CAT Night Classes

CAT Night ClassesTime Speed & Distance 2/5Average Speed ConceptPuzzle : vNikhil reaches school everyday at 5 p.m. to pick up his children. On a Saturday, theschool got over at 4 p.m. and the children started walking towards home. Nikhil metthem on their way and returned home 30 min earlier. How long did the children walk?

1. A car travelling at a constant speed hears two gunshots at an interval of 16 seconds. Ifthe shots were actually fired at an interval of 18 secs find the speed of the car if the speedof sound in air is 320m/sec(1) 15 m/sec(2) 20 m/sec(3) 30 m/sec(4) 40 m/sec

2. /17. A man covered a distance of 200 kms partly by train and partly by bus. Had hecovered the entire distance by bus, he would have taken 10 hours more and had hecovered the entire distance by train, he would have taken 6 hours less. What was thedifference between the distances (in kms) covered by him by bus and train?(1)60(2)75(3)50(4)90

3. A and B start from two locations P and Q respectively at the same time and meetevery day at X on the way. Uniform speeds of A and B are 20 km/hr and 15 km/hrrespectively. One day B starts t min late and meets A, 5 km ahead of X at Y. Find t.(1) 15 min(2) 20 min(3) 35 min(4) 25 min

4. A car overtakes a bus travelling from Bangalore to Chennai at 6:30 a.m. The carreaches Chennai at 8 a.m. After stopping there for 1 hour, it starts back towardsBangalore and meets the same bus at 9 : 30 a.m., which was moving towards Chennaiat that time. If both the car and the bus travel at uniform speeds on the same route,then what will be the time when the bus would reach Chennai?(1) 10:00 a.m.(2) 10:30 a.m.(3) 11:00 a.m.(4) 9:45 a.m.

5. A and B stay in the same apartment and study in the same school. A and B startwalking towards their school at speeds of 2 km/hr and 3 km/hr respectively. The fasterof the two reaches the school first, turns around and starts walking back. If A and Bmeet 200 m away from the home then what is the distance between their apartmentand their school?(1) 260 m(2) 240 m(3) 200 m(4) 250 m

6/16. A person shooting a target, which is 465 m away, hears the bullet strike it 4.5 safter he fires. A spectator, equidistant from the target and the shooting point (but out ofthe line of danger), hears the bullet strike 3 s after he hears the sound of the gun. Findthe speed of the sound.(1)300 m/s(2) 310 m/s(3) 333.3 m/s(4) 340 m/s

7/15. Only a single rail track exists between stations A and B on a railway line. One hourafter the northbound Super fast train N leaves station A for station B, a south-boundpassenger train S reaches station A from station B. The speed of the super fast train istwice that of a normal express train E, while the speed of a passenger train S is halfthat of E. On a particular day, N leaves for B from A, 20 min behind the normalschedule. In order to maintain the schedule, both N and S increased their speeds. If thesuper fast train doubles its speed, what should be the ratio (approximately) of thespeeds of passenger train to that of the super fast train so that the passenger train Sreaches exactly at the scheduled time at A on that day?(CAT)(1) 1 : 3(2) 1 : 4(3) 2 : 17(4) 3 : 17

8/18. Two boats start simultaneously towards each other at different speeds from theparallel and opposite banks of a lake. When they pass each other for the first time, theyare 300 m from one of the banks. After the first meeting, they continue to move towardsthe opposite banks. Once they reach the opposite banks, they turn around and movetowards each other once again. When they pass each other the second time, they are200 m from the other bank. Find the ratio of the speeds of the two boats.(Assume both the boats travel at uniform speed, speed of river is negligible and neglectvalues of turnaround time)(1) 2 : 1(2) 4 : 3(3) 7 : 3(4) None of these

11. The average speed of a train with stoppages is 80 km/hr, however withoutstoppages it averages 100 km/hr. If the average speed for the train while in motion issame in both the cases then calculate the number of stoppages per hour if each stoplasted for a duration of 4 minutes.(CAT)(1)3(2) 4(3) 5(4) 6

12. A car travels a distance AB with a average speed of 40 km/hr. At what speed must itreturn (i.e. travel from B to A) so that the average speed for the entire jouney is 80 km/hr?(1) 100 km/hr(2) 120 km/hr(3) 110 km/hr(4) Not possible

13. A man travels three-fifths of the total distance from A to B at a speed 3a, and theremaining at a speed 2b. If he goes from B to A and returns at a constant speed 5c inthe same time, then which of the following is true(1) 1 1 1(2) a b c(3) 1 1 2(4) None of thesea b ca b c

1314. Mandar travelled firstrd distance of his journey at a speed of 40 kmph,13of rdremaining distance at 20 kmph and the rest at 80 km/hr. Find his average speed.(1) 34.3 kmph(2) 36 kmph(3) 40 kmph(4) None of the abovethe

15. A car travels at 50 km/hr for the first half time of the journey, at 25 km/hr for the half ofthe remaining time of the journey, at 12.5 km/hr for the half of the remaining time of thejourney and so on until the car accomplishes its journey. The average speed of the car isapproximately equal to(1) 100 km/hr(2) 50 km/hr(3) 33 km/hr(4) 25 km/hr

16. Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started thejourney in Ram’s car at the rate of 25 kmph, while Shyam walked at 5 kmph. Aftersometime, Hari got off and started walking at the rate of 5 kmph and Ram went back topick up Shyam. All three reached the destination simultaneously. The number of hoursrequired for the trip was:(XAT 13)(1) 8(2) 7(3) 6(4) 5(5) 4

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4. A car overtakes a bus travelling from Bangalore to Chennai at 6:30 a.m. The car reaches Chennai at 8 a.m. After stopping there for 1 hour, it starts back towards Bangalore and meets the same bus at 9 : 30 a.m., which was moving towards Chennai at that time. If both the car and the