Question Bank - 100 CAT level questions on Time, Speed and Distance topic
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 anti-clockwise 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 sea-level 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 five-minute break at the end of every mile. Jennifer bikes at a constant rate which is three-quarters the rate that Rudolph bikes, but Jennifer takes a five-minute break at the end of every two miles. Jennifer and Rudolph begin biking at the same time and arrive at the 50-mile 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 in-between 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 one-fourth 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 one-third 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
(e) none of these
If 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?
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
Q73) Rajat started walking from point A to point B and Manoj started walking from point B to point A, both at 6 a.m. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then, both continued their journey. Since they had just had their breakfast, their speeds reduced to half of their initial speeds. After 1 hour, Manoj realised that their keys got exchanged, so he started running towards Rajat at two and a half times his present speed. If the ratio of Rajat’s and Manoj’s initial speeds was 3:2, at what time would Manoj meet Rajat?
Q74) 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.Find the ratio of the upstream speed of A to the downstream speed of B.
d) Cannot be determined
Q75) 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.Find the ratio of the upstream speed of A to the downstream speed of B.
d) Cannot be determined
Q76) DESISpiderman has to chase a gang of robbers riding on a car after looting a nearby bank . Spiderman is having coffee at a distance 36 kms south of the car initially when his spider senses give him an inkling. So he heads for the car immediately at a velocity of 50 km/hr as soon as the car also starts at a velocity of 40 km/hr. The gangsters drive the car towards the east with 40 km/hr. Spiderman keeps moving towards the car following his inkling. (i.e. the direction of Spiderman keeps changing and he keeps following the shortest path to the car.) The time in hours after which Spiderman reaches upto car and gives gangster the treatment is
(5) none of these
Q77) Bus A leaves the terminus every 20 minutes, it travels a distance 1 km to a circular road of length 10 km and goes clockwise around the road, and then back along the same road to the terminus (a total distance of 12 km). The journey takes 20 minutes and the bus travels at constant speed. Having reached the terminus it immediately repeats the journey. Bus B does the same except that it leaves the terminus 10 minutes after Bus A and travels the opposite way round the circular road. The time taken to pick up or set down passengers is negligible. A man wants to catch a bus a distance 0 < x < 12 km from the terminus (along the route of Bus A). Let f(x) the maximum time his journey can take. The value of x for which f(x) is a maximum is
Q78) Three friends, Raghu, Amit and Ninad are cycling around a circular track of length 1.2 km at different speeds. They start from the same place at the same time and Raghu and Amit reverse their directions every time they meet. Raghu meets Amit and Ninad for the first time after 40 seconds and 56 seconds respectively while Amit and Ninad meet for the first time after 30 seconds. What is the ratio of speeds of Raghu, Ninad and Amit?