. 4.14 kmph
C. 4.25 kmph
D. 4.4 kmph

Q37) In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:
A. 18 m
B. 20 m
C. 27 m
D. 9 m

Q38) A and B started running from the same point and in opposite directions around a circular track of radius 24.5 m. A’s speed was twice that of B’s speed. They met each other aиer 14 seconds. What was A’s speed?

Q39) Every morning Ravi and Beena start walking from A and B respectively towards each other. They meet at C. Ravi always starts at 5:30 am and Beena starts at 4:45 am. Ravi's speed is 6 km/hr whereas Beena's speed is 5 km/hr.
One fine morning, Beena started late by a few minutes and hence, met Ravi who started on time at D in between CB. CD=2.5 km. By how many minutes was Beena late in starting on that day?
a)25 min
b)30 min
c)55 min
d)Data InsufficientOne morning, ravi got late but Beena was on time and that day the 2 met at 7:00 am at E which was 2.5 km from C. What is the distance between Aand B?
a) 20.25 km
b) 17.25 km
c) 14.75 km
d) Data Insufficient

Q40) Two trains left from two stations P and Q towards station Q and station P respectively. 3 hours after they met, they were 675 Km apart. First train arrived at its destination 16 hours after their meeting and the second train arrived at its destination 25 hours after their meeting. How long did it take the first train to make the whole trip?
a) 18h
b) 36h
c) 25h
d) 48h

Q41) A man is running on a circular track with uniform speed and a source of light is placed on the ground at the centre of the circular track. The shadow of a man appears on a wall tangential to the circular track at the point of start. The height of the shadow was found to be twice the height of the man 30 min after the man had started running. It was found that the man was yet to complete one round of the circle. The time (hrs) taken by the man to complete 10 rounds is
A. 6
B. 30
C. Either (a) or (b)
D. 60

Q42) At 10:00 AM, A and B are moving in the same direction on a linear track with B 50km ahead of A. At 11:15 AM, A catches up with B and from then on A and B move at the same speed to reach their destination 150km away. If the average speed of A is 40 km/hr during the whole journey, then find the distance (in km) between A and B at 10:45 AM?
A. 20
B. 30
C. 15
D. 40

Q43) Two persons A and B start running from the opposite points of a linear track P and Q. A and B reach Q and P respectively after 25 s and 36 s from the instance they meet each other at the track. Find the time taken by A to comple one round of the track from P to Q.
A. 47s
B. 60s
C. 55s
D. 51s

Q44) 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 29kmph and 19kmph resp. Every time ajay overtakees 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?

Q45) At 3 p.m. every day, a man leaves new york for delhi and at the same time, a man leaves delhi for new york. Both take the same route. The travel time for each person being 384 hours, how many persons from new york will each man from delhi meet?

Q46) On a certain morning. Amar, Badri and Kedar start from a place P towards another place Q at 7:00 a.m., 7:25 a.m. and 7:50 a.m. respectively. They simultaneously reach a place M, which is twice as far from Q as it is from P, and continue their journey to Q. The fastest of them reaches Q at a time T and immediately turns back towards P, without changing his speed. and at the same time, the slowest of them increases his speed by a certain amount. Finally, all the three reach a place S (between M and Q) exactly 20 minutes after T. All three of them travel at constant speeds unless otherwise mentioned.
If the speed of Kedar when he started from P was 12 km/hr. what was the speed of Amar when he reached S?
a) 12 km/hr
b) 15 km/hr
c) 18 km/hr
d) Cannot be determinedWhen did they reach M
a) 8:40 a.m.
b) 9:20 a.m.
c) 9:10 a.m.
d) Cannot be determinedIf Amar had not increased his speed. when would Kedar have crossed Amar?
a) 11:00 a.m.
b) 10:53 a.m.
c) 10:43 a.m.
d) Cannot be determinedIf the speed of Kedar was 12 kmph, what is the distance between P and Q ?
a) 18
b) 20
c) 30
d) 36

Q47) Samwise Gamgee and Frodo Baggins borrow Shadowfax from Gandalf to go to Mordor to destroy the One Ring in the fires of Mount Doom. They start for Mount Doom simultaneously at 8 a.m. from the Shire. However, in order to save themselves from being poisoned by the One Ring, Samwise Gamgee rides the Shadowfax first at 15 km/hr, leaves it at Rivendell, and covers the remaining distance to Mordor on foot at 4 km/hr. Frodo Baggins who follows the same route reaches Rivendell on foot walking at 5 km/hr, and then rides the Shadowfax for the rest of the distance to Mordor at 12 km/hr. Both of them reach Mordor simultaneously at 9 a.m. How far is Mordor from the Shire?

Q48) X and Y are moving along a rectangle track ABCD. X starts cycling at 6 kmph from point A at 8am on the route ADCBA. Y start walking at 8.50am from point C at the speed 1kmph and takes the route CBADC. AB=6km & BC=4km. At what time X just overtake Y?
a. 10.15 am
b. 9.00 am
c. 9.50 am
d. 10.00 am