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

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?

Q61) A submarine needs to take in 1000 gallons of water if it wants to submerge 1 ft in water. The height of the submarine is 20 ft and it is currently submerged 2 ft in water. A battleship 150 km away sees it and fires a torpedo 2 ft below sealevel towards the submarine. If the submarine can take a maximum 3000 gallons of water in one minute, what should be the minimum constant speed of the torpedo for it to hit the submarine, if the submarine starts submerging just as the torpedo is fired?
a) 1080 km/hr
b) 1500 km/hr
c) 1350 km/hr
d) 1250 km/hr
e) 1099 km/hr

Q62) Rudolph bikes at a constant rate and stops for a fiveminute break at the end of every mile. Jennifer bikes at a constant rate which is threequarters the rate that Rudolph bikes, but Jennifer takes a fiveminute break at the end of every two miles. Jennifer and Rudolph begin biking at the same time and arrive at the 50mile mark at exactly the same time. How many minutes has it taken them?

Q63) In a race of 200 meters, A beats S by 20 meters and N by 40 metres. If S and N are running a race of 100 metres with exactly the same speed as before, then by how many metres will S beat N?
(1) 11.11 metres
(2) 10 metres
(3) 12 metres
(4) 25 metres

Q64) Sonia meets her husband everyday at 6 pm on the railway station and then he drives her to their home. One day, Sonia leaves from office early and arrives on the railway station at 5 pm. She then starts walking towards her home meets her husband on the way when he picks her up. They reach their home 10 minutes earlier than usual. For how much time did Sonia have to walk?

Q65) Arjun starts traveling from Andheri to Dadar by car and Bharat is traveling from Dadar to Andheri by bike on the same road at the same time. Speeds of Arjun and Bharat are 60 kmph and 15 kmph respectively. Arjun and Bharat meet at Bandra, which lie somewhere inbetween Andheri and Dadar. After reaching Dadar, Arjun takes rest for 1 hour and then returns to Andheri. The total time taken by Arjun to travel from Andheri to Dadar and then from Dadar to Andheri (including the halt) is 10 minutes more than the time required by Bharat to travel from Bandra to Andheri. Which among the following could be the distance between Bandra and Dadar?
a) 20 km
b) 10 km
c) 12.5 km
d) 8.33 km
e) 15 km

Q66) A and B start running simultaneosly from the diametrically opposite ends of a circular track towards each other at 15km/h and 25km/h respectively. After every 10 minutes their speed reduce to half of their current speeds . If the length of the circular track is 1.5km, then how many times they will meet ?

Q67) The road connecting two towns, A and B, goes only uphill or downhill, i.e., there is no stretch of road that is level. Vijay's car does a constant 40 kmph uphill and 80 kmph downhill. Find the distance between A and B, if it takes exactly nine hours for Vijay to make one round trip from A to B and back.
(A) 360 km
(B) 270 km
(C) 240 km
(D) Cannot be determined

Q68) Bhagat and Chandu start simultaneously from village X to village Y, with their respective speeds in the ratio of 3 : 2. After travelling onefourth of the total distance. Chandu triples his speed and travels for some more time, following which, he again changes his speed and completes the rest of the journey. Bhagat, however maintains his initial speed throughout the journey. If both Bhagat and Chandu reach the village Y at the same time, and the time for which Chandu travelled at thrice his initial speed was onethird of his total time of travel, then find the ratio of the respective speeds with which Bhagat and Chandu reach the village Y.

Q69) Pawan walked UP a descending escalators and took 154 steps in 100 sec to reach the top. Rishab started from simultaneously from the top taking 3 steps for every 4 steps taken by pawan reach the bottom in 40 sec. How many steps from the bottom were they when they crossed each other

Q70) There are three cities P,Q and R , not on the same straight road .Two buses X and Y starts simultaneously from P and Q respectively towards R .By the time Y reaches R,X is exactly half way to R .Immediately after Y reaches R ,it starts travelling towards P and it crosses X at a point 165 km from P .The ratio of the speeds of X and Y is 3:5.Assume that the road joining P to Q,Q to R and Q to P are all straight roads .
If initially ,instead of moving towards R ,X and Y starts moving towards each other ,which of the following cannot be possible distance from P at which they will cross each other
(a) 20 km
(b) 45
(c) 120
(d) 180
(e) none of theseIf Q is twice as far as from P as it is from R ,X takes 18 hours and 40 mints to cover the distance from P to Q , how much time would y take to cover the distance from R to P ?
(a) 2 hour 24 mins
(b) 3 hours
(c) 3 hours 56 mins
(d) 4 hours
(e) none of these

Q71) Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyoms steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?
a. 40
b. 50
c. 60
d. 80

Q72) Ram and Shyam started simultaneously from the same point on a circular track 1800m long in opposite directions with speeds of 6m/sec and 12 m/sec respectively .after every crossing they exchanged their speeds and continued to travel in the same direction .find the distance between them (measured along the track) when ram completes 3.5 rounds
a) 600m
b) 450m
c) 750m
d) 300m