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

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

Q49) Clark and Bruce start running simultaneously from the same point on a circular track of length 4200 m. If they run in opposite directions, they meet for the first time exactly after 2 minutes from the start and they meet at seven distinct points on the track. If they run in the same direction, they meet at three distinct points on the track. How much time (in minutes) does Bruce take to complete one round, if he is the slower runner?

Q50) At a 10,000 m race, The Flash starts first and is followed later by Bolt. The speed of Bolt is 1 m/s more than that of The Flash’s. When Bolt catches up with The Flash, The Flash increases his speed by 2 m/s, while that of Bolt remains unchanged. As a result, Bolt finishes 7 min 8 s after The Flash. If the distance had been 500 m more, then Bolt would have finished 7 min 33 s after The Flash. The time gap between the start of The Flash and Bolt is
a. 2 min
b. 2.5 min
c. 3 min
d. 1 min

Q51) In a mile race, Akshay can be given a start of 128 m by Bhairav. If Bhairav can give Chinmay a start of 4 m in a 100 m dash, then who out of Akshay and Chinmay will win a race of one and half miles, and what will be the final lead given by the winner to the loser? (One mile is 1,600 m.)
a. Akshay, 1/12 miles
b. Chinmay, 1/32 miles
c. Akshay, 1/24 miles
d. Chinmay, 1/16 miles

Q52) A watch, which gains uniformly, is 5 min slow at 8 o’clock in the morning on Sunday, and is 5 min 48 sec fast at 8 pm the following Sunday. When did it show the correct time?
(a) 7.20 p.m. on Tuesday
(b) 9.20 p.m. on Wednesday
(c) 7.20 p.m. on Wednesday
(d) 9.20 p.m. on Tuesday

Q53) A ladder is inclined to a wall making an angle of 30° with it. A man is ascending the ladder at the rate of 2 m/s. How fast is he approaching the wall?

Q54) Hogsmeade is 100 km from King’s Cross. At 3 p.m. Hogwarts Express leaves Hogsmeade for King’s Cross and travels at a constant speed of 30 kmph. One hour later, Orient Express leaves King’s Cross for Hogsmeade and travels at a constant speed of 40 kmph. Each train makes one stop only at a station 10 km from its starting point and remains there for 15 mins. Which train is nearer to Hogsmeade when they meet?
(a) Hogwarts Express
(b) Orient Express
(c) Both are equidistant
(d) Cannot be determined from the data.

Q55) Rashmi leaves office at 6.00 p.m. and catches a 6.30 p.m. local train that arrives in her town at 7.00 p.m. Her father leaves home to pick her up at 7.00 p.m. from the station as she gets off the train. Yesterday, Rashmi left her office early and took a 6.00 p.m. train and arrived at 6.30 p.m. As her father was not there to pick her up, she started walking towards home. Her father left home at the usual time, saw his daughter walking, turned around, picked her up and drove home arriving there 10 min earlier than usual. For how many minutes did Rashmi walk before her father picked her up?

Q56) The GhaziabadHapurMeerut EMU and the MeerutHapurGhaziabad EMU start at the same time from Ghaziabad and Meerut and proceed towards each other at 16km/hr and 21km/hr, respectively. When they meet, it is found that one train has traveled 60 km more than the other. The distance between two stations is:

Q57) Harvey’s watch is 10 min slow but he thinks it is 5 min fast. Mike’s watch is 5 min fast but he thinks it is 10 min slow. If both of them want to reach the airport at 6 O’clock, then which of the following would be true?
a. Mike will reach 30 minutes before Harvey.
b. Both will reach together at 6’O clock.
c. Harvey will reach 15 minutes before Mike.
d. Harvey will reach 30 minutes before Mike.

Q58) Vijay covers 910 km by boat, road and rail in the ratio 4 : 3 : 6 respectively. Surprisingly, the speeds at which the journey was covered were also in the ratio 4 : 3 : 6 respectively. The total time taken for the journey was 89 hours. The ratio of the time taken by boat, road and rail was
a) 3 : 4 : 2
b) 1 : 1 : 1
c) 6 : 3 : 4
d) 4 : 3 : 6

Q59) The Rajdhani Express travels a distance of 400 km. If however it travels a distance of d km at the normal speed and the remaining distance at 3/4th of its normal speed then it is late by an hour. If it travels a distance (d + 50) km at 3/4th of its normal speed and the remaining distance at normal speed, then it is late by half an hour. Find d and the train’s normal speed.
a) 150, 75 km/hr
b) 150, 100 km/hr
c) 100, 75 km/hr
d) 100, 100 km/hr

Q60) Seven children A, B, C, D, E, F and G started walking from the same point at the same time, with speeds in the ratio of 1 : 2 : 3 : 4 : 5 : 6 : 7 respectively and they are running around a circular park. Each of them was carry flags of different colours. Whenever two or more children meet then they place their respective flag at that point, however nobody places more than 1 flag at a same point. They are running in anticlockwise direction. How many flags will be there in total, when there will be no scope of putting more flags?